Robust and adaptive control via backstepping technique

Abstract

Most of the control systems are designed using linear techniques, which have been well developed. Practical physical systems are typically nonlinear. Nonlinear control is one of the biggest challenges in modern control theory. Nonlinear processes are difficult to control because there can be so many variations of the nonlinear behavior. One of the main recursive procedures to design a nonlinear controller is the backstepping. Adaptive backstepping achieved global stabilization in the presence of unknown parameters and robust backstepping achieved it in the presence of disturbances. The ease with which backstepping incorporated uncertainties and unknown parameters, contributed to its instant popularity and rapid acceptance. The backstepping provides a powerful design tool for nonlinear systems in the lower triangular form. The first part of the thesis is to explain backstepping technique for third order nonlinear systems. Robust backstepping technique for a system with bounded uncertainties and adaptive backstepping technique for a system with linear unknown parameters are illustrated and simulated. The second part of the thesis is to apply the adaptive backstepping and robust backstepping technique to a 2-DOF (degree of freedom) planar manipulator. Experimental and simulation results are obtained and compared with linear (PD) controller and nonlinear controller (Lyapunov based algorithm).