Switching Strategy for Optimal Adaptive Third Order Control Systems

Abstract

The conventional design of bang bang control systems for time optimal performance involves an accurate mathematical model of the system and complex computations to determine the optimal switching conditions. Such a design is normally based on the assumption that the system parameters remain fairly constant. Recomputation of optimal trajectories becomes necessary for any change in the parameters. This paper describes a simple adaptive-optimal control strategy for systems representable in phase space and can be easily adopted on a digital controller. Projections of optimal curves are obtained by storing sections of actual system trajectories in the form of tables in the computer memory. Optimal switching instants are determined by shifting and comparing the stored trajectory with the actual trajectory. Since no manipulations are required and the switching curves are obtained by constantly storing and updating the system trajectories, the control remains optimum even when there is a change in parameters. The proposed strategy requires only measurement of error in the system, derivatives of error are formed by using the difference equations, a method well suited for digital formulation of state variables.