Finite Settling Time Control of Nonlinear Systems

Abstract

Robust control design for nonlinear systems is one of the most explored topics in recent literature. Conventionally, techniques like Taylor’s approximation, feedback linearization, and gain-scheduling are applied on nonlinear system models to find their simplified linear equivalent models. The system can then be controlled using some linear control techniques like PD, PI, PID or LQR, etc. The performance of controllers designed based on linear control techniques is likely to suffer due to external disturbances and modeling uncertainties. Due to the limitations of linear control techniques, nonlinear model-based control techniques became the active research area. Among nonlinear control techniques, Lyapunov-based controllers guarantee robustness to matched and mismatched uncertainties. Moreover, sliding mode control is the most used Lyapunov method in nonlinear control because of its robustness to parametric uncertainties and matched disturbances. From the control design perspective, settling time is a very important parameter. For nonlinear systems, the desired settling time is pre-determined only by the use of terminal sliding mode control. Terminal sliding mode control used a nonlinear sliding surface and the problem with the terminal sliding mode is the singularity. However, terminal sliding mode control guarantees the convergence of states to zero after a finite time. In this thesis, a linear sliding surface is used to design a finite settling time nonlinear controller. The definition of finite settling time, in the context of this thesis, is the time after which the outputs of a system remain in the pre-assigned error margin. In the proposed method, the finite settling time of the system under matched perturbations can be pre-calculated and the output of the system is guaranteed to remain in a bound for all the time. The validation of methodology for higher-order single input single output nonlinear systems is shown by simulations of three practical systems including simple pendulum, solenoid actuator, and single-link flexible joint robotic manipulator.