A device to convert a control signal (as produced by the controller) into a physical action that directly affects the plant. A heating element is an actuator, as is a stepper motor. Actuators are transducers.

Because they are physical devices, actuators have limits in the action they can bring about. (A heating element has a maximum amount of heat it can generate per second, a motor has a maximum velocity, and so on. Notice in particular that a heating element is completely unable to generate any cooling action or negative heat flow.) At the same time, control signals can be arbitrarily large. Whenever an actuator is unable to follow the demands of the control signal, it is “saturated.” Actuator saturation means that the intended control actions are no longer applied and that the control loop is therefore broken. (See also Integrator clamping.)

A colloquial term for an on/off controller (as opposed to a controller that is capable of varying the magnitude in response to its input).

A smooth transition when switching between different controllers—for instance between manual control and closed-loop control or between different control strategies in a gain-scheduling scenario. When using a PID controller, a bumpless transfer requires that the value of the integral terms be synchronized before the transfer. (See also Integral preloading.)

Given a system with an input and output, the control problem for this system amounts to finding the input setting (or sequence of input settings) that will produce a desired output value (or sequence of output values).

Also known as “zero-frequency gain.” This is the ratio of an element’s output to a constant (zero-frequency) input while in the steady state (that is, after all transient behavior has disappeared).

Also known as “dead time.” This is the time interval during which no response to an input change is visible in a system’s output. (See also Lag.)

A controller whose output is proportional to the derivative of its input.

When using a derivative controller, a sudden setpoint change will lead to a response from the derivative term that can—in principle—be infinitely large. This “kick” is usually not desirable.

Any control strategy or implementation that uses digital controllers (as opposed to analog controllers made from physical devices). In a narrower sense, this term refers to control loops operating in discrete time steps.

A model of a plant or process that requires an infinite set of parameters to describe the momentary state of the plant. (See also Lumped parameter model.)

Influences to the controlled system that cannot be controlled directly. (See also Load disturbance, Measurement noise.)

The ability of the controller to maintain the output at the desired value, even in the presence of disturbances.

The dynamics of a system consist of the system’s time evolution and its response to inputs.

A closed-loop control strategy in which the tracking error e = r – y is used as input signal to the controller. Error feedback is subject to large control actions when the setpoint undergoes sudden changes. (See also Output feedback.)

A controller in which the output is proportional to the square of its input (usually the error). The square must be calculated as e · |e| in order to retain information about the sign of the error. (See also Linear controller.)

Also known as “closed-loop control.” This is a strategy for solving a control problem that is based on continuously comparing the actual process output against the reference value and then applying corrective actions to the input, in order to reduce the difference between the actual and the desired output. Because the actual process output is used in determining the new control input, feedback control “closes the loop” or introduces a “feedback path.” (See also Feedforward control.)

Any control strategy that does not take the actual process output into account when determining the new control input. Feedforward control requires relatively detailed knowledge about the behavior of the controlled system and cannot guarantee robustness to random, unforeseen disturbances. (See also Feedback control.)

The time evolution of a system is described by functions of time t. The information contained in these functions can also be expressed by functions of complex frequency s. Switching between both representations is accomplished through transformations such as the Laplace transform. When considering only functions of complex frequency, one is working in the frequency domain. (See also Time domain.)

Sometimes different circumstances require different controller gains (for example, there may be a “heavy traffic” and a “light traffic” regime). A gain schedule is a table that contains appropriate values for the gain factors applicable to each separate regime.

Also known as “velocity algorithm.” This is a controller that calculates only the change in control signal. Incremental controllers can be used with plants that maintain their own state and respond to updates of their control input.

Also known as “control input” or “manipulated variable.” This is a quantity that influences the behavior of the controlled system and that can be manipulated directly.

A controller whose output is proportional to the time integral of its past inputs.

Also known as “conditional integration.” Integrator clamping means that the integral term inside a PI or PID controller is not updated when the actuator is saturated. In the case of actuator saturation, tracking errors may persist for a long time (since the actuator is unable to apply the control action required to eliminate the error and the system is therefore running in an open-loop configuration). Integrator clamping prevents the controller’s integral term from becoming very large under these irregular (open-loop) conditions. (See also Integrator windup.)

