A Model-Free Control Algorithm Derived Using the Sliding Model Control Method

Abstract

In this work, a model-free sliding mode control scheme is derived and applied to linear and nonlinear systems that is solely based on observable measurements and therefore does not require a theoretical system model in developing the controller form. The general sliding mode controller form is derived for an nth-order system and is strictly limited to a single-input unit input influence gain case for this work. The controller form is based solely on system measurements assuming the order of the system is known. The switching gain form is developed so that stability of the closed-loop sliding mode controller system is guaranteed using Lyapunov’s Direct Method. The controller form is reformulated using a smoothing moving boundary layer to eliminate chattering of the control effort. A simulation study is presented for a single-input unit input influence gain case applied to both a linear and nonlinear system with and without a smoothing boundary layer. The measurement based controller form is shown to be identical regardless of the system’s kinematics to be controlled assuming the order is known. Results of the simulation efforts show good state tracking performance is achieved with stable convergence for the tracking performance regardless of the system to be controlled