A control system design technique for nonlinear discrete time systems

Abstract

A new control methodology is proposed for use with a class of nonlinear, single-input discrete time systems. The technique is based on a discrete time approach that parallels existing continuous time sliding surface concepts. Modifications to the basic algorithm allow for system models with time-variant or uncertain parameters, time delays in the control input, and external disturbances. A major feature of the method is its straightforward extension to an adaptive control form which can be used to improve performance and maintain stability in the presence of large parametric uncertainty or time-variant behavior. Techniques are proposed for overcoming instabilities that frequently arise when using adaptive control schemes based on reduced order system models or in the presence of disturbances. A framework is provided for the practical application of the methodology to continuous time systems. The discrete time nature of the development makes it especially well suited to applications where sensor data is infrequently available or computational power is limited. An experimental study is performed using an underwater remotely operated vehicle to verify the validity of the approach. The ability of the method to use a nonlinear model and adapt to large parametric uncertainty is shown to result in improved performance over the use of a linear or time-invariant model.