Institute for Systems Research

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Author: search.filters.author.Chiou, Hung-WenSubject: search.filters.subject.chemical process control

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    On the Quadratic Stability of Constrained Model Predictive Control
    (1994) Chiou, Hung-Wen; Zafiriou, Evanghelos; ISR
    Analytic and numerical methods are developed in this paper for the analysis of the quadratic stability of Constrained Model Predictive Control (CMPC). According to the CMPC algorithm, each term of the closed-form of control law corresponding to an active constraint situation can be decomposed to have an uncertainty block, which is time varying over the control period. By analytic method, if a quadratic Lyapunov function can be found for the CMPC closed-loop system with uncertainty blocks in the feedback control law by solving a Riccati type equation, then the control system is quadratic stable. Since no rigorous solving method has been found, this Riccati type equation is solved by a trial-and- error method in this paper. A numerical method that does not solve the Riccati type equation, the Linear Matrix Inequality (LMI) technique, was found useful in solving this quadratic stability problem. Several examples are given to show the CMPC quadratic stability analysis results. It is also noticeable that the quadratic stability implies a similarity to a contraction.
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    The Strong H∞ Performance of Constrained Model Predictive Control
    (1994) Chiou, Hung-Wen; Zafiriou, Evanghelos; ISR
    An off-line performance index for the Constrained Model Predictive Control (CMPC) is defined by the strongly H∞ performance criterion in this paper. From the CMPC algorithm, each term of the closed-form of CMPC control law corresponding to an active constraint situation can be decomposed to have an uncertainty block, which is time varying over the control period. To analyze the strong H∞ performance and quantify the minimum upper bound of L2-induced gain of CMPC system with this type of control law, a numerical method, the Linear Matrix Inequality (LMI) technique, was found useful. Several examples are given to show the results on quantification and analysis of the control system performance.
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    The Closed-Form Control Laws of the Constrained Model Predictive Control Algorithm
    (1993) Chiou, Hung-Wen; Zafiriou, Evanghelos; ISR
    The Analysis of quadratic Stability and strongly Hperformance of Model Predictive Control (MPC) with hard constraints (or called Constrained Model Predictive Control (CMPC)) can be accomplished by reformulating the hard constraints of CMPC. From the CMPC algorithm, each term of the closed-form of CMPC control law corresponding to an active constraint situation can be decomposed to have an uncertainty block, which is time varying over the control period. The control law also contains a bias from the bounds of the constraints which cause difficulty in stability and performance analysis. An alternative way to avoid this difficulty is to reformulate the hard constraints to adjustable constraints with time varying adjustable weights on the adjustable variables added to the on-line objective function. The time varying weights in the adjustable constraint control law make the control action just the same as the hard constrained control. Theoretical derivatives and examples are given. The same reformulation is applied to the softened constraint cases.

    On the analysis of the quadratic stability and strongly H performance, the control system for hard constraint control law without bias satisfies the stability and performance criteria if and only if the control system for adjustable constraint control law with time varying adjustable weights satisfies the same criteria. The details will be shown in the technical reports on quadratic stability and strongly Hperformance analysis, which are in preparation.

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    Frequency Domain Design of Robustly Stable Constrained Model Predictive Controllers
    (1993) Chiou, Hung-Wen; Zafiriou, Evanghelos; ISR
    The robust stability analysis of Constrained Model Predictive Control (CMPC) for linear time invariant and openloop stable processes is the main topic of this paper. Based on the CMPC algorithm, the feedback controller is a piecewise linear operator because of the constraints. This piecewise linear operator can be thought of as an array of linear feedback controllers in parallel, handling different types of predicted active constraint situations. Each term in the linear operator corresponding to the predicted active constraint situation can be decomposed to have an uncertainty block. Hence, the linear operator can be written as a linear closed-form with uncertainty block inside. According to the linear robust stability analysis method, the robust stability of CMPC can be analyzed and the computer aided off-line tuning for the stability of CMPC can also be developed by solving a minimum maximum problem based on the stability analysis method. Some examples are given to show the feasibility of the analysis and tuning methods.