Performance and stability analysis of LP-MPC and QP-MPC cascade control systems

Model predictive control (MPC) is used extensively in industry to optimally control constrained, multivariable processes. For nonsquare systems (with more inputs than outputs), extra degrees of freedom can be used to dynamically drive the process to its economic optimum operating conditions. This is accomplished by cascading a local linear programming (LP) or quadratic programming (QP) controller using steady-state models. Such a cascade control scheme (LP-MPC or QP-MPC) continuously computes and updates the set points used by the lower-level MPC algorithm. While this methodology has been in use by industry for many years, its properties have not been addressed in the literature. The properties of such cascaded MPC systems are analyzed from the point of view of implementation strategies, stability properties, and economic and dynamic performance. Some theoretical results on stability are derived along with a case study involving the Shell control problem.