TABLE OF CONTENTS The design of a control system is an attempt to meet a set of specifications that define the overall performance of the system in terms of certain measurable quantities. In the classical design method of control systems, the designer is given a set of specifications in time domain or in frequency domain with the system configuration. Peak overshoot, settling time, gain-margin, phase-margin, steady-state error, etc., are among the most commonly used specifications. These specifications have to be satisfied simultaneously in design. In practice, it may not be possible to satisfy all the desired specifications and hence, the design necessarily becomes a trial - and - error procedure. This trial - and - error design procedure works satisfactorily for single-input-single-output systems. However, for a system with multi-input-multi-output having a high degree of complexity, the trial - and - error approach may not lead to a satisfactory design.
The optimal control design is aimed at obtaining a best possible system of a particular type with respect to a certain performance index or design criterion-hence the word optimal. In the optimal control design, the performance index replaces the conventional design criteria, such as peak overshoot, settling time, gain-margin, phase-margin, steady-state error, etc. Of course, the designer must be able to select the performance index properly so that one may describe the goodness of the system response on the basis of this performance index.
A performance index is a function of...
