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.     

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.     

FPGA based QDMC control for reverse-osmosis water desalination system

Model-based predictive control (MPC) is a widely used advanced control algorithm in process industries, such as chemical plants and oil refineries. Quadratic dynamic matrix control (QDMC) is one of the popular MPC strategies. In this paper, the QDMC controller is used to control a simulated reverse-osmosis (RO) water desalination system with spiral wound element (SWM). A cascaded control system was designed with the QDMC controller and a PID controller for the desalination process, where the QDMC controller optimizes the set point of the PID controller and directly controls one output. In order to make the implementation more convenient, this paper also studies the implementation of QDMC control system based on a field programmable gate array (FPGA) chip. A support software is developed to help engineers adjust the parameters of the QDMC controller. Since the QDMC controller is implemented in an embedded system, the overall system cost is reduced, which is helpful to the application of RO desalination system.     

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.     

Feasible path optimization with sequential modular simulators

Optimization of large process simulations has typically been inefficient because many time-consuming flowsheet evaluations are usually required. Here we present three optimization methods based on the efficient successive quadratic programming (SQP) algorithm of nonlinear programming. Quadratic/Linear Approximation Programming (Q/LAP) and the Reduced and Complete Feasible Variant (RFV and CFV) algorithms perform efficiently and interface easily with most current sequential modular simulators. Two simple flash problem studies illustrate the mechanics of these algorithms and demonstrate their rapid performance. These results also help in formulating heuristics for the specification of algorithmic tuning parameters.     

Model based control of a high purity distillation column

In this paper, the problem of dual product composition control of an industrial high purity distillation column, a deisohexanizer (DIH), is addressed using a Generic Model Control framework. A dynamic simulation of the DIH was performed for preliminary studies of the performance of different controller strategies/algorithms. The performance of Generic Model Control incorporating different process models was studied. Process models are presented ranging from simple first order approximations to mechanistic short cut distillation models where a tradeoff between model complexity and model adaptivity is investigated. The different controllers were implemented and compared using a dynamic simulation of an industrial deisohexanizer (DIH) to select the best condidate controller. A controller using a nonlinear process model emerged as the best controller and was implemented on the actual process, resulting in improved performance over the original controller. Simulation results and industrial plant data are presented.     

Industrial Trials of Paste Drying in Spouted Beds Under QDMC

Abstract

Spouted bed has been extensively investigated by many authors for years, but the issue of controlling its operation still remains in basic developing stages. The present work consists of the application of an advanced control strategy (QDMC—Quadratic Dynamic Matrix Control) to automate the operation of a large-scale spouted bed dryer. The work on control strategies for spouted bed was motivated by the lack of references on this subject and the encouraging results obtained by Corrêa et al. (Corrêa, N.A.; Freire, J.T.; Corrêa, R.G. Improving operability of spouted beds using a simple optimizing control structure. Brazilian Journal of Chemical Engineering 1999 16 (4), 359–368; Corrêa N.A. Corrêa, R.G.; Freire, J.T. Adaptive control of paste drying in spouted bed using the GPC algorithm. Brazilian Journal of Chemical Engineering 2000 17 (4–7), 639–648; Corrêa, N.A.; Corrêa, R.G.; Freire, J.T. Self-tuning control of egg drying in spouted bed using the GPC algorithm. Drying Technology 2002 20 (4), 813–828.) for a laboratory-scale apparatus. The industrial-scale spouted bed dryer has a height of 4 m and a diameter of 66 cm. The same configuration of data acquisition unit, sensors, and interface developed for the laboratory-scale unit was employed. The dryer is capable of processing up to 20 L/h of pasty material. The powder moisture content (Ys), inferred from measurements of temperature at the exhaustion of the bed bulk, and the powder production rate (Pr), measured on-line by an electronic balance, are the controlled variables. The manipulated variables are: the paste inflow rate (W), regulated by an automatic pump, and the electrical power supply for air heating (P), regulated by a thyristor. The bed pressure drop, the airflow rate, and the information from the environment are monitored by means of an interfaced microcomputer. Experimental runs of drying up to 400 kg/day of an Al₂O₃ 10% aqueous suspension were carried out. The results showed that the QDMC control is robust with respect to the main variables involved and is efficient in maintaining the operation of the bed under the constraints of the system. The major aim concerning the scale-up of spouted bed, which is the determination of the minimum amount of energy required to ensure spout stability, was accomplished by the constrained control strategy.     