The process of initializing or otherwise adjusting the cumulative or integral term in a PID controller outside of regular, closed-loop operations. (See also Bumpless transfer.)

When the actuator has saturated, tracking errors may persist for a long time because the actuator is then unable to apply the control action required to eliminate the error. These persistent tracking errors will be added to the integral term inside the controller (unless the integrator is “clamped”). When the actuator is no longer saturated and the system is therefore operating in a closed-loop configuration again, the value of the integral term will nevertheless persist until it has been “unwound,” resulting in inappropriate control actions. (Compare: Integrator clamping.)

A controller that contains a model of the process (so that the model is “internal” to the controller) and uses the output from this model when computing control actions.

A system that initially responds with a partial response to an input change shows a lag. The term also refers to the duration until the system’s output does replicate the input. (See also Delay.)

Control scenarios in which the system output is to be kept within a range of values rather than tracking a given reference value (setpoint) exactly. (Example: the fluid level in a storage tank is allowed to fluctuate as long as the tank neither overflows nor runs empty.)

A controller in which the output is a linear function of its input (which is typically the error): doubling the input results in a doubling of the output. The PID controller is a linear controller.

A disturbance, such as noise, that affects the controlled system (that is, the plant or process). Since the controller provides the input to the plant, the plant constitutes the “load” that the controller must drive.

The introduction of additional elements (such as filters or compensators) into a control loop with the intent of changing the loop’s dynamic response.

Also known as “open-loop transfer function.” If several elements (such as a controller and a plant) are arranged in a closed loop, then the transfer function of the corresponding open loop may be simply referred to as the loop transfer function.

A model of a plant or process that describes the entire momentary state of the plant in a finite set of parameters. (See also Distributed parameter model.)

See Input.

Noise generated in the sensor that is used to monitor the plant’s output signal.

A mathematical description (typically in the form of a differential equation) of the behavior of a plant or system, including the plant’s dynamic behavior and its response to control inputs. (Before the advent of digital controllers, a “model” was a physical model of the plant, built to reproduce the actual plant’s response to inputs.)

See System identification.

The procedure by which a complicated mathematical model is replaced by a simpler one that nevertheless describes the observed behavior nearly as well. Basing a model on the theoretical knowledge about often results in models that are overly detailed. If experimental observations suggest that a simpler model will do as well, then one may attempt to simplify matters through model reduction.

As mathematical idealizations of a real system, models rarely describe the system perfectly. That imperfection introduces a certain amount of error into results, which is referred to as “model uncertainty.” To an outside observer, it is impossible to tell whether the errors are due to inaccuracies in the description of the plant (model uncertainty) or to changing environmental factors (load disturbances).

Also known as “inverse response system.” This is a system whose initial, transient response to an input is in the opposite direction to the input.

See Loop transfer function.

Also known as “process output” or “process variable.” This is the property of the controlled system that is to be influenced. Because it cannot be manipulated directly, the only way to influence it is by manipulating the controlled system instead.

A closed-loop control strategy in which the output y is used as input signal to the controller instead of the full tracking error e = r – y. Output feedback is less susceptible to spurious control actions in the case of sudden setpoint changes, but it gives equivalent results—in particular when the setpoint is held constant for extended periods of time. (See also Error feedback and Setpoint weighting.)

Also known as “two-term controller.” This is a linear controller that consists of a proportional and an integral term acting in parallel. The relative strength of each term is given by that term’s controller gain factor.

Also known as “three-term controller.” This is a linear controller that consists of a proportional, an integral, and a derivative term acting in parallel. The relative strength of each term is given by that term’s controller gain factor. The term “PID controller” is used even when one of the terms is absent (in particular, the derivative term is often not used).

Also known as “process.” This is the system that needs to be controlled. The system’s input is manipulated in order to achieve a particular behavior of the system’s output.

