Institute for Systems Research

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Author: search.filters.author.Zafiriou, EvanghelosSubject: search.filters.subject.optimization

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Now showing 1 - 6 of 6
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    State Estimation Model Based Algorithm for On-line Optimization and Control of Batch Processes
    (1994) Gattu, Gangadhar; Zafiriou, Evanghelos; ISR
    Batch/semi-batch processes are highly nonlinear and involve complex reaction mechanisms. Model-plant mismatch always exists. The lack of rapid direct or indirect measurements of the properties to be controlled makes the control task difficult. It is the usual practice to follow the prespecified setpoint profiles for process variables for which measurements are available, in order to obtain desired product properties. Modeling error can be the cause of bad performance when optimal profiles computed for the model, are implemented on the actual plant. In this paper, a state estimation model based algorithm is presented for on-line modification of the optimal profile and control with the goal of obtaining the desired properties at the minimum batch time. The effectiveness of the algorithm is demonstrated by its application to bulk polymerization of styrene.
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    State Estimation Nonlinear QDMC with Input-Output Models
    (1994) Gattu, Gangadhar; Zafiriou, Evanghelos; ISR
    A State Estimation NLQDMC algorithm is presented for use with nonlinear input-output models. The proposed algorithm extends the state estimation NLQDMC [5] to nonlinear models identified based on input-output information. The algorithm preserves the computational advantages of [5] when compared to the other algorithms based on nonlinear programming techniques. The illustrating example demonstrates the usage of tuning parameters and points out the benefits and shortcomings of the algorithm.
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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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    Nonlinear Quadratic Dynamic Matrix Control with State Estimation
    (1991) Gattu, Gangadhar; Zafiriou, Evanghelos; ISR
    Quadratic Dynamic Matrix Control (QDMC) with state estimation is presented for use with nonlinear process models. This formulation extends Garcia's nonlinear version of QDMC to open- loop unstable nonlinear processes and allows for better disturbance rejection. It also extends Ricker's linear state space formulation with state estimation to nonlinear systems. Stability and better performance is observed when compared to the algorithm without state estimation in rejecting disturbances for processes operating at unstable steady state setpoints, as illustrated with two simple examples. The algorithm requires that only a Quadratic Program be solved on-line. The modest computational requirements make it attractive for industrial implementation. the effectiveness of the approach is demonstrated by its successful application to the temperature control of a semibatch polymerization reactor. A model and related control requirements for this problem were presented at the 1990 AIChE Annual Meeting in a session on "Industrial Challenge Problems in Process Control."