Engine Start

When the ignition key is switched on initially, the mode control logic automatically selects an engine start control scheme that provides the correct temperature-dependent air/fuel ratio required for starting the engine. Once the engine RPM rises above the cranking value, the controller identifies the “engine started” mode and passes control to the program for the engine warm-up mode. This operating mode typically keeps the air/fuel ratio relatively low to prevent engine stall during cool or cold weather until the engine coolant temperature rises above some minimum value. The instantaneous desired air/fuel is a function of coolant temperature and ambient conditions. The particular value for the minimum coolant temperature is specific to any given engine type and, in particular, to the fuel metering system. (Alternatively, the low air/fuel ratio may be maintained for a fixed time interval following start, depending on start-up engine temperature.)

Open-Loop Mode

When the coolant temperature rises sufficiently, the mode control logic directs the system to operate in the open-loop control mode until the EGO sensor warms up enough to provide accurate readings. This condition is detected by monitoring the EGO sensor’s output for voltage readings above a certain minimum rich air/fuel mixture voltage set point (see Chapter 6 for EGO sensor voltage characteristics). When the sensor has indicated rich at least once and after the engine has been in open loop for a specific time, the control mode selection logic selects the closed-loop mode for the system. (Note: other criteria may also be used.) The engine remains in the closed-loop mode until the EGO sensor cools and fails to read a rich mixture for a certain length of time or a hard acceleration or deceleration occurs. If the sensor cools, the control mode logic selects the open-loop mode again.

Acceleration/Deceleration

During hard acceleration or heavy engine load, the control mode selection logic chooses a scheme that provides a rich air/fuel mixture for the duration of the acceleration or heavy load. This scheme has the capability to provide maximum torque, but depending on driver demand, suboptimal emissions control, and relatively poor fuel economy regulation as compared with a stoichiometric air/fuel ratio may occur. After the need for enrichment has passed, control is returned to either open-loop or closed-loop mode, depending on the control mode logic conditions that exist at that time. During periods of deceleration, the air/fuel ratio might be increased to reduce emissions of HC and CO due to unburned excess fuel. However, enleanment is limited to an air/fuel that avoids excess NOx production.

When idle conditions are present, control mode logic passes system control to the idle speed control mode. In this mode, the engine speed is controlled to reduce engine roughness and stalling that might occur because the idle load has changed due to air conditioner compressor operation, alternator operation, or gearshift positioning from park/neutral to drive, although stoichiometric mixture is used if the engine is warm. A detailed model and performance analysis of idle speed control is presented later in this chapter.

As explained above, in modern engine control systems, the controller is a special-purpose digital computer built around a microprocessor or microcontroller. An exemplary configuration of a typical modern digital engine control system is depicted in Figure 7.2.

The controller also includes ROM containing the main program (of several thousand lines of code). This ROM is accessed by the engine control system via address bus A and receives data via data bus D (see Chapter 4). There is also a section of ROM continuing parameter values for specific control modes and tables of data for various control functions as explained later in this chapter. Of course, any microprocessor-based system must have RAM for temporary storage of data during computation (see Chapter 4). The sensor signals are connected to the controller via an input/output (I/O) subsystem. Similarly, the I/O subsystem provides the output signals to drive the fuel injectors (shown as the fuel metering block of Figure 7.2) as well as to trigger pulses to the ignition system (described later in this chapter). In addition, this microprocessor-based control system includes hardware for sampling and analog-to-digital conversion such that all sensor measurements are in a format suitable for reading by the microprocessor. (Note: See Chapter 4 for a detailed discussion of these components.)

With reference to Figure 7.2, the sensors that measure various engine variables for control are as follows:

Other sensors that might be used on older model cars that are not given in Figure 7.2 include the following:

The control system selects an operating mode based on the instantaneous operating condition as determined from the sensor measurements. Within any given operating mode, the desired air/fuel ratio (A/F)_d is selected. The controller then determines the quantity of fuel to be injected into each cylinder during each engine cycle. This quantity of fuel depends on the particular engine-operating condition as well as the controller mode of operation, as will presently be explained.

Engine Crank

While the engine is being cranked, the fuel control system must provide an intake air/fuel ratio of anywhere from 2:1 to 12:1, depending on engine temperature. The lowest value for [A/f]_d would be applied for very cold temperatures. The correct air/fuel ratio (i.e., [A/F]_d) is selected from an ROM lookup table with interpolation (as explained later in this chapter) as a function of coolant temperature. Low temperatures affect the ability of the fuel metering system to atomize or mix the incoming air and fuel properly to achieve combustion. At low temperatures, the fuel tends to form into large droplets in the air, which do not burn as efficiently as tiny droplets. The larger fuel droplets tend to increase the apparent air/fuel ratio, because the amount of usable fuel (on the surface of the droplets) in the air is reduced; therefore, the fuel metering system must provide a decreased air/fuel ratio to provide the engine with a more combustible air/fuel mixture. During engine crank the primary issue is to achieve engine start as rapidly as possible. Once the engine is started the controller switches to an engine warm-up mode.

Engine Warm-Up

While the engine is warming up, an enriched air/fuel ratio relative to stoichiometry is still needed to keep it running smoothly, but the required air/fuel ratio changes as the temperature increases. Therefore, the fuel control system stays in the open-loop mode, but the air/fuel ratio commands continue to be altered due to the temperature changes. The emphasis in this control mode is on rapid and smooth engine warm-up. Fuel economy and emission control may be still a secondary concern. The controller selects a warm-up time from a lookup table based on the temperature of the coolant. In certain cases, a fully warmed engine is switched off by the driver for a brief period such that temperature remains sufficiently high that warm-up mode is either very short or not used at all.

A diagram illustrating the lookup table selection of desired air/fuel ratios is shown in Figure 7.3. Essentially, the measured coolant temperature (T_c) is converted to an address for the lookup table with interpolation as described below. This address is supplied to the ROM table via the system address bus (A/B). The data stored at this address in the ROM are desired air/fuel ratio (A/F)_d for the temperature. These data are sent to the controller via the system data bus (D/B).

The term lookup table refers to obtaining an output variable y that is a function of one or more inputs. It provides an alternative to calculation based upon a model (e.g., a polynomial model). It is often applied to empirically obtained data (e.g., from engine mapping) in which the optimum value of a variable (e.g., air/fuel) has been determined from measurements for various values of the independent variables. It is inherently limited to a finite number of discrete points in the relevant range for the independent variables.

On the other hand, during actual engine operation these same independent variables are continuous and rarely coincide perfectly with the stored values. In this case, the output variable corresponding to these independent variables is obtained by a process called interpolation. This process involves fitting the region between two successive data points with a function (normally linear). We illustrate linear interpolation with a two-dimensional data set. Let y_n be the value of a dependent variable (e.g. air/fuel) at independent data sensor output point x_n where n = 1,2…N. Let x be a measurement of independent variable (e.g., coolant temperature) for which the corresponding dependent variable y (e.g., desired air/fuel) is sought. Also, let x_m and x_m+1 be the nearest tabulated data points in the table in which x_m < x < x_m+1. The corresponding tabulated values for the dependent variable are y_m and y_m+1. For linear interpolation it is assumed that y varies linearly with x over the domain . The slope S over this domain is given by

(11)

The linearly interpolated value for y is given by

(12)

Alternatively, it is possible to obtain a polynomial model which gives the best fit to measured data in a least squared error sense. Let an empirical data set be given by {x_n, y_n: n = 1,2…N}. The polynomial which best represents this data is of the form

(13)

The mean squared error between this polynomial and the data is

(14)

There are many computer programs for finding the coefficient set {a_m: m = 0,1…M} such that MSE is minimized. For example, the MATLAB function polyfit (x_n, y_n, M) returns the coefficient set a_m (of order M), which yields the least MSE for the given data set. In this case, the digital engine control can calculate the desired dependent variable for any given measurement of the independent variable x. The choice between table lookup with interpolation and polynomial calculation can be assessed by the quality of fit of the polynomial to the data given by the MSE for the best polynomial fit and by the relative complexity of the two methods. The set of coefficients for any given data are normally determined during the development of an engine control system. These coefficients are stored in ROM such that the determination of y for any measurement x (during normal engine operation) is readily implemented in the control system using Eqn (13) and the stored values for {a_m} for the polynomial model method and by Eqn (12) for the lookup table and interpolation method.

