Model predictive control strategies for tracking dynamic target references

Abstract

Model predictive controllers (MPC) are widely used to control systems with characteristics common to many industrial and academic applications. The control law of an MPC is formulated by minimizing an objective function that considers the error between estimated predicted outputs and future references over a specified time horizon. These predicted outputs can be defined using either a nominal parametric model or a data-based model. Typically, in linear approaches, the minimization process generates an optimal sequence of inputs through the receding horizon principle, naturally incorporating system constraints into the solution. A well-known issue with constrained MPC is the loss of feasibility when reference changes occur. This happens due to the finite horizon and the constraints imposed by the controller, which may lead the optimizer to an unreachable target depending on the initial conditions of the problem, potentially causing failure in reference tracking. This work presents contributions to MPC strategies applied to time-varying references. It will be shown that MPC exhibits a conflicting cost function under such conditions, such that a simple modification can provide greater tuning flexibility, thus avoiding undesirable issues like excessively high controller gains caused by aggressive tuning. Initially, a filtered DMC approach is evaluated, where the prediction filter maintains sensitivity to high-frequency disturbances while MPC tuning improves reference tracking. Its effectiveness is assessed through simulations and experiments on temperature control of a thermoresistive sensor. Next, a modified cost function approach is proposed for a receptance-based MPC to reduce the nominal value of the cost function under time-varying reference conditions. Additionally, the receptance matrix-based modeling aims to simplify the identification stage of complex systems, eliminating the need for prior knowledge of the phenomenological model parameters of a multibody system. Simulation results were evaluated for an underactuated system, demonstrating its effectiveness in tracking periodic references. Finally, this work also addresses the issue of MPC with robust stability guarantees through the use of artificial references and analytical reformulation of the desired target. The efficiency of this approach is validated through numerical simulation analysis, and its practical applicability is demonstrated in trajectory control of an unmanned ground vehicle (UGV).