See Process reaction curve.

A location at which a transfer function approaches infinity. Since transfer functions are typically rational functions in the complex frequency s, a pole is a value of s such that the denominator of the transfer function vanishes. A pole s in the frequency domain corresponds to a mode exp(st) in the time domain. Knowledge about the system’s poles therefore amounts to knowledge about the system’s modes in the time domain.

A process of manipulating the loop’s transfer function in order to move its poles into positions that yield desirable dynamic behavior.

See Plant.

Also known as “static process characteristic.” This is a curve showing the steady-state output of a process as function of the magnitude of the (constant) input.

The application of methods from control theory and engineering to processes and installations in the chemical and manufacturing industry.

Knowledge about the static (steady-state) input/output relationship for a plant or process and about its dynamic response to arbitrary inputs. Process knowledge can be gained either analytically (if the laws governing the process are known) or empirically. Process knowledge is captured in the process model. (See also Process model, Model uncertainty, and System identification.)

A theoretical description of a plant or process—in particular of its dynamic response to control inputs. Process models can describe a specific installation in detail; however, the term is also used in an abstract sense to refer to broad categories of behaviors (such as “self-regulating process,” “accumulating process,” “oscillatory process,” and so on). (See also Model uncertainty.)

Also known as “plant signature.” This is a curve showing the dynamic development of a process’s output in response to a step input.

See Output.

A controller whose output is proportional to its input.

Under strictly proportional control, the system’s steady-state output will always be smaller than the setpoint. The higher the controller gain, the smaller the droop. In general, it is necessary to employ integral control to entirely eliminate a steady-state tracking error.

See Velocity feedback.

Regulators are controllers that seek to maintain the system at its steady state and to reject disturbances. Regulators are used in situations where the setpoint is constant for extended periods at a time. (See also Tracker.)

A device that transforms a physical quantity into a control signal. A thermocouple is a sensor that transforms temperature into voltage.

Also known as a “servo.” See Tracker.

Also known as “reference,” “reference value,” or “target.” This is the desired value that the output of the controlled system is supposed to replicate.

The ability of a control system to track the setpoint accurately—especially in situations where the setpoint itself is undergoing changes.

Dynamic response of a controlled, closed-loop system to changes in the setpoint—in particular to sudden, steplike changes.

When calculating the tracking error e = αr – y that is to be used as controller input, the weight α of the setpoint r can be changed relative to the process output y. Choosing α = 1 amounts to error feedback; choosing α = 0 amounts to output feedback. (See also Error feedback and Output feedback.)

A control strategy to handle systems whose dynamic behavior exhibits a significant delay.

The behavior of the system after the disappearance of all transient responses. The steady-state output is usually dominated by the control inputs of the system. (See also Transient response.)

An input that undergoes a sudden change in magnitude at a specific point in time (usually taken to be the beginning of the observation period, t = 0).

The process of measuring a plant’s behavior for the purpose of identifying and fitting a mathematical model.

The time evolution of a system is described by functions of time t. When considering the actual dynamic behavior of a system, one is working in the time domain. (See also Frequency domain.)

A controller designed to follow a setpoint that is changing over time. (See also Regulator.)

Any device that converts between physical actions or quantities and control signals. Actuators and sensors are transducers. Control signals are often, but not always, electrical signals.

The frequency-space representation of the laws governing an element’s dynamics. Transfer functions are usually obtained through the Laplace transformation of the differential equation describing the element. To obtain the response of the element to an arbitrary input, the transfer function is multiplied by the Laplace transform of the input signal; the resulting product is then transformed back into the time domain to obtain the dynamic response.

Also known as “transients” or “transient behavior”. This is that part of the dynamic response to an input change that decays and disappears over time. Transients are usually due to the internal dynamics of the controlled system, not to its control inputs. (See also Steady state.)

See Incremental controller.

Also known as “rate feedback.” This is a closed-loop control strategy in which the rate of change of the plant’s output (that is, its derivative) is fed back and used to calculate the new control input. (Not to be confused with “Velocity algorithm.”)