Returning to the discussion of coolant temperature for setting (A/F)_d, there is always the possibility of a coolant temperature failure. Such a failure could result in excessively rich or lean mixtures, which can seriously degrade the performance of both the engine and the three-way catalytic converter (3 wcc). One scheme that can circumvent a temperature sensor failure involves having a time function to limit the duration of the engine warm-up mode. The nominal time to warm the engine from cold soak at various temperatures is known. The controller is configured to switch from engine warm-up mode to an open-loop (warmed-up engine) mode after a sufficient time by means of an internal timer.

Open-Loop Control

For a warmed-up engine, the controller will operate in an open loop if the closed-loop mode is not available for any reason. For example, the engine may be warmed sufficiently but the EGO sensor may not provide a usable signal. In any event, as soon as possible it is important to have a stoichiometric mixture to minimize exhaust emissions.

It was shown above that the quantity of fuel to be delivered to cylinder m during the nth engine cycle can be computed from MAF sensor measurements and can be regulated by means of a fuel injector pulse duration τ_F(n, m). For the present, it is helpful to assume that intake air is uniformly distributed to all M cylinders. In this case, the fuel injector open duration is

(15)

This quantity of fuel is actually delivered to each cylinder during the open-loop mode and is often termed the “base pulse duration.” Until conditions permit closed-loop mode of fuel control the fuel quantity is determined from MAF measurements. As a means of denoting open-loop operation the notation for base pulse duration is τ_b(n):

(16)

Corrections of the base pulse width occur whenever any conditions affect the accuracy of the fuel delivery. For example, low battery voltage might affect the pressure in the fuel rail that delivers fuel to the fuel injectors. Corrections to the base pulse width are then made using the actual battery voltage.

Closed-Loop Control

Perhaps the most important adjustment to the fuel injector pulse duration comes when the control is in the closed-loop mode. In the open-loop mode, the accuracy of the fuel delivery is dependent upon the accuracy of the measurements of the important variables (e.g., MAF). However, any component of a given physical system is susceptible to changes with operating conditions (e.g., temperature) or with time (aging or wear of components). Such failures or degradation of sensor/actuator calibration can adversely affect exhaust emissions in the open-loop mode.

To avoid degraded emission control, it is important for the control system to switch to the closed-loop mode as soon as possible and to remain in this mode for as much of the engine operation as possible. The closed-loop mode can only be activated when the EGO (or HEGO) sensor is sufficiently warmed. Recall from Chapter 6 that for a fully warmed EGO sensor, the output voltage of the sensor is high (approximately 1 V) when the exhaust oxygen concentration is low (i.e., for a rich mixture relative to stoichiometry). The EGO sensor voltage is low (approximately 0.1 V) whenever the exhaust oxygen concentration is high (i.e., for a mixture that is lean relative to stoichiometry).

Chapter 1 presented a discussion of the theory of the closed-loop control of a dynamic system in which a measurement of the dynamic system output variable that is being regulated/controlled is compared with the desired value. The controller produces an input to the plant that changes the output variable in such a way as to minimize the error between actual and desired output. Ideally, control of exhaust emissions would require a sensor for measuring the concentration of each regulated gas component in the engine exhaust as explained in Chapter 5. A large body of theory (both linear and nonlinear) exists which is applicable in the design of a control system provided a sensor exists that can yield an accurate measurement with sufficient bandwidth of the variable being regulated.

However, as explained in Chapters 5 and 6, no cost-effective sensor for measuring these regulated exhaust gases is available for production vehicles. On the other hand, as explained in Chapter 5, the use of a three-way catalytic converter enables tailpipe emissions to be controlled within regulatory limits provided the intake mixture remains sufficiently close to stoichiometry. Furthermore, it was explained that the exhaust gas oxygen concentration changes abruptly as the mixture transitions from rich to lean or from lean to rich at stoichiometry. As explained in Chapter 6, the EGO sensor generates an output voltage that follows exhaust gas concentration. A model for the EGO sensor voltage as a function of exhaust equivalence ratio (λ) was given in Chapter 5.

Unfortunately, a measurement of a switching output variable is compatible only with a limit cycle controller. None of the linear control theory of Chapter 1 including design, performance analysis, and stability is applicable to a limit cycle control system. Although such theory exists for a limit cycle controller, this theory is beyond the scope of this book. However, as will be shown below, it is possible to develop a dynamic simulation model for a limit cycle fuel control system. Using this simulation, it is possible to investigate the influence of various physical and design parameters on the system performance.

The physical configuration for the closed-loop fuel control system is depicted in Figure 7.4a. In this figure, the engine (Eng) receives fuel and air mixture in the intake system via the M fuel injectors (denoted FI ‒ one for each cylinder).

The mixture flowing into the engine is represented by the intake equivalence ratio (λ_i). This mixture is determined by the intake mass airflow rate and the fuel injector pulse duration τ_F(n) for the nth engine cycle as explained above. The exhaust equivalence ratio λ_o can be modeled as a time-delayed version of λ_i where the time delay is modeled below. The exhaust gas oxygen concentration is a function of λ_o such that the output voltage v_o of the EGO sensor can be represented in the ideal case by a binary model as given below. Closed-loop fuel control consists of determining τ_F(n) as a function of the EGO sensor output voltage. This pulse duration consists of a base pulse duration τ_b(n) and a closed-loop correction factor (C_L(n)) in the representative form

(17)

One commonly employed algorithm for computing this correction factor is a linear combination of a proportional-like term and a discrete time integral-like term as given below

(18)

where I(n) is the integral term, P(n) is the proportional term, α is the integral gain, and β is the proportional gain.

The integral-like term is determined in the digital control system as a function of the EGO sensor voltage v_o. As explained in Chapter 5, this voltage is a function of exhaust gas oxygen concentration. This voltage can also be characterized in terms of a variable called the exhaust equivalence ratio (λ_o). After a given engine cycle is complete, this exhaust gas equivalence ratio is given approximately by a time-delayed version of λ_i in the form

(19)

where T_e is the engine cycle time

With this notation, the EGO sensor voltage is given by

(20)

where V_H is the EGO sensor “high” level ≈1 volt and V_L is the EGO sensor “low” level (≈0.1 V).

Using the above notation, the integral control algorithm at computation time is given by

(21)

In this algorithm, the computation time t_k is given by

In determining the value of I(n) for the nth engine cycle, the most recent value for I(t_k) is taken. During engine operation I(k) continuously increases or decreases linearly with time t_k depending upon λ₀.

The “proportional” term for the nth engine cycle is the average over the K previous samples of the EGO sensor voltage:

(22)

where v_om is the EGO sensor mid-range value (corresponding to stoichiometry). The linear combination above for C_L(n) is representative of closed-loop correction calculations used by a digital fuel control system to modify the base pulse duration.

A fundamental characteristic of a limit cycle control system is the oscillatory behavior of its control variable. The C_L(n) term continuously oscillates about a nominal value even for a steady engine load and RPM. In the case of the fuel control, the frequency of oscillation and the amplitude of the deviation vary inversely with T_e.

To illustrate the behavior of a limit cycle controller a MATLAB/SIMULINK simulation was constructed for the example block diagram of Figure 7.4b. The sample period was T_s = 0.01 s and the RPM was taken to be about 1000 RPM. The closed-loop control parameters were taken to be α = 2T_s, β = 0.025.

The simulation block diagram uses an ideal model for the EGO sensor (see Figure 6.23), combined with the integral control logic of Eqn (21). Since the time steps are in multiples of T_s and since the integrator is integrating a constant magnitude with only a sign change, the actual stepwise function of Eqn (21) is very closely approximated using the continuous time integrator (which is simpler to implement in the simulation than the discrete time version). The hysteresis is 0.1 air/fuel ratio for this ideal sensor. The time delay is T_e = 0.067 s and is implemented in a transport delay SIMULINK block.

Figure 7.5 is a sample of the waveform where the solid curve is the EGO sensor output voltage and the dashed curve is the integral portion of the C_L and the deviation of the air/fuel ratio is the dash-dot curve. Note that this deviation is ±0.1 air/fuel ratios.

