Optimal noncausal set-point regulation of scalar systems

This paper presents a novel system inversion approach to the set-point regulation of linear scalar minimum-phase systems. This approach uses closed-form expressions of cause/e!ect pairs that make possible an arbitrarily smooth transition between two given output set-points. The cause/e!ect pairs are based on the introduced concept of `transitiona polynomials. Simple optimization procedures are then proposed to solve the relevant optimal output synthesis and optimal input synthesis. The potentiality of the method is highlighted by the examples presented, namely, a synthesis of elevator velocity pro"les and the performance improving of a PID controller. ( 2000 Elsevier Science Ltd. All rights reserved.