On the use of optimization theory for practical control system design

Abstract

The approach to control system design discussed in this paper has as its purpose the more effective utilization of optimal control theory for the development and the evaluation of practical system designs. Rather than specifying initially a single performance index (or an arbitrary scalar function of several indices), the performance bounds relating the various competing performance requirements of the system are first evaluated using optimization techniques, so that the ultimate trade offs achievable between these requirements are well understood. These performance bounds then form the basis not only for a more meaningful specification of optimum system performance, but also for the evaluation of sub-optimal designs which are developed from approximations of the optimal control strategies, from previous designs, and from the experience and insight of the designer. The specific example of the satellite attitude control problem is used to illustrate this design approach. Performance bounds between control fuel expenditure and control time are obtained over a range of initial conditions. Using this information and the knowledge of the form of the minimum-fuel control law, a simple feedback control design is developed which is superior to either the well-known minimum-time or the minimum-fuel solutions, both from the point of view of achieving on-the-bound performance which represents the best compromise between these competing performance requirements and from the point of view of practical implementation. The final portion of the paper describes the computer-aided design program which has been undertaken to extend this design approach to more complex control problems.