Chapter 4

# 4.1 Introduction

Recall that the Implicit Control Objective is to ensure that the closed loop system is stable. Once that is achieved, the Explicit Control Objective is to force the process output to follow, or track, a desired reference signal, even in presence of an unexpected, and unwanted, disturbance. The reference signal may be constant, in which case we refer to the control system as the Regulator System, or varying, in which case we refer to the control system as the Tracking System. A special case of Regulation is when the constant reference signal is equal to zero. In Regulation, the most important objective is to effectively reject disturbances. In the case of tracking, the accuracy, or quality, of the response (i.e. how close the output is to the reference) is important both in the steady state and in transient.

Examples of signals – steps, ramps, sinusoids, parabolic, and any arbitrary time-varying signals. Note that in a Linear Time-Invariant (LTI) system, an arbitrary time signal can be seen as a superposition of a set of standard signals. We need to evaluate how well the process is doing. The quality of response has to be quantified. This can be done through:

- Performance Specifications
- Performance Indices
- Transient behaviour specifications – based on Step Response
- Steady state behaviour specifications – Error Analysis