QUADRATIC PROGRAMMING SOLUTION OF DYNAMIC MATRIX CONTROL (QDMC)

QDMC is an improved version of Shell's Dynamic Matrix Control (DMC) multivariable algorithm which provides a direct and efficient method for handling process constraints. The algorithm utilizes a quadratic program to compute moves on process manipulated variables which keep controlled variables close to their targets while preventing violations of process constraints. Several on-line applications have demonstrated its excellent constraint handling properties, transparent tuning and robustness, while requiring minimal on-line computational load.     

Modified dynamic matrix control

DMC (Dynamic Matrix Control) has been used successfully in industry for the last decade. It can deal with constraints and unusual dynamic behavior directly. It also shows a good control performance for the servo problem. Relatively, it can’t reject disturbances systematically. We propose a modified DMC method to control the regulatory process more efficiently. The proposed DMC method makes the control output by subtracting the estimated disturbance from the control output of the original DMC. Here, the disturbance is estimated by a new disturbance estimator. It shows better control performances than the original DMC.     

Integrating process and controller models for the design of self-optimizing control

The steady-state behavior of an existing plant depends on the independent input variables, process equipment and process controllers. This paper presents a method for formulating models that represent the effects of controllers when they are included within a steady-state process flowsheet. The method replaces the controller equations with the equivalent stationarity conditions representing the relationship between the controlled variables and the implemented manipulated variables at steady state. The method is demonstrated for the centralized multivariable Dynamic Matrix Control algorithm applied to two processes, binary distillation and gasoline blending. The integrated process and control system simulation is used to design controllers that improve the profitability of processes without extensive real-time calculations; this is sometimes termed self-optimizing control. For both processes, controllers were designed that yielded higher profit than standard control methods and that approached the highest possible profit achieved by frequent real-time optimization.     

Control of a reactor-flasher system

This paper presents a case study in which several multivariable control strategies were tested for a reactor-flasher system of an industrial chemical process. This reactor-flasher system which has three manipulated variables and three controlled variables is open loop unstable. Since the system variables interact severely, controlling the system is very difficult with the traditional PID control. We examined various control strategies such as multiloop single variable control, modified single variable control with compensators, and PI control combined with Linear Quadratic Regulator (LQR), Linear Quadratic Gaussian(LQG)/Loop Transfer Recovery(LTR) and Dynamic Matrix Control (DMC) combined with LQR. DMC combined with LQR showed better control performance than the others while remaining robust in the face of modeling errors.     

A MODEL-BASED DIRECT ADAPTIVE PI CONTROLLER FOR NONLINEAR PROCESS CONTROL

This article proposes a model-based direct adaptive proportional-integral (PI) controller for a class of nonlinear processes whose nominal model is input-output linearizable but may not be accurate enough to represent the actual process. The proposed direct adaptive PI controller is composed of two parts: the first is a linearizing feedback control law that is synthesized directly based on the process's nominal model and the second is an adaptive PI controller used to compensate for the model errors. An effective parameter-tuning algorithm is devised such that the proposed direct adaptive PI controller is able to achieve stable and robust control performance under uncertainties. To show the robust stability and performance of the direct adaptive PI control system, a rigorous analysis involving the use of a Lyapunov-based approach is presented. The effectiveness and applicability of the proposed PI control strategy are demonstrated by considering the time-dependent temperature trajectory tracking control of a batch reactor in the presence of plant/model mismatch, unanticipated periodic disturbances, and measurement noises. Furthermore, for use in an environment that lacks full-state measurements, the integration of a sliding observer with the proposed control scheme is suggested and investigated. Extensive simulation results reveal that the proposed model-based direct adaptive PI control strategy enables a highly nonlinear process to achieve robust control performance despite the existence of plant/model mismatch and diversified process uncertainties.     

Observer based nonlinear quadratic dynamic matrix control for state space and input/output models

An observer based nonlinear Quadratic Dynamic Matrix Control (QDMC) algorithm is developed for use with nonlinear input-output (I/O) and state space models. It generalizes and extends previously published nonlinear QDMC algorithms. The extension to I/O models is particularly important due to the increased use of neural networks and other types of nonlinear black box models in the chemical industry. Disturbance rejection and offset free tracking is addressed in a general setting utilizing concepts from filtering theory. Various kinds of disturbance models can be incorporated in the formulation. Even though nonlinear models are utilized for model prediction, the on-line optimization is formulated as a single Quadratic Program, thus preserving the computational advantages of nonlinear QDMC as compared to Model Predictive Control algorithms based on nonlinear programming techniques. The examples illustrate parameter tuning for open-loop unstable and stable processes and point out both benefits and shortcomings of the algorithm.     

