APPROXIMATE LINEARIZATION OF CONTROL-SYSTEMS WITH DISCONTINUOUS NONLINEARITIES

The class of systems containing elements with discontinuous input-outp ut characteristics (such as jumps, hysteresis, etc.) presents a seriou s challenge to control specialists. They are so difficult to treat ana lytically that they are normally dealt with using heuristic methods. I n this paper a mathematical framework for such problems is presented a nd precise criteria for measuring the non-linearity are introduced. Li nearization is considered in a restricted but realistic sense (on aver age or at discrete times only). In this context the most common practi cal techniques such as dithering and pulse width modulation are analys ed. In addition, a simple new approach for feedforward control is deve loped. It produces a locally optimal control, providing results that a re superior to those from more standard precompensation techniques. An application of these ideas to a small travelling wave motor is includ ed. Such motors have considerable dry friction and therefore provide s ignificant examples of the kind of systems under consideration.