Design of Multiloop Control Systems Based on Linear Programming

A. Hofer (Austria)


Linear programming, superstability, optimal control, mul tiloop control systems


In this paper a method for the design of multiloop discrete time control systems based on the concept of superstabil ity is presented. Superstable linear discrete time systems are a subset of bounded-input bounded-output (BIBO) sta ble systems with the important property that stability can be checked using conditions which are linear in the coeffi cients of the denominator polynomial of the transfer func tion. This fact is crucial for the development of a controller design procedure leading to linear programming problems. A multiloop tracking control system is considered and it is shown, how a linear controller with prescribed order can be designed such that the closed loop system is superstable and an upper bound for the peak magnitude of the track ing error takes a minimum value. Hard constraints posed on some (internal) signals of the control system are also taken into account which makes the design procedure more suitable for real world problems. The efficiency of the pro posed method is demonstrated by an example where a hy draulic drive made up as a pump-displacement controlled rotational piston motor is considered.

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