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 `transition' 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.