The time delay between the integral part of C_L(n) and the EGO sensor output is too small to be evident from the figure. Only a short time interval of the waveforms is presented in order to show the detailed response. Also apparent in this figure is the relationship between the exhaust gas concentration and the slope of the integral part of C_L(n). Whenever the EGO sensor voltage is high, corresponding to a rich mixture relative to stoichiometry, the integral component is decreasing which decreases τ_F causing the mixture to become leaner. Conversely, a low EGO sensor voltage causes the integral part to increase, thereby enriching the mixture.

In Figure 7.5, it can be seen that the air/fuel oscillates within ±0.1 air/fuel ratio of stoichiometry (14.7). This performance should be sufficient that the tail pipe gases after passing through the three-way converter should meet government-mandated limits.

Acceleration Enrichment

During periods of heavy engine load such as during hard acceleration, fuel control is adjusted to provide an enriched air/fuel ratio to maximize engine torque and very briefly neglect fuel economy and emissions. This condition of enrichment is permitted within the regulations of the EPA as it is only a temporary condition. It is well recognized that hard acceleration is occasionally required for maneuvering in certain situations and is, in fact, related at times to safety. A relatively large increase in throttle angle corresponds to heavy engine load and is an indication that heavy acceleration is called for by the driver. In some vehicles, a switch is provided to detect wide open throttle. The fuel system controller responds by increasing the pulse duration of the fuel injector signal for the duration of the heavy load. This enrichment enables the engine to operate with a torque greater than that allowed when emissions and fuel economy are controlled. Enrichment of the air/fuel ratio to about 12:1 is sometimes used and corresponds roughly to a maximum engine brake torque.

Alternatively, heavy acceleration can be detected from the time derivative of throttle angle θ_T. In discrete time control systems, the rate of throttle change r_T is given by

(23)

Enrichment is enabled whenever r_T exceeds a predetermined threshold value (r_Tt). For r_T > r_Tt, enrichment is accomplished by increasing τ_F from its normal closed-loop value. For example, τ_F for r_T > r_Tt can include an extra term of the following form:

where F(r_T) is often an empirically determined function for a given vehicle engine configuration.

Deceleration Leaning

During periods of light engine load and high RPM such as coasting or deceleration, the engine may operate with a very lean air/fuel ratio to reduce excess emissions of HC and CO. Deceleration is indicated by a sudden decrease in throttle angle or by closure of a switch when the throttle is closed (depending on the particular vehicle configuration). When these conditions are detected by the control computer, it computes a decrease in the pulse duration of the fuel injector signal. The fuel may even be turned off completely for very heavy deceleration. This decrease can be represented by the equation for acceleration in which the function

(24)

where r_Td is a threshold value for r_T below which enleanment is required and where F_d(r_T) is the enleanment function.

Idle Speed Control

The idle speed control mode is used to prevent engine stall during idle. The goal is to allow the engine to idle at as low an RPM as possible, yet keep the engine from running rough and stalling when power-consuming accessories, such as air conditioning compressors and alternators, turn on.

The control mode selection logic switches to idle speed control when the throttle angle reaches its zero (completely closed) position as detected by a switch on the throttle that is closed and engine RPM falls below a minimum value. This condition often occurs when the vehicle is stationary. Idle speed is controlled by using an electronically controlled throttle bypass valve, as seen in Figure 7.6a, which allows air to flow around the throttle plate and produces the same effect as if the throttle had been slightly opened such that sufficient flows to maintain engine operation.

There are various schemes for operating a valve to introduce bypass air for idle control. One relatively common method for controlling the idle speed bypass air uses a special type of motor called a stepper motor. One stepper motor configuration consists of a rotor with permanent magnets and two sets of windings in the stator that are powered by separate driver circuits. The configuration of a stepper motor is similar to that of a brushless DC motor as explained in Chapter 6 (see Figure 6.36). Such a motor can be operated in either direction by supplying pulses in the proper phase to the windings as explained in Chapter 6. This is advantageous for idle speed control since the controller can very precisely position the idle bypass valve by sending the proper number of pulses of the correct phasing.

A digital engine control computer can precisely determine the position of the valve in a number of ways. In one way, the computer can send sufficient pulses to close completely the valve when the ignition is first switched on. Then it can open pulses (phased to open the valve) to a specified (known) position. The physical configuration for the idle speed control is depicted in Figure 7.6a. The variables have the same notation as given in Chapter 5.

In addition, the digital engine control system receives digital on/off status inputs from several power-consuming devices attached to the engine, such as the air conditioner clutch switch, park-neutral switch, and the battery charge indicator. These inputs indicate the load that is applied to the engine during idle.

Closed-Loop Ignition Timing

The ignition system described in the foregoing is an open-loop system. The major disadvantage of open-loop control is that it cannot automatically compensate for mechanical changes in the system. Closed-loop control of ignition timing is desirable from the standpoint of improving engine performance and maintaining that performance in spite of system changes.

One scheme for closed-loop ignition timing is based on the improvement in performance that is achieved by advancing the ignition timing relative to TDC. For a given RPM and manifold pressure, the variation in torque with spark advance is as depicted in Figure 7.15.

One can see that advancing the spark relative to TDC increases the torque until a point is reached at which best torque is produced. As introduced above and explained qualitatively in Chapter 5, this spark advance is known as the SA for mean best torque, or MBT.

When the spark is advanced too far, an abnormal combustion phenomenon occurs that is known as knocking. Although the details of what causes knocking are beyond the scope of this book, it is generally a result of a portion of the air–fuel mixture abruptly igniting (autoigniting), as opposed to being normally ignited by the advancing flame front that occurs in normal combustion following spark ignition. Roughly speaking, the amplitude of knock is proportional to the fraction of the total air and fuel mixture that autoignites. It is characterized by an abnormally rapid rise in cylinder pressure during combustion, followed by very rapid oscillations in cylinder pressure. The frequency of these oscillations is specific to a given engine configuration and is typically in the range of a few kilohertz. Figure 7.16 is a graph of a representative cylinder pressure versus time under knocking conditions. A relatively low level of knock is arguably beneficial to performance, although excessive knock is unquestionably damaging to the engine and must be avoided.

One control strategy for spark advance under closed-loop control is to advance the spark timing until the knock level becomes unacceptable. At this point, the control system reduces the spark advance (retarded spark) until acceptable levels of knock are achieved. Of course, a spark advance control scheme based on limiting the levels of knocking requires a knock sensor such as that explained in Chapter 6. This sensor responds to the acoustical energy in the spectrum of the rapid cylinder pressure oscillations, as shown in Figure 7.16.

Figure 7.17 is a diagram of an exemplary instrumentation system for measuring knock intensity. Output voltage V_E of the knock sensor is proportional to the acoustical energy in the engine block at the sensor mounting point. This voltage is sent to a narrow bandpass filter that is tuned to the knock frequency (for the particular engine configuration). The filter output voltage V_F is proportional to the amplitude of the knock oscillations, and is thus a “knock signal.” The envelope voltage of these oscillations, V_d, is obtained with a detector circuit which can, for example, be implemented with a rectifier-type circuit which includes a diode and a capacitor (see Chapter 3).

Following the detector in the circuit of Figure 7.17 of the example knock detection system is an electronic gate that normally blocks V_d for much of the engine cycle but passes it during the portion of the engine cycle for which the knock amplitude is largest (i.e., shortly after TDC). The gate is, in essence, an electronic switch that is normally open, but is closed for a short interval (from 0 to T) following TDC. It is during this interval that the knock signal is largest in relationship to engine noise. The probability of successfully detecting the knock signal is greatest during this interval. Similarly, the possibility of mistaking normal engine acoustic noise for true knock signal is smallest during this interval.

