Guaranteed performance in reaching mode of sliding mode controlled systems

Abstract

Conventionally, the parameters of a sliding mode controller (SMC) are selected so as to reduce the time spent in the reaching mode. Although, an upper bound on the time to reach (reaching time) the sliding surface is easily derived, performance guarantee in the state/error space needs more consideration. This paper addresses the design of constant plus proportional rate reaching law-based SMC for second-order nonlinear systems. It is shown that this controller imposes a bounding second-order error-dynamics, and thus guarantees robust performance during the reaching phase. The choice of the controller parameters based on the time to reach a desirable level of output tracking error (OTE), rather than on the reaching time is proposed. Using the Lyapunov theory, it is shown that parameter selections, based on the reaching time criterion, may need substantially larger time to achieve the OTE. Simulation results are presented for a nonlinear spring-mass-damper system. It is seen that parameter selections based on the proposed OTE criterion, result in substantially quicker tracking, while using similar levels of control effort.