Design of Control Systems with Multiple Backlash Nonlinearities Subject to Inputs Restricted in Magnitude and Slope

Abstract

This paper develops a computational method for designing a control system that is an interconnection of transfer functions and multiple decoupled backlash nonlinearities where each backlash is modelled as an uncertain band containing multi-valued functions. The design objective is to ensure that the system outputs and the nonlinearity inputs always stay within their prescribed bounds in the presence of all inputs whose magnitude and whose slope are bounded by respective numbers. By using a known technique, each backlash is decomposed as a linear gain and a bounded disturbance. Essentially, the original design problem is replaced by a surrogate design problem that is related to a linear system and thereby can readily be solved by tools available in previous work. Moreover, as a result of using the convolution algebra A, the method developed here is applicable to rational and nonrational transfer functions. To illustrate the usefulness of the method, linear decentralized controllers are designed for a binary distillation column where valve stiction characteristics are taken into account.