PARAMETER IDENTIFICATION AND RELATED PROBLEMS FOR THE DYNAMIC MATRIX CONTROL MODEL

The parameter identification and related problems for the Dynamic Matrix Control model are studied in this work. A recursive algorithm is employed, and a modified version of it equipped with a useful stopping rule is proposed. The probabilistic approach is taken and the stochastic aspects of the problem is emphasized. It is demonstrated that the algorithm is consistent and possesses certain nice properties. The parameter set reduction problem has also been addressed thoroughly. By using the Kolmogorov-Smirnov statistic, a systematic procedure of hypothesis testing is developed. Various simulation results are demonstrated.     

Characteristic equations and robust stability of a simplified predictive control algorithm

In predictive control, control calculations are done such that the difference between the desired and the predicted response of the process is minimized. The number of points on the prediction horizon at which the error is minimized and the number of future control moves considered affect the on-line computational effort involved in the solution of the constrained optimization problem. Earlier papers have shown that the control performance obtained using the DMC algorithm can also be obtained by using a simplified algorithm where the error is minimized at one point and one future control move is calculated. Because of its computational advantages, the simplified algorithm is analyzed further in this paper. Its transfer function is compared with the transfer function of the DMC algorithm. Characteristic equations to select tuning parameters are presented. The paper also compares the robust stability of the simplified and the DMC algorithms on SISO and MIMO process models. The results provide additional support to the viability of the simplified algorithm and thus indicate that it is possible for some processes to benefit from predictive control with only modest computational resources.     

Generic model control — A case study revisited

The application of the Generic Model Control (GMC) algorithm to the control of an evaporator has been reported recently by Lee et al. (1989). The results of their case study are claimed to demonstrate the superiority of the nonlinear GMC algorithm over conventional techniques including Dynamic Matrix Control. In this note it is shown that for the evaporator example the improved performance arises primarily from the full multivariable and feedforward nature of the control law, rather than from the nonlinear nature of GMC.     

Parametric and nonparametric model based control of a packed distillation column

Parametric and nonparametric model based control systems were applied to control the overhead temperature of a packed distillation column separating methanol–water mixture. Experimental and theoretical studies have been done to observe the efficiency and performance of both control systems. Generalized predictive control (GPC) system based on a parametric model has been tried to keep the overhead temperature at the desired set point. First, a parametric model which is controlled auto regressive integrated moving average (CARIMA) was developed and then the parameters of this model were identified by applying pseudo random binary sequence (PRBS) and using Bierman algorithm. After that this model was used to design the GPC system. Tuning parameters of the GPC system have been calculated using the simulation program of the packed distillation column. Using the predicted parameters, experimental and theoretical GPC systems were found very effective in controlling the overhead temperature. Dynamic matrix control (DMC) system based on a nonparametric model has been used to track the overhead temperature of the packed distillation column. For this purpose, a nonparametric model known as the dynamic matrix was determined using the reaction curve method. A step change in heat input to the reboiler was applied to the manipulated variable and the temperature of the overhead product was observed. After that, the dynamic matrix was used to design the DMC system. Several calculations have been done to define the DMC control parameters. The best values of the tuning parameter were used to realize the DMC system for controlling the overhead temperature experimentally and theoretically. In the presence of some disturbances, the DMC system gives oscillation and offset in experimental studies.     

Model predictive control for the reactant concentration control of a reactor

The reactant concentration control of a reactor using Model Predictive Control (MPC) is presented in this paper. Two major difficulties in the control of reactant concentration are that the measurement of concentration is not available for the control point of view and it is not possible to control the concentration without considering the reactor temperature. Therefore, MIMO control techniques and state and parameter estimation are needed. One of the MIMO control techniques widely studied recently is MPC. The basic concept of MPC is that it computes a control trajectory for a whole horizon time minimising a cost function of a plant subject to a dynamic plant model and an end point constraint. However, only the initial value of controls is then applied. Feedback is incorporated by using the measurements/estimates to reconstruct the calculation for the next time step. Since MPC is a model based controller, it requires the measurement of the states of an appropriate process model. However, in most industrial processes, the state variables are not all measurable. Therefore, an extended Kalman filter (EKF), one of estimation techniques, is also utilised to estimate unknown/uncertain parameters of the system. Simulation results have demonstrated that without the reactor temperature constraint, the MPC with EKF can control the reactant concentration at a desired set point but the reactor temperator is raised over a maximum allowable value. On the other hand, when the maximun allowable value is added as a constraint, the MPC with EKF can control the reactant concentration at the desired set point with less drastic control action and within the reactor temperature constraint. This shows that the MPC with EKF is applicable to control the reactant concentration of chemical reactors.     

