Implementação de uma abordagem de controle preditivo em um pêndulo de duas rodas em ambiente de simulação numérica

Abstract

The main advantages of the Model-based Predictive Control (MPC) strategy are constraint handling, computation of the control action by minimizing a performance index and applicability on SISO (Single-Input and Single-Output) and on MIMO (Multiple-Input and Multiple-Output) systems. In order to study such control strategy, this work involves the stabilization of a two-wheel pendulum in the vertical position using MPC. For this purpose, at first, a MPC formulation with recursive feasibility guarantee was investigated. Such guarantee ensures that, if the optimization problem is initially feasible, then it will be feasible at all the following sampling instants. This formulation was successfully implemented on a double integrator. However, the simulation results on the inverted pendulum were not satisfactory. More specifically, it was noted that angular position of the wheel diverged. The problem was solved by modifying (as proposed in the literature) the cost function to obtain convergence guarantee, where only the minimization of the predictive control effort was considered. In other words, to ensure that the control action enforces the system state to the equilibrium point. This last formulation presented good results on controlling the inverted pendulum, including in simulations on the non-linear model with measurement noise and model mismatches. This reinforces the importance of applying MPC techniques with nominal guarantees of recursive feasibility and convergence, which can be interpreted as guarantee of stability.