Control of Single-Input Single-Output Systems

There is an extensive body of theory and practice devoted to the design of feedback controls for linear time-invariant systems. This chapter contains a brief introduction to the subject with emphasis on the design of digital controllers for continuous-time systems. Before we begin it is important to appreciate the limitations of linearity and of feedback. There are situations where it is best not to use feedback in the control of a system. Typically, this is true for systems that do not undergo much perturbation and for which sensors are either unavailable or too inaccurate. There are also limits to what feedback can accomplish. One of the most important examples is the nonlinearity that is present in virtually all systems due to the saturation of the actuator. Saturation will limit the range of useful feedback gains even when instability does not. It is important to keep this in mind when designing controllers for real systems, which are only linear within a limited range of input amplitudes.