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.
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December 6th, 2007 at 12:17 pm
an intensive course will be given on model predictive control and hybrid dynamical systems. The course is intended for students and engineers that want to learn about the theory and practice of Model Predictive Control (MPC) and of optimization of constrained linear systems and hybrid dynamical systems. MPC was first proposed by industry to deal with the control of multivariable systems with a large number of inputs and outputs subject to constraints. The constraints can arise from limits on manipulated variables and controlled outputs. In the last few years a theoretical basis for MPC has emerged for providing stability and robustness guarantees, for dealing with hybrid systems, and for dealing with fast sampling processes. The course will make use of the new MPC Toolbox for Matlab distributed by The MathWorks, Inc., and of the Hybrid Toolbox by A. Bemporad. There will be exercise sessions throughout the course, where students can test their understanding of the material. Outline: - General concepts of MPC. MPC based on QP. General stability properties.
- MPC Toolbox: model/problem setup, MPC objects, MPC Simulink block (exercises)
- QP/LP solvers. Multiparametric programming and Explicit MPC. MPC based on LP. Robust Explicit MPC.
- Hybrid MPC: modeling, MPC control, explicit forms, applications (exercises).
Intended audience: The course is meant for graduate students specializing in Systems Theory, Automatic Control, Process Control, Signal Processing, Optimization, Robotics, Automomous Systems, and related fields, for last year undergraduate students interested in one of the above areas, and for control engineers active in industry. Prerequisites: A basic course in automatic control and in optimization. Suitable reading: - Copies of overhead slides
- Selected scientific articles
- MPC Toolbox User’s Guide
- Hybrid Toolbox User’s Guide
December 6th, 2007 at 12:18 pm
Model predictive control (MPC) has gained widespread acceptance in the chemical process industry, as well as in other industrial sectors (Qin and Badgwell, 2003). Key attributes are its ability to accommodate dead time and multivariable interactions directly, and its explicit constraint-handling capability. Commercial MPC systems are generally implemented in conjunction with a linear programming (LP) or quadratic programming (QP) optimizer that utilizes a linear, steady-state model to generate feasible set-points for the model predictive controller (Qin and Badgwell, 2003; Yousfi and Tournier, 1991; Sorensen and Cutler, 1998). The LP or QP may optimize an economic objective function directly, or minimize the deviation from set-point targets generated by a real-time optimization (RTO) system. In the latter application, the RTO system typically employs a more complex, nonlinear model, and the key function of the LP or QP layer is to make appropriate adjustments to the set-points in response to higher-frequency disturbances. However, despite the apparent success of LP-MPC cascade systems, poor performance characteristics have also been reported (Shah et al., 2002; Kozub, 2002). This includes high variability in the computed set-points (observed to exceed that of the corresponding controlled variables), and unexpectedly high fluctuations in the set of manipulated variables at constraints. This paper explores the effects of several factors on the performance of the overall LP-MPC cascade control system.
First, two methods for the LP model bias update were evaluated and compared in a variety of scenarios with different plant/model mismatch, constraints and LP objective function. Application to case studies indicated superior stability and performance properties for a bias update scheme that used the steady-state model directly, even with quite significant plant/model mismatch.
A multi-input, multi-output (MIMO) case study based on the Shell Standard Control Problem (Prett et al., 1990) demonstrated that the selected control structure may have a significant effect on the stability and control performance of an LP-MPC cascade control system. Chattering of the set-points was observed when an auxiliary output was constrained but not controlled. The set-points stabilized with an increased LP execution frequency, but poor dynamic performance was observed. Changing the control structure to include the auxiliary output as a controlled variable resulted in superior performance.
Finally, the effect of high frequency disturbances on the two-level control system behavior was investigated. Analysis, verified by simulation studies, showed that in MIMO systems, the LP may have an effect of amplifying the system noise through the bias term which is used for the model update. This is dependent on the model gains and active constraint set. 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.