Performance Analysis of LP-MPC Cascade Control Systems

Abstract

Model Predictive Control (MPC) algorithms are widely applied in the chemical process industry. The main advantage of these controllers over others is their ability to provide multivariable control of the process subject to specified constraints. The presence of degrees of freedom in the plant provide an opportunity for the introduction of an optimization level (Real-Time Optimization (RTO) level), to determine optimal set points and target values for controlled variables and manipulated variables respectively, and the constraints the plant should follow to provide maximum profit. Industrial MPC controllers typically include an upper level steady-state optimizer, which usually comprises a linear programming (LP) or quadratic programming (QP) problem. This local optimizer may serve either as an integrating level between the low frequency nonlinear steady-state RTO and regulatory level, or as an independent optimizer with an economic objective function. Many researchers have reported success of LP-MPC cascade control system implementations (Sorensen and Cutler, 1998; Verne et al., 1999). However, despite its apparent success, poor LP-MPC cascade system performance and possible instability have also been reported. In particular, Shah et al. (2002) show that in the presence of a steady-state LP optimizer, the set-points could have a large variation relative to the controlled variable variation; thus the LP could degrade the MPC performance by sending highly variable set-points to the controller. Kozub (2002) indicates that in a control system with an LP steady-state optimizer, an LP instability problem may arise under certain conditions. These observations motivated research which aims to investigate the effect of the various factors on the stability and performance of the two-level LP-MPC cascade control system. Such factors include plant/model mismatch, the frequency of LP implementation, the LP objective function, constraints and type of disturbances. Since the optimization can be executed at different frequencies, two most common scenarios are considered: (i) when the LP is implemented at steady-state only and (ii) when the LP is implemented at every MPC iteration. Initially, steady-state LP optimization only is considered and it is shown that the set-points may fail to converge to constant values in the absence of external disturbances under certain conditions. Then, the effects of optimization frequency and control structure on the closed-loop properties of the LP-MPC control system are investigated. Results of a number of case studies are shown, and root causes for observed behavior discussed. As a part of the regulatory level analysis, the calculation of the closed-loop equilibrium of a process controlled by constrained MPC is studied. This problem arises in process design and operations, and is often applied within an optimization framework. It is shown that the effect of the control system on the resulting steady-state must be explicitly accounted for, and that in the general case, the use of a steady-state process model only is not sufficient for this calculation to be correctly executed. Two solution strategies, sequential and simultaneous, are presented and evaluated. The effect of high frequency noise-like disturbances on the two-level control system behavior is analyzed. The analysis which verified by case studies, showed that the LP may have an effect of amplifying the system noise through the bias term which is used for the model update. Such amplification may result in high variation of the LP set points provided to the MPC, thereby degrading the overall performance of the two-level system.