Sliding mode control for performance improvement of linear systems

This paper includes a method to design sliding mode control law for typical single-input-single-output systems. In real time applications, the model of the systems obtained by empirical technique gives higher order model. In the proposed method, there is no need to use model order reduction technique as the higher order model can be directly used to design the sliding law. The sliding surface is (n-1)
^th
n - order differential equation of error obtained from output and desired reference trajectory, where n is order of the system whose performance has to improve. As per the theory of sliding mode, the total control law is obtained using the proposed method by selecting sliding surface and smooth hyperbolic tangent function. The hyperbolic tangent function is used to reduce chattering phenomenon that occurs in many cases when there are use of sliding mode strategy. The single variable processes with delay time, lower or higher order, monotonic or oscillatory behavior are effectively controlled by the proposed sliding mode algorithm. The Lyapunov function is used to ensure the stability and simulation examples are incorporated to show the effect of proposed method.