Sub-optimal nonlinear controllers for relay and saturating control systemst

Abstract

The optimal control signal for saturating or relay control systems is a complicated function of several state variables. A sub-optimal technique is to use instead a function which is simply a linear combination of functions each of which has only one state variable as argument. When the plant consists of a set of pure integrators, previous work has shown how to reduce the resulting sub-optimal controller design problem to the determination of a few parameters. In the present paper the choice of these parameters is considered. For a third-order system it is shown that the motion can be depicted in a ‘reduced state space’ having only two coordinates. The portrait in this state plane enables pathological behaviour (instability and excessively slow sliding motion caused by incorrect adjustment of controller parameters) to be recognized and avoided. The sub-optimal controller can then be adjusted so that settling times about 30° greater than the optimal values can be obtained. The reduced state space is also u...