The final stage in the exemplary knock-measuring instrumentation is integration with respect to time. Integration can be accomplished numerically in the engine control or as a part of the knock sensor instrumentation using an operational amplifier circuit configured to perform analog integration. For example, the circuit of Figure 7.18a could be used to integrate the gate output. In our example system, the electronic gate is implemented via a pair of switches S₁ and S₂. Switch S₁ is normally open and S₂ closed but S₁ is closed and S₂ opened at t = 0 corresponding to the beginning of the period where knock can occur. The end of this period is t = T. This gate operation is repetitive and occurs following TDC for the power stroke of the associated cylinder. The output voltage V_K at the end of the gate interval T is given by

(53)

This voltage increases sharply in magnitude but is negative for V_d as depicted in Figure 7.18b because the input is connected to the op amp inverting input. Figure 7.18b is a plot of the absolute magnitude of V_k (i.e., |V_k|). This voltage reaches a maximum amplitude at the end of the gate interval, as shown in Figure 7.18b, provided knock occurs. However, if there is no knock, V_K remains near zero.

The level of knock intensity is indicated by voltage |V_K(T)| at the end of the gate interval. The spark control system compares this voltage with a threshold voltage to determine whether knock has or has not occurred.

This envelope-detected voltage is sent to the controller, where it is compared with a level corresponding to the knock intensity threshold. Whenever the knock level is less than the threshold, the spark is advanced. Whenever it exceeds the threshold, the spark is retarded. The comparator function is normally implemented in the digital control system by numerically comparing the integrated knock intensity signal with a threshold T_K (under program control; see Figure 7.19).

In such an implementation, the controller generates a binary-valued variable (denoted K in Figure 7.19) having the following algorithm:

(54)

Knock detection with the above algorithm has two types of error: (1) missed detection in which knock has occurred but the system output is K = 0 and (2) false alarm in which there is normal combustion but the system output is K = 1. The quantitative error analysis for the above knock detection method generally is covered in the field of statistical decision theory. The theory of this topic is outside the scope of this book. However, for those readers having a background in statistical analysis, we present the following brief models and analysis of the probability of error in the above knock detection system.

Essentially, the voltage of any point in the exemplary knock detection system is a random process. In this exemplary knock detection system, the detection of knock is based upon the voltage V_K(T) and is, in effect, a form of statistical hypothesis testing. This method can perhaps best be explained from the histogram of Figure 7.20 for voltage V_K(T) for a large sample of engine cycles under the two hypotheses:

For notational convenience, we let x = |V_K(T)| in Figure 7.20. In this figure, the number of occurrences of x at a particular value for hypothesis H₀ is denoted and for hypothesis H₁ is denoted . For a sufficiently large sample space, these histograms approach the continuous probability density functions for the two hypotheses that are denoted and , respectively.

The detection threshold T_K is depicted in Figure 7.20. The total probability of error P_e for our example knock detection method is given by

(55)

where the first term corresponds to false alarm errors and the second to missed detection errors. For any such knock detection method, an optimum threshold that minimizes the total probability of error can be determined empirically.

Although this scheme for knock detection has shown a constant threshold, there are some production applications that have a variable threshold. The threshold in such cases increases with RPM because the competing acoustical noises in the engine increase with RPM.

Spark Advance Correction Scheme

Although the details of spark advance control vary from manufacturer to manufacturer, there are generally two classes of correction that are used: fast correction and slow correction. In the fast correction scheme, the spark advance is decreased for the next engine cycle by a fixed amount (e.g., 5°) whenever knock is detected. Then the spark advance is incremented in one-degree increments every 5–20 crankshaft revolutions.

The fast correction ensures that minimum time is spent under heavy knocking conditions. Further, this scheme compensates for hysteresis (i.e., for one degree of spark advance to cause knocking, more than one degree must be removed to eliminate knocking). The fast correction scheme is depicted qualitatively by the waveform depicted in Figure 7.21.

In the slow correction scheme (Figure 7.22), spark advance is decreased by one (or more) degree each time knock is detected, until no knocking is detected. The spark advance proceeds in one-degree increments after many engine cycles.

The slow correction scheme is more of an adaptive closed-loop control than is the fast correction scheme. It primarily is employed to compensate for relatively slow changes in engine condition or fuel quality (i.e., octane rating).

Secondary Air Management

Secondary air management is used to improve the performance of the catalytic converter by providing extra (oxygen-rich) air either to the converter itself or to the exhaust manifold. The catalyst temperature must be above about 200 °C to efficiently oxidize HC and CO and reduce NOx. During engine warm-up when the catalytic converter could be cold, HC and CO are oxidized in the exhaust manifold by routing secondary air to the manifold. This creates extra heat to speed warm-up of the converter and EGO sensor, enabling the fuel controller to go to the closed-loop mode relatively quickly.

The converter can be damaged if too much heat is applied to it. This can occur if large amounts of HC and CO are oxidized in the manifold during periods of heavy loads, which call for fuel enrichment, or during severe deceleration. In such cases, the secondary air is directed to the air cleaner, where it has no effect on exhaust temperatures.

After warm-up, the main use of secondary air is to provide an oxygen-rich atmosphere in the second chamber of the three-way catalyst, dual-chamber converter system. In a dual-chamber converter, the first chamber contains rhodium, palladium, and platinum to reduce NOx and to oxidize HC and CO. The second chamber contains only platinum and palladium. The extra oxygen from the secondary air improves the latter converter’s ability to oxidize HC and CO in the second converter chamber.

The computer program for the control mode selection logic can be modified to include the conditions for controlling secondary air. In one configuration, the engine controller regulates the secondary air by using two solenoid valves similar to the EGR valve. One valve switches airflow to the air cleaner or to the exhaust system. The other valve switches airflow to the exhaust manifold or to the converter. The air routing is based on engine coolant temperature and air/fuel ratio. The control system diagram for secondary air is shown in Figure 7.23.

Evaporative Emissions Canister Purge

In pre-emission controlled vehicles, the fuel stored in the fuel system tended to evaporate and release hydrocarbons (HCs) into the atmosphere. In contemporary vehicles, to reduce these HC emissions, the fuel tank is sealed and evaporative gases are collected by a charcoal filter in a canister. The collected fuel is released into the intake through a solenoid valve controlled by the computer. This normally is done during closed-loop operation to reduce fuel calculation complications in the open-loop mode.

Automatic System Adjustment

Another important feature of microcomputer engine control systems is their ability to be programmed to adapt to parameter changes. Many control systems use this feature to enable the computer to modify lookup table values for computing open-loop air/fuel ratios. While the computer is in the closed-loop mode, the computer checks its open-loop calculated air/fuel ratios and compares them with the closed-loop average limit cycle values. If they match closely, the open-loop lookup tables are unchanged. If the difference is large, the system controller corrects the lookup tables so that the open-loop values more closely match the closed-loop values. This updated open-loop lookup table is stored in separate memory (RAM), which is always powered directly by a car battery or a separate “keep alive” battery so that the new values are not lost while the ignition key is turned off. The next time the engine is started, the new lookup table values will be used in the open-loop mode and will provide more accurate control of the air/fuel ratio than the unmodified values. This feature is very important because it allows the system controller to adjust to long-term changes in engine and fuel system conditions. This feature can be applied in individual subsystem control systems or in the fully integrated control system. If not available initially, it may be added to the system by modifying its control program.

System Diagnosis

Another important feature of microcomputer engine control systems is their ability to diagnose failures in their control systems or components and alert the operator. Sensor and actuator failures or misadjustments can be detected readily by the computer under certain operating conditions. For instance, the computer will detect a malfunctioning MAF sensor if the sensor’s output goes above or below certain specified limits, or fails to change for long periods of time. A prime example is the automatic adjustment system just discussed. If the open-loop calculations consistently come up different from those indicated in closed-loop mode, the engine control computer may determine that one of the many sensors used in the open-loop calculations has experienced a calibration change or has failed completely.

If the computer detects the loss of a primary control sensor or actuator, it may switch to in a different mode until the problem is repaired. The operator is notified of a failure by an indicator on the instrument panel (e.g., check engine indicator). Because of the flexibility of the microcomputer engine control system, additional diagnostic programs might be added to accommodate different engine models that contain more or fewer sensors. Keeping the system totally integrated gives the microcomputer controller access to more sensor inputs so they can be checked. Chapter 10 discusses system diagnosis in detail. Often, there is sufficient redundancy to permit suboptimal engine operation when a component has failed such that the vehicle can be driven to a repair facility in an operating mode that has been termed a “limp home mode.”

