A hybrid formulation and design of model predictive control for systems under actuator saturation and backlash

In this paper, we develop a hybrid design framework of model predictive controller (MPC) for multivariable systems that simultaneously and explicitly addresses the actuator saturation and backlash. The discrete characteristics of the actuator backlash allows us to mathematically express it as a set of mixed-integer linear inequalities constraint in the inputs. As a result, the constrained MPC design is formulated as solving a mixed-integer quadratic programming (MIQP) problem. Furthermore, the proposed MIQP-based design is applied only in the proximity of steady state operating points after locating the active backlash and providing the estimate of the backlash size. Simulation studies are presented to demonstrate how the hybrid MPC performs when applied to an industrial case study of fluid catalytic cracking unit. It is shown that in the presence of actuator saturation and backlash the closed-loop performance can be improved substantially when applying the hybrid method as compared to the traditional design approaches.