Fixed‐Time Terminal Sliding‐Mode Controller

Summary

In classic sliding mode control, the state variables reach the sliding surface and converge asymptotically. When a controller is designed to ensure the asymptotic stability of the closed‐loop system, the convergence of states to the equilibrium point occurs over an infinite time horizon. This chapter presents the finite‐time terminal sliding‐mode controller and investigates the dependency of finite convergence time to initial conditions. Finite‐time terminal sliding mode controllers enables system states to reach a neighborhood of equilibrium points within a finite time, though this time is dependent on the initial conditions of the system. The chapter proposes the fixed‐time terminal sliding‐mode control and discusses its characteristics and compares with finite‐time sliding‐mode controller. The sliding structure provides fast convergence and accurate tracking and independence from initial conditions. The chapter also investigates the simulation of the inverted pendulum system with the fixed time nonsingular terminal sliding mode method.