Integral Sliding Mode Based Composite Nonlinear Feedback Control

Introduction

In this chapter we discuss the problem of improving performance yet preserving the invariance towards the matched disturbances from a different perspective. In the previous chapters, we proposed various schemes in which the nonlinear surfaces are designed for different types of systems for the improvement of performance. In this chapter we propose a nonlinear surface which considers actuator saturation and the elimination of the reaching phase with improvement in the performance. For any practical system, actuator output can not take any amplitude. Actuator capacity is always bounded, therefore it is necessary to consider the effect of saturation actuator a priori. In conventional sliding mode, the motion of the trajectory is constrained to lie in an (n − − m) dimensional manifold with a discontinuous control action. Here m is the number of inputs and n is the order of the system. The motion of the trajectory from the initial condition towards sliding surface until it hits the sliding surface is called the reaching phase. During the reaching phase, the system is not robust and even matched disturbances can affect the system performance. To solve this problem, in [100], an integral sliding mode (ISM) concept is proposed. An integral term is incorporated in the sliding manifold, this guarantees that the system trajectories will start in the manifold right from the beginning thus, the reaching phase is eliminated; and the system becomes invariant towards matching perturbation right from the beginning. The main idea behind the ISM controller is to define the control law as a sum of a nominal control and a discontinuous control. Nominal control takes care of the nominal plant dynamics and the discontinuous control rejects the disturbances. The nominal control can be of any form which is able to follow the reference trajectory within a given accuracy. In this work we have taken Composite Nonlinear Feedback (CNF) controller, which is based on variable damping ratio, as a nominal controller along with the ISM controller to reject disturbance.