Advanced Modern Control System Theory and Design

6

INTRODUCTION TO OPTIMAL CONTROL THEORY AND ITS APPLICATIONS

6.1. INTRODUCTION

From the presentation of linear and nonlinear systems in Chapters 2, 3, and 5, we recognize that the conventional design of feedback control systems has several disadvantages. The most serious disadvantage is that the control-system configurations we have analyzed and designed in the previous chapters were always assumed to be known in advance. But we never knew whether they were the best system to do the job. In contrast, optimal theory is concerned with obtaining a system which is the best possible with respect to a standard against which we can measure real performance. We denote this standard as the performance criterion (see Chapter 5^‡ for a discussion of performance criteria). The task of designing control systems that are optimal, in some sense, is one of the most important and complex problems facing control engineers today.

Wiener [1], in the late 1940s, developed the concept of optimum design that was based on optimizing a performance criterion. McDonald [2] first applied the concept of optimization to control systems in 1950. His objective was to minimize the transient response time of a relay-type feedback control system to step inputs. In 1957, Draper and Li [3] wrote a booklet discussing the theoretical concepts of optimal control for an internal combustion engine. Their system attempted to minimize (or optimize) the consumption of fuel. Since that time many articles have been written ...