Engine Crank (Start)

The following list is a summary of the engine operations in the engine crank (starting) mode, wherein the primary control concern is rapid and reliable engine start:

Engine Warm-Up

While the engine is warming up, the engine temperature is rising to its normal operating value. Here, the primary control concern is rapid and smooth engine warm-up. A summary of the engine operations during this period is as follows:

Open-Loop Control

The following list summarizes the engine operations when the engine is being controlled in an open-loop mode. This mode is used before the EGO sensor has reached the correct temperature for closed-loop operation. Fuel economy and emissions are closely controlled.

Closed-Loop Control

For the closest control of emissions and fuel economy under various driving conditions, the electronic engine control system is in a closed loop. Fuel economy and emissions are controlled very tightly. The following is a summary of the engine operations during this period:

Hard Acceleration

When the engine must be accelerated quickly or if the engine is under heavy load, it is in a special mode. Now, the engine controller is primarily concerned with providing maximum performance. Here is a summary of the operations under these conditions:

Deceleration and Idle

Slowing down, stopping, and idling are combined in another special mode. The engine controller is primarily concerned with reducing excess emissions during deceleration, and keeping idle fuel consumption at a minimum. This engine operation is summarized in the following list:

Automatic Transmission Control

The vast majority of cars and light trucks sold in the United States are equipped with automatic transmissions. The majority of these transmissions are controlled electronically. The configuration of an automatic transmission consists of a torque converter and a sequence of planetary gear sets.

The transmission (whether automatic or manual) is a gear system that adjusts the ratio of engine speed to wheel speed. Essentially, the transmission enables the engine to operate within its optimal performance range regardless of the vehicle load or speed. It provides a gear ratio between the engine speed and vehicle speed such that the engine provides adequate power to drive the vehicle at any speed. Any gear system connecting a pair of shafts along which torque/power is transmitted is the mechanical equivalent of an electrical transformer. Just as a transformer can maximize the power transmitted from a source to a load, a gear system has the capability of maximizing the transfer of engine power to the load at the drive wheels while maintaining engine speed (under load) at acceptable values.

To accomplish optimal power transfer to the load with a manual transmission, the driver selects the correct gear ratio from a set of possible gear ratios (usually three to five for passenger cars). An automatic transmission selects the gear ratio by means of an automatic control system.

The configuration for an automatic transmission consists of a fluid-coupling mechanism, known as a torque converter, and a system of planetary gear sets. The torque converter is formed from a pair of structures of a semitoroidal shape (i.e., a donut-shaped object split along the plane of symmetry). Figure 7.24 is a schematic sketch of a torque converter showing the two semitoroids.

One of the toroids is driven by the engine by the input shaft and is called the pump. The other is in close proximity and is called the turbine. Both the pump and the turbine have vanes that are nearly in axial planes. In addition, a series of vanes are fixed to the frame and are called the reactor. The entire structure is mounted in a fluid-tight chamber and is filled with a hydraulic fluid (i.e., transmission fluid). As the pump is rotated by the engine, the hydraulic fluid circulates as depicted by the arrows in Figure 7.24. The fluid impinges on the turbine blades, imparting a torque to it. The torque converter provides a fluid coupling to transmit engine torque and power to the turbine from the engine. The torque that is applied to the pump portion of the torque converter is the engine brake torque (T_b). Denoting the torque applied to the output shaft by the turbine T_T, this latter torque is given by T_T = T_RT_b where T_R is the torque multiplication factor of the torque converter. However, the properties of the torque converter are such that when the vehicle is stopped corresponding to a nonmoving turbine, the engine can continue to rotate (as is does when the vehicle is stopped with the engine running). Normally, with the vehicle stopped and the torque converter output shaft not rotating, the engine is at idle and producing minimal T_b. The turbine blades are in a stalled condition and T_T is sufficiently low that only a small torque applied to the wheels by the brakes is capable of stopping the vehicle.

A detailed analytical model for a torque converter is given in a paper by Allen Kotwicki.^∗ In this paper, it is explained that a torque converter is a form of fluid coupling device in which a reactor is added which is rigidly connected to the transmission housing and normally does not rotate. However, torque converter efficiency is improved whenever the torque reaction on the fluid is zero by allowing the reactor to rotate freely. The torque converter is filled with transmission fluid that is caused to circulate through the pump–turbine–reactor by rotation of the pump by the engine crankshaft rotation. This fluid flows in an annular path as depicted in Figure 7.24. The operating physical principle upon which a fluid coupling or a torque converter is based is that torque in any such system results from a time rate of change of angular momentum. In the reference cited above it is shown that the torques of the pump T_p and turbine T_t are given by

(56)

where ω_p = the pump angular speed (rad/s),

where ρ is the transmission fluid density.

In these equations a double subscript on a variable means: first subscript p → pump, r → reactor, t → turbine and the second subscript e → entrance, x → exit. The double-subscripted parameters have the following meaning:

It is further shown that the volume flow rate is given by

(57)

where E, F, G, H, and I are constants given in the cited reference. In this reference empirical evaluation of coefficients for a first-order linear regression-based polynomial for Q of the form is developed:

where

where S is the speed ratio.

Using this approximation, it is shown in the reference that the torque ratio T_R is given by

(58)

where

This simplified model is shown in the reference to correlate well with experimental data and is normally sufficient for development of transmission controls.

The planetary gear system consists of a set of three types of gears connected together as depicted in Figure 7.25a. The inner gear is known as the sun gear. There are three gears meshed with the same gear at equal angles, which are known as planetary gears. These three gears are tied together with a cage that supports their axles. The third gear, known as a ring gear, is a section of a cylinder with the gear teeth on the inside. The ring gear meshes with the three planetary gears.

In operation, one or more of these gear systems are held fixed to the transmission housing via a set of hydraulically actuated clutches. The action of the planetary gear system is determined by which set or sets of clutches are activated. For example, if the ring gear is held fixed and input power (torque) is applied to the sun gear, the planetary gears rotate in the same direction as the sun gear but at an increased torque. We denote the input torque applied to the sun gear and the angular speed of the shaft driving this gear system by T_i and ω_i, respectively. The output torque and its speed are denoted T_o and ω_o, respectively. A model for this gear system is given by

(59)

where g is the gear ratio

N_s is the number of teeth on the sun gear and N_p is the number of teeth on a planetary gear.

If the planetary gear cage is fixed, then the sun gear drives the ring gear in the opposite direction as is done when the transmission is in reverse. If all three sets of gears are held fixed to each other rather than the transmission housing, then direct drive (gear ratio = 1) is achieved.

A typical automatic transmission has a number of planetary gear systems (denoted g₁, g₂, g₃ in Figure 7.25b), each with its own set of hydraulically actuated clutches as depicted schematically in Figure 7.25b. In an electronically controlled automatic transmission, the clutches are electrically or electrohydraulically actuated via solenoid type actuators such as are described in Chapter 6.

Most automatic transmissions have three forward gear ratios, although a few have two and some have four or more and all have reverse. A properly used manual transmission normally has efficiency advantages over an automatic transmission (because of power losses in the torque converter), but the automatic transmission is the most commonly used transmission for passenger automobiles in the United States. In the past, automatic transmissions have been controlled by a hydraulic and pneumatic system, but it is common in contemporary vehicles to use electronic controls as part of an integrated powertrain control system. The control system must determine the correct gear ratio by sensing the driver-selected command, accelerator pedal position, engine load, and vehicle motion. Once again, as in the case of electronic engine control, the electronic transmission control can optimize transmission control. However, since the engine and transmission function together as a power-producing unit, it is sensible to control both components in a single electronic controller. The proper gear ratio is actually computed in the electronic transmission control portion of the powertrain control system.