Process control: An overview and personal perspective

This paper presents an overview and personnal perspective on recent developments and current practice in computer process model. The basic concepts behind conventional process control are reviewed to provide a starting point for the non-control specialist and process engineer. The ensuing sections on Internal Model Control (IMC), Model Predictive Control (MPC) and adaptive control illustrate the evolution of control technology from the traditional multiloop strategies to the modern, multivariable, model-based, computer control systems now being used in industry. The paper does not provide a complete, critical review of process control. However, the discussion and the recommended references should provide a good starting point for anyone wanting to become familiar with current practice and some of the new directions of process control.     

Model predictive control for multivariable unstable processes with constraints on manipulated variables

The original MPC(Model Predictive Control) algorithm cannot be applied to open loop unstable systems, because the step responses of the open loop unstable system never reach steadystates. So when we apply MPC to the open loop unstable systems, first we have to stabilize them by state feedback or output feedback. Then the stabilized systems can be controlled by MPC. But problems such as valve saturation may occur because the manipulated input is the summation of the state feedback output and the MPC output. Therefore, we propose Quadratic Dynamic Matrix Control(QDMC) combined with state feedback as a new method to handle the constraints on manipulated variables for multivariable unstable processes. We applied this control method to a single-input-single-output unstable nonlinear system and a multi-input-multi-output unstable system. The results show that this method is robust and can handle the input constraints explicitly and also its control performance is better than that of others such as well tuned PI control. Linear Quadratic Regulator (LQR) with integral action.     

Predictive Control of a Circulating Fluidized Bed Combustor

The acceptance of CFB combustion in process and utility industries for generating steam has been increasing because of its ability to burn a wide variety of fuels efficiently and in an environmentally acceptable manner. Work on control of this emerging technology is beginning to appear. This paper evaluates the performance of two predictive control algorithms (the Dynamic Matrix Control and a simplified version) for control of temperature and pressure drop in a pilot scale CFB combustor. The robustness of the algorithms is studied on a model of the CFB combustor. The experimental and simulation results show the suitability of the two control algorithms for control of the CFB combustor.     

基于动态矩阵控制的比值控制新算法

在Hagglund的调和比值控制（Blend Station）算法的基础上,提出一种基于动态矩阵控制（DynamicMatrix Control,DMC）的比值控制新算法。给出该算法的详细推导过程,并通过多个仿真实例将该算法的控制效果与固定比值控制、基于PI的自适应比值控制效果进行比较,仿真结果证实了该算法的有效性。     

COMPARISON AMONG PI,DMC, QDMC,AND GPC ALGORITHMS IN THE CONTROL OF THE SPOUTED BED DRYER

This article presents comparative analysis between the classical PI (proportional-integral control) and MPC (model predictive control) techniques for a drying process on spouted beds. The on-line experimental setups were carried out in a laboratory-scale plant of a spouted bed dryer. The main objective was to optimize the plant operation by searching for the best control structure to be used in future scale enlargement. The major drawbacks encountered in this kind of system were high interactivity among variables, a malfunction as a result of calculated variables out of the operational window, and modeling mismatch. Despite the robustness of the operational PI, the control actions of this strategy did not overcome the variable interactions. The DMC (dynamic matrix control) and the QDMC (quadratic dynamic matrix control) algorithms performed satisfactorily over the major drawbacks. Special attention was given to the latter algorithm due to its ability to hold the variables under constrained oscillations. However, the best results were found for the adaptive GPC (generalized predictive control) algorithm whose actions prevailed over the modeling mismatch due to the strong nonlinear behavior intrinsic to the process. The main goal of the present work is to describe a procedure that can be standardized for other types of dryers and different scales. This is especially the case for the adaptive GPC, whose control structure is independent of the dryer nature and scale and whose implementation does not require previous identification procedures (self-tuning) and/or structural changes.     

