An Implementable and Stabilizing Model Predictive Control Strategy for Inverted Pendulum-Like Behaved Systems

Abstract

In control theory, the inverted pendulum is a class of dynamic systems widely used as a benchmarking for evaluating several control strategies. Such a system is characterized by an underactuated behavior. It is also nonlinear and presents openloop unstable and integrating modes. These dynamic features make the control more difficult, mainly when the controller synthesis seeks to include constraints and the guarantee of stability of the closed-loop system. This chapter presents a stabilizing model predictive control (MPC) strategy for inverted pendulum-like behaved systems. It has an offset-free control law based on an only optimization problem (one-layer control formulation), and the Lyapunov stability of the closedloop system is achieved by adopting an infinite prediction horizon. The controller feasibility is also assured by imposing a suitable set of slacked terminal constraints associated with the unstable and integrating states of the system. The effectiveness of the implementable and stabilizing MPC controller is experimentally demonstrated in a commercial-didactic rotary inverted pendulum prototype, considering both cases of stabilization of the pendulum in the upright position and the output tracking of the rotary arm angle.