Control Design Based on Input–Output Inversion

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This chapter deals with the input–output system inversion of fractional-order minimum-phase scalar linear systems. Given an arbitrarily smooth output function, the corresponding input is computed explicitly in order to obtain a smooth transition of the system from a steady-state value to a new one in a predefined time interval. The minimum-time constrained transition problem is addressed. Given the predefined output function and set of constraints on the input and output signals and their derivatives, the existence of an optimal feasible input is proven under very mild conditions. The proposed methodology is conveniently used in the second part of the chapter for the synthesis of the feedforward action for a fractional control system in order to achieve a predefined process variable transition from a steady-state value to another. In particular, the feedforward action is implemented either as a signal to be added to the feedback control variable or as a command signal to be applied (instead of the typical step signal) to the closed-loop system. Finally, the approach is combined with the robust controller synthesis of Chap. 6 in order to minimize the worst-case settling time for family of systems subject to constraints on the control variable and on the maximum overshoot of the system output.