Model Predictive Control with Input and Output Constraints

Among the several predictive control approaches proposed in the literature (hysteresis-based, trajectory-based, deadbeat, etc.), Model Predictive Control (MPC) surely represents the most promising one due to its inherent flexibility and versatility. In fact, MPC cost function generally consists of a sum of several terms, whose weights can be tuned in accordance with different criteria. As a result, an accurate choice of MPC cost function enables an appropriate optimization of several non-linear systems (electrical, mechanical, chemical, etc.), especially those characterized by several inputs and/or outputs. One of the most important feature of MPC consists of more easily taking into account both input and output constraints compared to other predictive control approaches, because they can be accounted by the MPC cost function. However, this solution does not guarantee that they are always satisfied, may impairing system performance optimization at the same time. A viable solution consists of appropriately managing input and output constraints in order to guarantee system optimization. In particular, system operating boundaries should be determined at first, within which a number of MPC objective functions should be minimized in a descending order of priority. Although such an approach is generally quite complex compared to conventional MPC, it leads to a better system exploitation. In addition, higher computational efforts can be easily handled by means of fast processing units, like Field Programmable Gate Arrays (FPGA); in fact, they allow very fast execution times, even for advanced MPC-based control systems, making them particularly suitable in replacing traditional control techniques in industrial applications. This chapter addresses the problem of accurate management of input and output constraints for MPC. Thus, firstly referring to a generic system, problem statement and formulation are firstly introduced and briefly discussed. Subsequently, reference is made to a case study, namely a Surface-Mounted Permanent Magnet Synchronous Machine (SPM). In particular, its mathematical modelling is briefly introduced at first, as well as its operating constraints (voltage saturation, current limitations, etc.). Subsequently, the design of an MPC algorithm is reported, which is based on accurate management of SPM operating constraints in order to guarantee optimal SPM performances, over both steady-state and dynamic operation. Both simulation and experimental results are also enclosed in order to highlight the effectiveness of this MPC approach; in particular, the former is achieved by means of Matlab-Simulink, whereas the latter refers to the employment of an appropriate FPGA-based control board.