Figure 7.25b depicts schematically the powertrain denoting the engine E, the torque converter (TC), the gear system, the differential D (having gear ratio g_D), and the axles with the drive wheels (which could be front or rear). The configuration and operating principles of the differential are explained later in this chapter. For simplicity, it is convenient to assume that both right and left drive wheels (or all four drive wheels for four-wheel drive) are identical and present a combined load torque T_L to the drive axle. In this case, the transmission output torque T_o is given by

The gear system consists of a set of planetary gear units each having a gear ratio g_n (n = 1,2…N). The appropriate gear is selected by the control system, which operates the correct set of clutches via an electrohydraulic actuator (e.g. solenoid-operated valve supplying transmission fluid under pressure to a set of sprag clutches). For gear systems connected in series, the total gear ratio g from the torque converter output to the load is given by

(60)

Otherwise, for a parallel connected system of gears as shown in Figure 7.25b, the gear ratio is given by

(61)

Although there are many possible powertrain control modes depending upon vehicle operating conditions and driver command, an illustrative example mode is maximizing the power delivered to the load (drive wheels) for a given engine brake power (P_b = T_bω_e). For example, under certain powertrain operating conditions, the gear ratio, which maximizes this transfer of engine power to load power (P_L = T_Lω_L) g,^∗ is given approximately by

The controller selects the nearest available gear ratio from the set of possible choices.

Another control mode for the transmission is to maximize drive axle torque T_L, thereby maximizing vehicle acceleration whenever the driver command yields wide open throttle (WOT). This mode calls for the maximum available gear ratio subject to the constraint that engine RPM remains near the point for maximum brake torque.

The relevant clutches are activated by the pressure of transmission fluid acting on piston-like mechanisms. The pressure is switched on at the appropriate clutch via solenoid-activated valves that are supplied with automatic transmission fluid under pressure. The solenoids are actuators that receive an electrical signal from the powertrain control system as explained in Chapter 6.

During normal driving, the electronic transmission controller determines the desired gear ratio from measurements of engine load and RPM as well as transmission output shaft RPM. These RPM measurements are made using noncontacting angular speed sensors (usually magnetic in nature) as explained in Chapter 6. Once this desired gear ratio is determined, the set of clutches to be activated is uniquely determined, and control signals are sent to the appropriate clutches.

Normally, the highest gear ratio (i.e., ratio of input shaft speed to output shaft speed) is desired when the vehicle is at low speed such as in accelerating from a stop. As vehicle speed increases from a stop, a switching level will be reached at which the next lowest gear ratio is selected. This switching (gear-changing) threshold is an increasing function of load as measured by the MAF or MAP sensor.

At times (particularly under steady vehicle speed conditions), the driver demands increasing engine power (e.g., for heavy acceleration). In this case, the controller shifts to a higher gear ratio, resulting in higher acceleration than would be possible in the previous gear setting. At a steady-cruise condition, the transmission gear ratio is unity and the total gear ratio from engine to drive wheels is g_D (i.e., differential gear ratio). The functional relationship between gear ratio and operating condition is often termed the “shift schedule,” which is programmed into ROM.

Torque Converter Lock-Up Control

As explained above, automatic transmissions use a hydraulic or fluid coupling to transmit engine power to the wheels. There is some relatively small power loss in the TC such that the fluid coupling is less efficient than the nonslip coupling of a pressure-plate manual clutch used with a manual transmission. Thus, fuel economy is usually lower with an automatic transmission than with a standard transmission. This problem has been partially remedied by placing a clutch functionally similar to a standard pressure-plate clutch inside the torque converter of the automatic transmission and engaging it during periods of steady cruise. This enables the automatic transmission to provide fuel economy near that of a manual transmission and still retain the automatic shifting convenience.

The torque converter locking clutch (TCC) is activated by a lock-up solenoid controlled by the engine control system computer. The computer determines when a period of steady cruise exists from throttle position and vehicle speed changes. It pulls in the locking clutch and keeps it engaged until it senses conditions that call for disengagement. This condition is known as “torque converter lock-up.”

Differential and Traction Control

The transmission output shaft is coupled to the drive axles via the differential. The differential is a necessary component of the drivetrain because the left and right drive wheels turn at different speeds whenever the car moves along a curve (e.g., turning a corner). Whenever a car is executing a turn, the outside drive wheel rotates at a higher angular speed than the inside wheel. The differential achieves this function permitting both wheels to propel the vehicle. Figure 7.26 depicts the configuration for a differential. Unfortunately, wherever there is a large difference between the tire/road friction from left to right, the differential will tend to spin the low friction wheel. An extreme example of this occurs whenever one drive wheel is on ice and the other is on dry road. In this case, the tire on the ice side will spin and the wheel on the dry side will not. Typically, the vehicle will not move in such circumstances.

Certain cars are equipped with so-called traction control devices that can overcome this disadvantage of the differential. Such cars have differentials that incorporate electrohydraulic solenoid-activated clutches somewhat similar to those used in an automatic transmission that can “lock” the differential, permitting power to be delivered to both drive wheels. It is only desirable to activate these clutches in certain conditions and to disable them during normal driving, permitting the differential to perform its intended task.

A traction control system incorporates sensors for measuring wheel speed and a controller that determines the wheel slip condition based on these relative speeds. Wherever a wheel spin condition is detected, the controller sends electrical signals to the solenoids, thereby activating the clutches to eliminate the wheel slip.

Hybrid Electric Vehicle Powertrain Control

The concept of a hybrid electric vehicle (HEV), in which propulsive power comes from an internal combustion engine (ICE) and an electric motor (EM), has emission and fuel advantages relative to a conventional vehicle powered only by an ICE. As explained in Chapter 5, the hybrid vehicle combines the low (ideally zero) emissions of an electric vehicle with the range and performance capabilities of IC-engine-powered cars. However, optimization of emission performance and/or fuel economy is a complex control problem.

There are differential types of hybrid electric vehicles based upon the degree of hybridization. A vehicle that can operate on either the ICE or the electric propulsion or a combination of both is known as a full hybrid. In order to have any practical range for electric propulsion only, the vehicle must have a suitable very high capacity battery pack. This battery pack is capable of storing far more energy than a conventional storage battery found in ICE only vehicles.

On the other hand, there are certain hybrids which are incapable of electric propulsion only. These vehicles, which are commonly called “mild hybrids,” require the ICE for some of their propulsion. In one configuration, a mild hybrid has an ICE connected to a motor that serves several functions including starting the ICE, adding a power boost to the ICE, and regenerative braking to recover and store some energy during deceleration. In regenerative braking, the electric motor acts as a generator that receives its mechanical drive power from the vehicle momentum and delivering its output electrical power to the battery pack. The discussion of induction motors in Chapter 6 explains this operation of a motor acting as a generator.

There are numerous issues and considerations involved in hybrid vehicle powertrain control, including the efficiencies of the IC engine and electric motor as a function of operating condition; the size of the vehicle and the power capacity of the IC engine and electric motor; the storage capacity and state of charge of the battery pack; accessory load characteristics of the vehicle; and, finally, the driving characteristics of the driver. With respect to this latter issue, it would be possible to optimize vehicle emissions and performance if the exact route, including vehicle speed, acceleration, deceleration, road inclination, and wind characteristics, could be programmed into the control memory before any trip were to begin. It is highly impractical to do such preprogramming. However, by monitoring instantaneous vehicle operation, it is possible to achieve good, though suboptimal, vehicle performance and emissions.

Depending on operating conditions, the controller in a full hybrid can command pure electric vehicle operation, pure IC engine operation, or a combination. Whenever the IC engine is operating, the controller should attempt to keep it at its peak efficiency.

Certain special operating conditions should be noted. For example, the IC engine is stopped wherever the vehicle is stopped. Clearly, such stoppage benefits vehicle fuel economy and improves air quality when the vehicle is driven in dense traffic with long stoppages such as those that occur while driving in large urban areas.

There are two major types of hybrid electric vehicles depending on the mechanism for coupling the IC engine (ICE) and the electric motor (EM). Figure 7.27 is a schematic representation of one hybrid vehicle configuration known as a series hybrid vehicle (SHV).

In this SHV, the ICE drives a generator (G) and has no direct mechanical connection to the drive axles. The vehicle is propelled by the electric motor (EM), which receives its input electrical power from a high-voltage bus. This bus, in turn, receives its power either from the engine-driven generator (for ICE propulsion) or from the battery pack (for EM propulsion), or from a combination of the two. In this figure, mechanical power is denoted MP and electrical power EP. The mechanical connection from the EM to the transaxle (T/A) provides propulsive power to the drive wheels (DWs). The term transaxle refers to the entire drive system from the EM to the drive wheels.

