Institute for Systems Research

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Author: search.filters.author.Zafiriou, EvanghelosSubject: search.filters.subject.Chemical Process Systems

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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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    Observer Based Nonlinear Quadratic Dynamic Matrix Control for State Space and I/O Models
    (1994) Gattu, Gangadhar; Zafiriou, Evanghelos; ISR
    Observer based nonlinear QDMC algorithm is presented for use with nonlinear state space and input-output models. The proposed algorithm is an extension of Nonlinear Quadratic Dynamic Matrix Control (NLQDMC) by Garcia (1984) and its extension by Gattu and Zafiriou (1992a). Garcia proposed an extension of linear Quadratic Dynamic Matrix Control (QDMC) to nonlinear processes. Although a nonlinear model is used, only a single Quadratic Program (QP) is solved on-line. Gattu and Zafiriou extended this formulation to open-loop unstable systems, by incorporating a Kalman filter. The requirement of solving only one QP on-line at each sampling time makes this algorithm an attractive option for industrial implementation. This extension of NLQDMC to open-loop unstable systems was ad hoc and did not address the problem of offset free tracking and disturbance rejection in a general state space setting. Independent white noise was added to the model states to handle unstable processes. The approach can stabilize the system but leads to an offset in the presence of persistent disturbances. To obtain offset free tracking Gattu and Zafiriou added a constant disturbance to the predicted output as done in DMC-type algorithms. This addition is ad hoc and does not result from the filtering/prediction theory. The proposed algorithm eliminates the major drawbacks of the algorithm presented by Gattu and Zafiriou and extends that algorithm for nonlinear models identified based on input-output information. An algorithm schematic is presented for measurement delay cases. The algorithm preserves the computational advantages when compared to the other algorithms based on nonlinear programming techniques. The illustrating examples demonstrate the usage of tuning parameters for unstable and stable systems and points out the benefits and short comings of the algorithm.
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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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    State Estimation Nonlinear QDMC with Input-Output Models
    (1993) 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 (Gattu and Zafiriou, 1992a) to nonlinear models identified based on input-output information. The algorithm preserves the computational advantages 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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    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.
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    Output Constraint Softening for SISO Model Predictive Control
    (1993) Zafiriou, Evanghelos; Chiou, Hung-Wen; ISR
    The presence of constraints in the on-line optimization problem solved by model predictive Control algorithms results in a nonlinear control system, even if the plant and model dynamics are linear. This is the case both for physical constraints, like saturation constraints, as well for performance or safety constraints on outputs or other variables of the process. Performance constraints can usually be softened by allowing violation if necessary. This is advisable, as hard constraints can lead to stability problems. The determination of the necessary degree of softening is usually a trial-and-error matter. This paper utilizes a theoretical framework that allows to relate hard as well as soft constraints to closed-loop stability. We focus on the special case of output constraints for single-input single-output systems and develop a non- conservative condition. This condition allows the determination of the appropriate amount of softening either numerically or via a suitable Nyquist plot.
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    On the Stability of Nonlinear Quadratic Dynamic Matrix Control
    (1992) Gattu, Gangadhar; Zafiriou, Evanghelos; ISR
    The extension of Quadratic Dynamic Matrix Control (QDMC) to nonlinear process models is an attractive option for industrial implementation. Although a nonlinear model is utilized, one has to solve only a single Quadratic Program on-line. In this paper, we present the stability properties for the global asymptotic stability of the closed-loop system under NLQDMC law. The conservativeness of these properties is examined by following the steps of the proofs when this algorithm is applied to a simple example. We also demonstrate the application of the nonlinear version of QDMC to processes for which the sign of the system gain changes around the operating point.