Optimal controller design for nonlinear systems

Abstract

The commonly used LQR method can be effective for systems with linear characteristics and for performance criteria that well match the minimisation of a quadratic functional form of a cost function. It may not produce a control that demonstrates optimal characteristics for systems which include hard nonlinearities such as nonlinear friction, asymmetric properties and limits imposed on the system states and control actuation. A controller design method is presented termed abbreviated dynamic programming control (ADPC) which condenses the large amount of data generated from the dynamic programming method into a time-invariant nonlinear feedback controller. An empirical system modelling technique is proposed in this research and applied to a single-link robot system to obtain both a linear and nonlinear system model. Using these system models an LQR and ADPC controller are established for this system. The abilities of these two controllers in minimising a predefined quadratic cost function are evaluated through both computer simulations and experimental test runs of this robot system. The ADPC controller is proved to be more effective at minimising the cost function and therefore providing optimal control.