High Performance Robust Controller Design Using Nonlinear Surface

Many practical systems call for an improvement in transient performance along with the steady state accuracy. For example, many electro-mechanical, robotics and power converter systems require a quick response without any overshoot. It is a well understood fact that a low overshoot can be achieved at the cost of high settling time. However, a low settling time is also necessary for a quick response. Thus, most of the design schemes make a tradeoff between these two transient performance indices and the damping ratio is chosen as a fixed number. As explained in the first chapter, a variable damping ratio improves the system performance significantly. This chapter presents a method to design a nonlinear sliding surface for a linear uncertain system; and the method is also extended for a class of nonlinear system. A nonlinear sliding surface is designed by using the principle of composite nonlinear control [70, 94, 21]. Using a nonlinear sliding surface, the damping ratio of a system can be changed from its initial low value to final high value. The initial low value of damping ratio results in a quick response and the later high damping avoids overshoot. Thus the proposed surface ascertains the reduction in settling time without any overshoot. Furthermore, systems’s damping ratio changes continuously as per the chosen function. Both regulator and tracking cases are considered in this chapter. The proposed approach inherits the robustness of SMC and delivers high performance due to change of damping ratio through the nonlinear sliding surface. During sliding mode, because of the order reduction, system response is unaffected by

m

poles. For a systems of order higher than 2, the damping ratio is specified by considering the contribution of dominant poles. However, non-dominant poles always affect the system response to some extent depending on their relative locations with respect to the dominant poles. Due to the order reduction property of SMC,

m

non-dominant poles will not contribute in the system response and thus, the performance specifications can be achieved more closely. The proposed nonlinear sliding surface achieves high performance and robustness unlike a sliding surface designed by assigning eigenvalues or by minimizing a quadratic index, which normally lead to a linear sliding surface. This chapter contains some results from [2] and several additional results.