### Browsing by Author "Zafiriou, Evanghelos"

###### Results Per Page

###### Sort Options

Item The Closed-Form Control Laws of the Constrained Model Predictive Control Algorithm(1993) Chiou, Hung-Wen; Zafiriou, Evanghelos; ISRThe Analysis of quadratic Stability and strongly Hperformance 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 Hperformance analysis, which are in preparation.

Item Design of Resilient Processing Plants. New Characterization of the Effect of RHP Zeros.(1987) Morari, Manfred; Zafiriou, Evanghelos; Holt, Bradley R.; ISRRight Half Plane (RHP) zeros restrict the achievable closed loop performance independent of controller design. A new characterization of all achievable closed loop set-point/output transfer matrices is provided in terms of "zero-directions." The zero directions also give some insight into what forms of partial decoupling are preferable.Item Frequency Domain Design of Robustly Stable Constrained Model Predictive Controllers(1993) Chiou, Hung-Wen; Zafiriou, Evanghelos; ISRThe 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.Item Nonlinear Quadratic Dynamic Matrix Control with State Estimation(1991) Gattu, Gangadhar; Zafiriou, Evanghelos; ISRQuadratic 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."Item Observer Based Nonlinear Quadratic Dynamic Matrix Control for State Space and I/O Models(1994) Gattu, Gangadhar; Zafiriou, Evanghelos; ISRObserver 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.Item On the Quadratic Stability of Constrained Model Predictive Control(1994) Chiou, Hung-Wen; Zafiriou, Evanghelos; ISRAnalytic 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.Item On the Stability of Nonlinear Quadratic Dynamic Matrix Control(1992) Gattu, Gangadhar; Zafiriou, Evanghelos; ISRThe 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.Item An Operator Control Theory Approach to the Design and Tuning of Constrained Model Predictive Controllers.(1989) Zafiriou, Evanghelos; Chiou, Hung-Wen; ISRModel Predictive Control algorithms minimize on-line and at every sampling point an appropriate objective function, subject to the satisfaction of possible hard constraints on the process outputs, inputs or other state variables. The presence of the hard constraints in the on-line optimization problem results in a nonlinear closed-loop system, even though the process dynamics are assumed linear. This paper describes a procedure for analyzing the nominal and robust stability properties of such control laws, by utilizing the Operator Control Theory framework.Item Output Constraint Softening for SISO Model Predictive Control(1993) Zafiriou, Evanghelos; Chiou, Hung-Wen; ISRThe 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.Item Robust Optimal Input Profile Determination for Semi-Batch Processes.(1989) Zafiriou, Evanghelos; Bamgbose, Adebola O.; ISRThe input profiles (trajectories) that are implemented during the operation of a semi-batch process are obtained by using the available model of the process. Since modeling error is always present, the performance could be very different when these inputs are applied to the actual plant. This paper examines the problem of determining the optimal input trajectory for semibatch processes in spite of the presence of modeling error, by using information from previous batches to modify the trajectories that are applied to the subsequent ones. The proposed approach does not require the complex remodeling of the process, but instead it redetermines the input profile directly, so that a steady improvement is accomplished from batch to batch.Item Robust Stability of SISO Quadratic Dynamic Matrix Control with Hard Output Constraints(1991) Zafiriou, Evanghelos; Marchal, Andre L.; ISRThe inclusion of output constraints in the on-line optimization problem solved by Quadratic Dynamic Matrix Control (QDMC) can result in a closed-loop unstable system, even when the corresponding unconstrained algorithm is stable. The presence of constraints in the optimization problem produces a nonlinear closed-loop system, although the plant and model dynamics are assumed linear. This paper quantifies the effect of output constraints on both nominal and robust stability for single-input single-output (SISO) processes. Stability conditions are provided which can be used to select the QDMC parameters and constraint window. The ability of these conditions to capture the nonlinear effect of the constraint is illustrated through examples that demonstrate that tuning rules developed for the unconstrained case should not be used with output constraints. an example with deat time error is used to illustrate the use of this framework to guarantee the robustness the robustness of constrained QDMC with respect to modeling error.Item State Estimation Model Based Algorithm for On-line Optimization and Control of Batch Processes(1994) Gattu, Gangadhar; Zafiriou, Evanghelos; ISRBatch/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.Item State Estimation Nonlinear QDMC with Input-Output Models(1993) Gattu, Gangadhar; Zafiriou, Evanghelos; ISRA 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.Item State Estimation Nonlinear QDMC with Input-Output Models(1994) Gattu, Gangadhar; Zafiriou, Evanghelos; ISRA 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.Item The Strong H∞ Performance of Constrained Model Predictive Control(1994) Chiou, Hung-Wen; Zafiriou, Evanghelos; ISRAn 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.Item User's Guide for QDMC Version 1.0 A Set of Fortran Programs for Constrained Quadratic Dynamic Matrix Control Simulation and Stability/Performance Study(1990) Chiou, Hung-Wen; Zafiriou, Evanghelos; ISRQDMC is a set of Fortran programs for constrained Quadratic Dynamic Matrix Control Simulation and property study of the QDMC "equivalent" feedback linear controllers. Based on the time invariant impulse response model and plant, the simulation program minimizes a quadratic objective function subject to hard constraints on manipulated variables and/or on controlled variables. On-line stability conditions are also calculated in this program.There are five programs created for studying the properties of the controller. Program CJI creates QDMC "equivalent" feedback linear controllers as frequency files which depend on the active constraints situation. Program CJINOM is for nominal stability test of these controllers. Program CJISEP is used to separate them into tuning parameter dependent and independent sets. Program PREL is for testing the practical relevance of a set of QDMC active constraints. Program ALLPREL finds all such practically relevant sets.