Nonlinear/Linear Switched Control of Inverted Pendulum System: Stability Analysis and Real-Time Implementation

Abstract

This paper treats the problems of stability analysis and control synthesis of the switched inverted pendulum system with nonlinear/linear controllers. The proposed control strategy consists of switching between backstepping and linear state feedback controllers on swing-up and stabilization zones, respectively. First, the backstepping controller is implemented to guarantee the rapid convergence of the pendulum to the desired rod angle from the vertical position. Next, the state feedback is employed to stabilize and maintain the system on the upright position inherently unstable. Based on the quadratic Lyapunov approach, the switching between the two zones is analyzed in order to determine a sufficient domain in which the stability of the desired equilibrium point is justified. A real-time experimentation shows a reduction of 84% of the samples below the classical scheme when using only the backstepping control in the entire operating region. Furthermore, the reduction percentage has become 92% in comparison with the composite linear/linear controller.