Comparative Assessment of Predictive Controllers for an Inverted Pendulum with Three Conflicting Control Objectives

Model predictive control (MPC) designates a class of moving-horizon optimal control techniques based on the use of a process model to make predictions of the plant output. Over the past 30 years, several MPC formulations have been reported in the literature. These formulations differ from each other mainly in the type of process and disturbance models adopted, as well as in the cost function to be minimized. Given a specific problem, the selection of the most appropriate MPC approach may not be straightforward. In fact, control tasks usually involve multiple conflicting objectives, which cannot be easily combined in a single performance index for comparative assessment of different control laws. Moreover, the proper use of MPC requires the tuning of several design parameters such as horizon lengths and cost function weights. Therefore, a fair comparison between predictive controllers can only be carried out if they have been suitably tuned with respect to the control objectives under consideration. This paper presents a multi-objective approach for comparison of control strategies employing the concepts of dominance and Pareto optimality. This approach is illustrated in a simulated case study involving the control of an inverted pendulum coupled to a cart. Three conflicting objectives are considered, namely (1) fast response to setpoint changes in the cart position, (2) robustness with respect to model uncertainties and (3) low sensitivity to sensor noise. Two different MPC formulations are compared in terms of their Pareto boundaries for these three objectives. The results show that the proposed approach may be a useful aid in the selection and tuning of appropriate controllers for a given task.