Sensitivity analysis of LP-MPC cascade control systems

Model predictive control (MPC) has found wide application in the chemical process industry as well as other industrial sectors. Commercial MPC systems are typically implemented in conjunction with a steady-state linear or quadratic programming optimizer, whose key functions are to track the economic optimum and to provide feasible set-points to the model predictive controller. The two-level system is complementary to real-time optimization which typically utilizes more complex models and is executed less frequently. Despite the widespread adoption of LP-MPC systems, occurrences of poor performance have been reported, where large variations in the computed set-points were observed. In this paper, we analyze the sensitivity of the LP solution to variation in the LP model bias, through which feedback to the LP layer occurs. We consider both multi-input, single-output (MISO) and multi-input, multi-output (MIMO) systems. Principles are illustrated through graphical representation as well as case studies. The performance of the two-level LP-MPC closed-loop system is evaluated and explained using results of the LP sensitivity analysis.