Design of an optimized sliding mode control for loaded double inverted pendulum with mismatched uncertainties

In this paper, the stabilization problem of loaded double inverted pendulum using an optimized state feedback sliding mode control is investigated. ADAMS/Matlab co-simulation environment is used for building a virtual nonlinear model for loaded double inverted pendulum system and the state feedback sliding mode control law is designed for stabilizing the system. Mismatched uncertainties represented by payload variations is considered. Genetic Algorithms are used to optimize the parameters of the sliding mode controller based on a performance index containing the sum of squared errors. The proposed control scheme can significantly suppress chattering effect and improves the performance of the system against uncertainties. Simulation results show the effectiveness of the approach and the robustness of the system against payload changes.

I. Introduction

Inverted pendulum system is a benchmark control problem for stability and robustness studies. It is a naturally unstable and under-actuated system. The control of inverted pendulum is a challenging problem; it can be divided into three aspects, swing-up [1], [2], stabilization [3], [4] and tracking control problems [5]. On the other hand, controlling a double inverted pendulum (DIP) is more challenging than the common inverted pendulum as increasing the number of links does increase the complexity and uncertainty of the system. Stabilization of a loaded double inverted pendulum (LDIP) is the scope of this work. Several Stabilization control problems can be simplified as an inverted pendulum stabilization problem. For instance, keeping a Humanoid [6], [7] in an upright posture under large disturbance, keeping a space shuttle balanced during launching, and stabilization of a segway vehicle during its motion [8], [9].