4.1.  INTRODUCTION

From the frequency-domain viewpoint, system order refers to the highest power of s in the denominator of the closed-loop transfer function of a system. In the time domain, system order refers to the highest derivative of the controlled quantity in the equation describing the control system’s dynamics. System order is a very significant parameter for characterizing a system.

Second-order systems are very important to the control-system engineer. This type of system characterizes the dynamics of many control-system applications found in the fields of servomechanisms, space-vehicle control, chemical process control, bioengineering, aircraft control systems, ship controls, etc. It is interesting to note that most control-system designs are based on second-order system analysis. Even if the system is of higher order, as it usually is, the system may be approximated by a second-order system in order to obtain a first approximation for preliminary design purposes with reasonable accuracy. A more exact solution can then be obtained in terms of departures from the performance of a second-order system.

Because of the importance of second-order systems, this chapter is devoted to presenting its characteristic response in the time domain and analyzing its state-variable signal-flow graph. In addition, several important control-system definitions are presented. The closed-loop frequency response of second-order systems is presented in Chapter 6, where techniques for obtaining the closed-loop frequency characteristics are derived. A method for modeling the transfer functions of control systems is also presented.