Model predictive control based on the output prediction-oriented model: a dual-mode approach, and robust distributed algorithms. - Sêncio, Rafael Ribeiro (2022)
The output prediction-oriented model (OPOM) is a state-space model with incremental inputs that is derived from the analytical form of the system step response. This model has the prediction of the output at steady state as part of the state vector, which is useful for imposing the terminal constraint in an infinite horizon MPC formulation suitable for setpoint tracking. In this work, stabilizing MPC approaches based on the output prediction-oriented model are proposed, namely, a dual-mode MPC and three robust cooperative distributed MPC algorithms. First, a method to transform a state-space model with positional inputs into an OPOM-like model is presented. The resultant model can be viewed as a generalization of the traditional OPOM, being able to represent systems with stable, integrating and unstable poles as well as with pole multiplicity and time delays. Deploying a terminal control law and applying the concept of an invariant set for tracking, the proposed dual-mode MPC with OPOM has embedded integral action and guaranteed stability and feasibility under any setpoint change. In this approach, the characterization of steady outputs and inputs is based only on terminal states and inputs, avoiding parametrization of system equilibria. Such a method allows the computation of artificial references that are consistent with the true plant steady state, even in the presence of plant-model mismatch or unmeasured disturbances. The proposed MPC also addresses the case of output zone control and optimizing input targets. It is proved that, if the desired operating point is not admissible, the proposed controller steers the system to the operating point that minimizes an offset cost function. Concerning the proposed algorithms for robust cooperative distribute MPC, the multi-model system representation is adopted, and a plantwide performance index is optimized while imposing a cost-contracting constraint for all the models. This strategy results in a QCQP (quadratically constrained quadratic programming) problem that is solved for each subsystem. Local solutions are shared between the agents and an iterative procedure is applied to improve the overall solution. This approach is extended and two alternative algorithms are proposed. One is based on computing optimal weights of the convex combination of agents solutions, which improves the convergence over iterations. The other enforces the robustness constraint only after iterations terminate, thereby turning the optimization problem solved by each agent into a QP (quadratic programming) problem. This strategy reduces the number of QCQP problems solved at each time step, which also reduces the CPU time spent by the agents. The proposed distributed algorithms are suitable for dealing with both setpoint tracking and zone control problems, and have guaranteed recursive feasibility, convergence and stability. Numerical examples are presented to illustrate the application of the proposed controllers.