Adaptive sliding mode control of the furuta pendulum

Abstract

In this chapter an adaptive slidingmode controller for the Furuta pendulum is proposed. The Furuta pendulum is a class of underactuated mechanical systems commonly used in many control systems laboratories due to its complex stabilization which allows the analysis and design of different nonlinear and multivariable controllers that are useful in some fields such as aerospace and robotics. Sliding mode control has been extensively used in the control of mechanical systems as an alternative to other nonlinear control strategies such as backstepping, passivity based control etc. The design and implementation of an adaptive sliding mode controller for this kind of system is explained in this chapter, along with other sliding mode controller variations such as second order sliding mode (SOSMC) and PD plus slidingmode control (PD+SMC) in order to compare their performance under different system conditions. These control techniques are developed using the Lyapunov stability theorem and the variable structure design procedure to obtain asymptotically stable system trajectories. In this chapter the adaptive sliding mode consist of a sliding mode control law with an adaptive gain that makes the controller more flexible and reliable than other sliding mode control (SMC) algorithms and nonlinear control strategies. The adaptive sliding mode control (ASMC) of the Furuta pendulum, and the other SMC strategies shown in this chapter, are derived according to the Furuta’s pendulum dynamic equations making the sliding variables, position errors and velocity errors reach the zero value in a specified reaching time. Themain reason of deriving two well known sliding mode control strategy apart from the proposed control strategy of this chapter (adaptive sliding mode control) is for comparison purposes and to evince the advantages and disadvantages of adaptive sliding mode control over other sliding mode control strategies for the stabilization of the Furuta pendulum. A chattering analysis of the three SMC variations is done, to examine the response of the system, and to test the performance of the ASMC in comparison with the other control strategies explained in this chapter.