COMPARISON AMONG PI, DMC, QDMC, AND GPC ALGORITHMS IN THE CONTROL OF THE SPOUTED BED DRYER

This article presents comparative analysis between the classical PI (proportional-integral control) and MPC (model predictive control) techniques for a drying process on spouted beds. The on-line experimental setups were carried out in a laboratory-scale plant of a spouted bed dryer. The main objective was to optimize the plant operation by searching for the best control structure to be used in future scale enlargement. The major drawbacks encountered in this kind of system were high interactivity among variables, a malfunction as a result of calculated variables out of the operational window, and modeling mismatch. Despite the robustness of the operational PI, the control actions of this strategy did not overcome the variable interactions. The DMC (dynamic matrix control) and the QDMC (quadratic dynamic matrix control) algorithms performed satisfactorily over the major drawbacks. Special attention was given to the latter algorithm due to its ability to hold the variables under constrained oscillations. However, the best results were found for the adaptive GPC (generalized predictive control) algorithm whose actions prevailed over the modeling mismatch due to the strong nonlinear behavior intrinsic to the process. The main goal of the present work is to describe a procedure that can be standardized for other types of dryers and different scales. This is especially the case for the adaptive GPC, whose control structure is independent of the dryer nature and scale and whose implementation does not require previous identification procedures (self-tuning) and/or structural changes.     

Model predictive control for multivariable unstable processes with constraints on manipulated variables

The original MPC(Model Predictive Control) algorithm cannot be applied to open loop unstable systems, because the step responses of the open loop unstable system never reach steady states. So when we apply MPC to the open loop unstable systems, first we have to stabilize them by state feedback or output feedback. Then the stabilized systems can be controlled by MPC. But problems such as valve saturation may occur because the manipulated input is the summation of the state feedback output and the MPC output. Therefore, we propose Quadratic Dynamic Matrix Control(QDMC) combined with state feedback as a new method to handle the constraints on manipulated variables for multivariable unstable processes. We applied this control method to a single-input-single-output unstable nonlinear system and a multi-input-multi-output unstable system. The results show that this method is robust and can handle the input constraints explicitly and also its control performance is better than that of others such as well tuned PI control. Linear Quadratic Regulator (LQR) with integral action.     

BATCH-TO-BATCH OPTIMAL CONTROL OF BATCH PROCESSES BASED ON RECURSIVELY UPDATED NONLINEAR PARTIAL LEAST SQUARES MODELS

A batch-to-batch optimal control approach for batch processes based on batch-wise updated nonlinear partial least squares (NLPLS) models is presented in this article. To overcome the difficulty in developing mechanistic models for batch/semi-batch processes, a NLPLS model is developed to predict the final product quality from the batch control profile. Mismatch between the NLPLS model and the actual plant often exists due to low-quality training data or variations in process operating conditions. Thus, the optimal control profile calculated from a fixed NLPLS model may not be optimal when applied to the actual plant. To address this problem, a recursive nonlinear PLS (RNPLS) algorithm is proposed to update the NLPLS model using the information newly obtained after each batch run. The proposed algorithm is computationally efficient in that it updates the model using the current model parameters and data from the current batch. Then the new optimal control profile is recalculated from the updated model and implemented on the next batch. The procedure is repeated from batch to batch and, usually after several batches, the control profile will converge to the optimal one. The effectiveness of this method is demonstrated on a simulated batch polymerization process. Simulation results show that the proposed method achieves good performance, and the optimization with the proposed NLPLS model is more effective and stable than that with a batch-wise updated linear PLS model.     

BATCH-TO-BATCH OPTIMAL CONTROL OF BATCH PROCESSES BASED ON RECURSIVELY UPDATED NONLINEAR PARTIAL LEAST SQUARES MODELS

A batch-to-batch optimal control approach for batch processes based on batch-wise updated nonlinear partial least squares (NLPLS) models is presented in this article. To overcome the difficulty in developing mechanistic models for batch/semi-batch processes, a NLPLS model is developed to predict the final product quality from the batch control profile. Mismatch between the NLPLS model and the actual plant often exists due to low-quality training data or variations in process operating conditions. Thus, the optimal control profile calculated from a fixed NLPLS model may not be optimal when applied to the actual plant. To address this problem, a recursive nonlinear PLS (RNPLS) algorithm is proposed to update the NLPLS model using the information newly obtained after each batch run. The proposed algorithm is computationally efficient in that it updates the model using the current model parameters and data from the current batch. Then the new optimal control profile is recalculated from the updated model and implemented on the next batch. The procedure is repeated from batch to batch and, usually after several batches, the control profile will converge to the optimal one. The effectiveness of this method is demonstrated on a simulated batch polymerization process. Simulation results show that the proposed method achieves good performance, and the optimization with the proposed NLPLS model is more effective and stable than that with a batch-wise updated linear PLS model.