Abstract
The optimal control signal for saturating or relay control systems is usually a complicated function of several state variables. A sub-optimal control method is to use instead a simpler signal which is a linear combination of functions each of which has only one state variable as argument. Persson has investigated this type of sub-optimal control for plants consisting of a set of pure integrators. In the present paper the theoretical basis of Persson's controller is developed by invoking dimensional considerations. It is shown that the optimal system has certain types of invariance under changes of scale. If a similar property for the sub-optimal system is adopted, the controller design problem can be reduced to the determination of a few parameters.
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