Chapters authored
Nonlinear Feedback Control of Underactuated Mechanical Systems
This chapter presents control of a class of mechanical underactuated system using feedback linearization technique. The MIMO mechanical system is modeled by a set of nonlinear differential equations in which mathematical model is divided into two subsystems: one for actuated outputs and the other for unactuated outputs. The nonlinear feedback of states is used to “linearize” the closed-loop system. In other word, the control structure is constructed by linearly combining two components that are separately obtained from the nonlinear feedback of actuated and unactuated states. Lyapunov technique will be applied to investigate the system stability. As illustration example, nonlinear feedback control of a three-dimensional (3D) overhead crane is presented to investigate the proposed theory.
Part of the book: Nonlinear Systems
Hierarchical Sliding Mode Control for a 2D Ballbot That Is a Class of Second-Order Underactuated System
2D Ballbot is an actual under-actuated system with second-order nonholonomic velocity constraints and input coupling case where only control input is employed to control two outputs of the system. Controlling such a system is not easy because it faces many changelings including nonlinearities, external disturbances, and uncertainties. This study proposed a robust control system for a Ballbot mobile robot. The proposed control scheme is constructed using the hierarchical sliding mode control technique. The kinematics and dynamics of the Ballbot are derived. A Lyapunov function is used to prove the stability of the closed-loop control system. The stabilizing and transferring problems are investigated through several simulations and experiments by using the actual Ballbot platform.
Part of the book: Production Engineering and Robust Control