Figure 7.28 is a schematic of a hybrid vehicle type known as a parallel hybrid. The parallel hybrid of Figure 7.28 can operate with ICE alone by engaging both solenoid-operated clutches on either side of the EM but with no electrical power supplied to the EM. In this case, the MP supplied by the ICE directly drives the transaxle T/A, and the EM rotor spins essentially without any mechanical drag. This hybrid vehicle can also operate with the EM supplying propulsive power by switching off the ICE, disengaging clutch C₁, engaging clutch C₂, and providing electrical power to the EM from the high-voltage bus (HVB). Of course, if both ICE and EM are to produce propulsive power, then both clutches are engaged. Not shown in Figure 7.28 is a separate controller for the motor. Also not shown in this figure but discussed later in this section is the powertrain controller that optimizes performance and emissions for the overall vehicle and engages/disengages clutches as required.

The HEV of Figure 7.29 operates similarly to that of Figure 7.28 except that mechanical power from ICE and EM are combined in a mechanism denoted coupler. For the system of Figure 7.29 pure ICE propulsion involves engaging clutch C_1, disengaging clutch C₂, and providing no electrical power to the EM. Alternatively, pure EM propulsion involves disengaging clutch C₁, switching off the ICE, engaging clutch C₂, and providing electrical power to the EM via the high-voltage bus (HVB). Simultaneous ICE and EM propulsion involves running the ICE, providing electrical power to the EM, and engaging both clutches.

In principle, any type of electric motor could be used to provide the electric propulsion in a hybrid vehicle. However, in practice, there are two main types in common use today: the brushless DC motor and the induction motor. Both are explained and modeled in Chapter 6. It should be recalled that the brushless DC motor incorporates a permanent magnet rotor normally with multiple poles. The stator has multiple windings that are excited by AC currents. Typically, the stator windings are arranged for three-phase operation.

However, the stored electric power in a hybrid vehicle is DC (from the battery pack). The frequency condition for this type of motor requires that the rotational frequency ω_m be identical to the stator excitation frequency ω_s since the rotor excitation is at ω_r = 0.

Operation of the brushless DC motor in a hybrid vehicle during electric propulsion requires that an electric system convert the stored DC electric power to 3-phase AC power. This conversion is accomplished in a motor control system that creates an electric control signal at frequency ω_s in addition to power switching circuits (normally implemented via high-power switching transistors). Ideally, the stator excitation should be three sinusoidal voltages of equal amplitude which in phasor notation are given by

(62)

However, in practice, the excitation waveforms are not sinusoidal. Rather, they are more often of a form of square or trapezoidal waveform. Motor control requires correct phasing relative to the orientation of the rotor. Such phasing requires a noncontacting rotor position sensor (e.g., Hall effect; see Chapter 6).

In order to provide torque and power levels required for hybrid vehicle operation a brushless DC motor is made using powerful magnets having so-called rare earth elements. A typical magnet for a hybrid vehicle brushless DC motor is made of an alloy of iron, boron, and, the relatively expensive rare earth, element, neodynium.

A brushless DC motor can also function as an alternator. The motion of the rotor creates a time-varying flux linking the stator turns Ф_A, Ф_B, and Ф_C. This time-varying flux linkage, in turn, creates a voltage given by V_AV_BV_C in each winding:

The zero phase corresponds to the rotor rotation angle for which Ф_A is a maximum.

These voltages can be converted to DC using a set of transformers (to achieve correct voltage levels) and rectifier circuits (see Chapter 3). The corresponding DC power can be supplied to the battery pack to increase its state of charge. In this way, the motor acting as a generator can provide braking torque to decelerate the vehicle and recover some of the vehicle kinetic energy that would otherwise be dissipated in brakes. Such generator action is known as regenerative braking.

Other electric motor types also have application in hybrid vehicle propulsion. In Chapter 6 the induction motor was explained. Induction motors of high torque/power output and high efficiency can be built without requiring rare earth magnetic material. A model for an induction motor was presented in Chapter 6 where it was shown that the frequency condition for average torque generation is automatically satisfied.

Induction motors for hybrid vehicle use are normally three-phase, meaning that three separate windings (one for each phase) are required for both stator and rotor. In Chapter 6 it was shown that the torque produced by the induction machine (with current excitation amplitude I_s) is given by

(63)

where ω_s is the excitation frequency and ω_m is the motor rotational frequency.

All parameters in this model for T_e are defined in Chapter 6. It is also shown in Chapter 6 that the steady-state motor speed for a given excitation is the motor angular speed ω_o at which the motor torque T_e(ω_o) balances the load torque T_L:

(64)

This point is illustrated for a hypothetical hybrid vehicle being propelled solely by an induction motor. The load torque at the motor output is proportional to the force F_V required to move the vehicle at the commanded speed.

We consider first a hybrid vehicle moving along a steady speed on a straight, level road. There are two primary contributions to F_V: tire rolling resistance F_rr and aerodynamic drag D. The rolling resistance is essentially independent of vehicle speed but is proportional to vehicle weight and varies as a decreasing function of tire pressure. If we assume that all tires are equally inflated, then the total rolling resistance force is given by

where W_V is the vehicle weight and μ_rr is the coefficient of rolling resistance of tires. The coefficient μ_rr is generally in the range 0.02 ≤ .μ_rr ≤ 0.04.

The aerodynamic drag D is given by

where ρ is the local air density (kg/m³ or slug/ft³), C_D is the drag coefficient, S_ref is the a reference area (m² or ft²), and V is the vehicle speed (m/s or ft/s).

The reference area is an arbitrary choice that ultimately determines the value for C_D. It is common practice to choose S_ref as the vehicle projected area on a vertical plane normal to the vehicle plane of symmetry. The force necessary to move the vehicle along a straight, level road at a constant speed V is given by

The above expression for F_V is valid for a level road. Whenever the vehicle encounters a nonzero slope (i.e., along a hill), this force includes a term that is proportional to the vehicle weight and the slope of the hill. For a vehicle traveling along a road with a slope (relative to horizontal) of angle θ, the total force F_V is given by

(66)

Thus, a road with nonzero slope can shift load torque on the motor (T_L) up or down depending upon whether sign (θ) is + or θ, respectively.

In the hypothetical example, the induction motor drives the vehicle wheels through a transmission and differential such that ω_m is proportional to V. The load torque at the motor output T_V is proportional to the force F_V:

(67)

where g_V is the gear ratio from motor to drive wheels and r_T is the tire effective radius.

Figure 7.30 is a plot of normalized motor torque T_m and load torque T_L (normalized to the maximum motor torque T_max) vs. the ratio ω_m/ω_s where

where for a given excitation T_max is defined as

The steady-state operating motor speed is at the intersection of these two curves (i.e., at ). A change in load torque (e.g., due to a nonzero road slope) causes the load curve to shift to a new motor operating point. The system is stable as long as

The efficiency of the induction motor is influenced, in part, by the steady-state operating point. In general, as long as the steady-state operating point (i.e., ω_m = ω_o) is in the negative slope region of T_e(ω_m) (and operation is stable), the motor produces torque that varies in proportion to slip s. However, motor efficiency varies inversely with slip.

The induction motor controller can regulate T_e(ω_m) via the excitation frequency (ω_s) and current amplitude I_s or motor voltage V_s. One hypothetical control strategy would vary the excitation and synchronous excitation frequency (ω_s) to optimize the motor efficiency. However, there are many other factors that influence the overall vehicle efficiency including the choice of ICE and/or electric propulsion, battery status, vehicle-operating conditions and driving patterns (e.g., urban or highway), etc.

The current that provides the induction motor excitation I_s is determined by the source voltage V_s and motor impedance. Normally, motor control is preferably done via regulation of V_s directly rather than via I_s. We consider next the model for the motor torque based upon the excitation voltage V_s.

The stator current magnitude I_s is related to the complex terminal voltage amplitude V_s. For sinusoidal excitation and using the parameter notation for induction motors from Chapter 6, the relationship between V_s and I_s is given by

(68)

This expression gives the voltage/current relationships for each phase. See Chapter 6 for the definitions of all parameters. Solving the above equation for I_s and substituting it into the equation for motor torque yields

(69)

The above equation provides a basis for motor torque control in hybrid vehicle applications.

