**Nonlinear Feedback Control of Underactuated Mechanical Systems Provisional chapterNonlinear Feedback Control of Underactuated Mechanical Systems**

Le Anh Tuan and Soon-Geul Lee Le Anh Tuan and Soon-Geul Lee

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/64739

#### **Abstract**

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.

**Keywords:** underactuated mechanical systems, feedback linearization, Lyapunov's linearization theorem, overhead cranes