For an induction motor at constant supply voltage amplitude V_s the slip s will vary until the motor torque is the same as load torque T_L:

There is a family of curves of T_e(s) for each excitation voltage that is similar in form to that given for current excitation (see Figure 7.30). Normal operation of an induction motor is in a region in which

and s is relatively small. In this region, the motor torque is given approximately by

(70)

On the other hand, when slip is relatively large the torque can be shown to be given approximately by

(71)

The above approximate expressions can be used to control motor torque for the two distinct regions of operation. In any event, the motor control can regulate torque by controlling excitation voltage as well as frequency ω_s as explained later in this chapter.

For either series or parallel hybrid vehicle, dynamic braking is possible during vehicle deceleration, with the EM acting as a generator. The EM/generator supplies power to the high-voltage bus which is converted to the low-voltage bus (LVB) voltage level by the power electronics subsystem. In this deceleration circumstance, the energy that began as vehicle kinetic energy is recovered with the motor acting as a generator and is stored in the battery pack. This storage of energy occurs as an increase in the state of charge (SOC) of the battery pack. This process (regenerative braking) was discussed above with respect to the brushless DC motor, but applies equally well with an induction motor drive system.

In addition to the lead acid battery in common use today, there are new energy storage means including nickel–metal hydride (NiMH) and even special capacitors called ultra-caps. Each of these electrical energy storage technologies has advantages and disadvantages for hybrid vehicle application.

The battery pack has a maximum SOC that is fixed by its capacity. Dynamic braking is available as an energy recovery strategy as long as SOC is below its maximum value. Nevertheless, dynamic braking is an important part of hybrid vehicle fuel efficiency. It is the only way some of the energy supplied by the ICE and/or EM can be recovered when the vehicle is traveling along a road with a negative slope or is decelerating instead of being dissipated in the vehicle brakes.

For each battery type, there is a maximum rated stored charge q_r which is determined by construction. The SOC for the battery is normally expressed by the instantaneous q expressed as a fraction of q_r. A storage battery is, in effect, a type of nonlinear capacitor (with a nonlinear source resistance) in which the open circuit voltage V_oc is a function of stored charge q:

The storage of the energy recovered during dynamic braking requires that the corresponding electrical energy be direct current and at a voltage compatible with the battery pack. Since most automotive systems apart from the motor operate at 12 V (nom), a common battery pack might consist of a connection of multiple 12-volt batteries.

Conversion of electrical power from one voltage level V₁ to a second V₂ is straightforward using a transformer as long as this power is alternating current. Figure 7.31 schematically illustrates transformer structure and the conversion of voltages from one level to another.

A transformer consists of a core of magnetically permeable material (usually a ferromagnetic material) around which a pair of closely wrapped coils are formed. One coil (termed the primary) consists of N₁ turns and the other (termed the secondary) consists of N₂ turns. In a well-designed transformer essentially all of the magnetic flux in the core links all turns in both coils.

Assuming (arbitrarily) that AC electrical power comes from a source (e.g., an AC generator) at peak voltage V₁, then the power flowing from the transformer secondary to a load will be at a peak voltage V₂ where

Conversion of DC electrical power from one voltage to another can be accomplished using a transformer only if the DC power is first converted to AC and then converted back to DC as explained below. Figure 7.32a is a greatly simplified schematic of a DC-to-DC converter in which a transistor is used to convert an input DC signal to AC that is sent to a transformer for conversion to a different voltage.

The control electronics supplies a pulsating signal to the base B of transistor Q₁, alternately switching it on and off. When Q₁ is on (i.e., conducting), voltage V₁ is applied to the transformer primary (i.e., N₁). When Q₁ is off (i.e., nonconducting), transformer primary voltage is zero. In this case, the pulsating AC voltage that is alternately V₁ and 0 applied to the primary results in an AC voltage in the secondary that is essentially N₂/N₁ times the primary voltage. This secondary voltage is converted to DC by rectification using diode D₁ and filtering via capacitor C (see Chapter 3). The secondary voltage is fed back to the control electronics, which varies the relative ON and OFF times to maintain V₂ at the desired level.

A variation of the circuit of Figure 7.32a appears in the power electronics module for conversion between the battery pack or from an ICE-driven generator and the hybrid vehicle motor driver. Regardless of the type of motor used, the generation of the voltages that provide the motor excitation (i.e., V_A V_B V_C for a three-phase motor) can be accomplished using circuits of the configuration shown in Figure 7.32b. Although this figure depicts a single phase (i.e., V_A), a separate driver transistor such as Q₁ along with a transformer (of N₁ primary and N₂ secondary turns) is required for each phase. The control electronics internally computes the signals that control the phases (i.e., 0, 2π/3 and 4π/3) of the remaining three phases. This control is normally implemented in the powertrain control system. Of course, the specific details of the relevant power electronics depend on the hybrid vehicle manufacturer.

Powertrain control for a hybrid vehicle is achieved using a multimode digital control system. It is somewhat more complicated than the digital engine control system discussed earlier in this chapter in that it must control an IC engine as well as an EM motor. In addition, it must achieve the balance between ICE and EM power, and it must engage or disengage the solenoid-operated clutches (if present).

The inputs to this controller come from sensors that measure the following:

The system outputs include control signals to

Depending upon the HEV configuration, there may be no direct mechanical link from the accelerator pedal to the throttle. Rather, the throttle position (as measured by a sensor) is set by the control system via an electrical signal sent to an actuator (motor) that moves the throttle in a system called drive-by-wire.

The control system itself is a digital controller using the inputs and outputs listed above and has the capability of controlling the hybrid powertrain in many different modes. These modes include starting from a standing stop, steady cruise, regenerative braking, recharging battery pack, and many others that are specific to a particular vehicle configuration.

In almost all circumstances, it is desirable for the IC engine to be off at all vehicle stops. Clearly, it is a waste of fuel and an unnecessary contribution to exhaust emissions for an IC engine to run in a stopped vehicle. Exceptions to this rule involve cold weather operations in which it is desirable or even necessary to have some limited engine operations with a stopped vehicle in order to maintain engine and catalytic converter at proper temperature. In addition, a low-battery SOC might call for ICE operation at certain vehicle stops in order to provide charge to the battery pack.

When starting from a standing start, normally the EM propulsion is used to accelerate the car to desired speed, assuming the battery has sufficient charge. If charge is low, then the controller can engage the clutch to the ICE such that the EM can begin acceleration and at the same time crank the ICE to start it. Then, depending on the time that the vehicle is in motion, the ICE can provide propulsive power and/or battery charge. Should the vehicle go to a steady cruise at low battery SOC for engine operation near its optimum, then the control strategy normally is to switch off the electric power to the EM and power the vehicle solely and recharge the battery pack with the ICE. In other cruise conditions, the controller can balance power between ICE and EM in a way that maximizes total fuel economy (subject to emission constraints).

For urban driving with frequent stops, the control strategy favors EM operation as long as SOC is sufficient. In this operating mode, regenerative braking may be used (in which energy is absorbed by vehicle deceleration), and the recovered energy appears as increased SOC.

The various operating modes and control strategies for an HEV depend on many factors, including vehicle weight; relative size and power capacity of ICE/EM; and exhaust emissions and fuel economy of the ICE (as installed in the particular vehicle). It is beyond the scope of this book to attempt to cover all possible operating modes for all HEV configurations. However, the above discussion has provided background within which specific HEV configurations’ operating modes and control strategies can be understood.

In addition to the HEV, there is also the pure electric vehicle (EV) that has no ICE for powering the vehicle. This vehicle incorporates many of the components of an HEV including an electric motor, a battery pack for storing electric energy, and an electronic controller that provides the motor excitation. As any EV is driven, the battery SOC decreases.

Control of the EM in an EV is accomplished in a way that is similar to that described above for EM motor control in an HEV. This control is done by regulating the excitation voltage or current as well as the excitation frequency (which must satisfy the frequency condition for any motor). At some point, the battery pack requires recharging. The power for this recharging comes from the electric power grid. It is worth remembering that although an EV has essentially zero vehicle-out emissions, the creation of the electric power to recharge the batteries is done at some electric utility. Depending on the type of power generation at the electric utility, there may be increased emissions from that plant to meet the power requirements to recharge EV battery packs except for nuclear electric power generators. In this sense, the EV is not always a pure zero-emission vehicle.