RELATIVE ORDER REDUCTION OF MULTIVARIABLE NONLINEAR PROCESSES FOR GENERIC MODEL CONTROL (GMC)

To be implemented within Generic Model Control, a process model must have a relative order of one. When systems have relative orders greater than one (“high relative order systems”) techniques are required to enable model based control to take place. In this paper, a relative order model reduction algorithm is presented, which reduces high relative order models to relative order one. The reduction algorithm is based on the singular perturbation model reduction method. The reduction method conserves some of the important linear qualities of the system, making implementation of the model within a nonlinear model based controller such as GMC attractive.     

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.     

Extended kalman filter‐based nonlinear model predictive control of a continuous KCl‐NaCl crystallizer

An extended Kalman filter (EKF)‐based nonlinear quadratic dynamic matrix control (EQDMC) for an evaporative cooling draft‐tube baffled (DTB) KCl crystallizer is developed. The controller is used to maintain the productivity, crystal mean size and impurity of crystals. Since these controlled variables are not directly measurable, the EKF is used to estimate them. The nonlinear controller is a combination of an extended linear dynamic matrix control (EDMC) and the quadratic dynamic matrix control (QDMC). This combination provided good control of the system despite the process nonlinearity, constraints, and inadequate reliable online measurement of the controlled variables. The performance of the controller in the presence of plant/model mismatch, disturbance, wrong estimation and simultaneous step changes in the controller setpoints is discussed.     

一种约束一般模型控制新方法

在引入近似预测模型的基础上 ,应用基于二次规划的滚动优化算法 ,处理被控量、操作量及其变化速率的线性约束 .将此优化算法与经典的一般模型控制 (GMC)方法相结合 ,给出了一种基于二次规划的约束一般模型控制新方法 .     

PROCESS/MODEL MISMATCH COMPENSATION FOR MODEL-BASED CONTROLLERS

Process model-based control algorithms that employ a process model directly in the controller, have been shown to produce good control performance and robust behaviour, despite process modelling errors. However, when the process/model mismatch is large, the closed-loop response, while still being better than responses obtained by conventional controllers, will be degraded. This paper presents a new approach to compensate for process/model mismatch errors, and is based upon the Generic Model Control (GMC) algorithm. This approach is applicable to both linear and nonlinear model-based algorithms. Simulation results are presented to illustrate the efficiency of the approach     

近红外光谱技术在中药质量控制应用中的化学计量学建模:综述和展望

近红外光谱(NIR)是制药工业领域应用最为广泛的过程分析技术(PAT),在中药产品质量的在线实时检测和控制中越来越受到重视。和化学药相比,由于中药组成的复杂性和生产加工过程的特殊性,对利用化学计量学建立NIR预测模型,提出了新的挑战。本文对NIR在中药质量控制应用中的化学计量学建模方法和技术进行了综述并对未来发展做了展望。综述涉及到NIR数据的采集、预处理、分组,特征波段自动选取,建模以及模型的验证和评价。讨论了平滑、导数、标准化算法、数据增强算法和主元分析等预处理方法对模型影响。特征波段的选取述及间隔偏最小二乘、遗传算法、无信息变量消除、随机蛙跳法、竞争自适应重加权采样和重要变量投影法等;建模方法论及线性和非线性技术包括主元回归、偏最小二乘回归、人工神经网络和支持向量机回归等。未来的NIR建模平台应该是一个在后台集成各种复杂的数学算法和实现数据的无缝共享,面向用户的前台则是友好、简单、智能的半自动界面环境。论述结合具体的实例进行。     

OPTIMAL TEMPERATURE CONTROL IN A BATCH POLYMERIZATION REACTOR USING NONLINEAR GENERALIZED PREDICTIVE CONTROL

The application of Non-Linear Generalized Predictive Control (NLGPC) to the free radical solution polymerization of styrene in a jacketed batch reactor has been realized. The dynamic behavior of polymerization reactor is modelled and simulated for control purposes. The optimal temperature policies for minimum time, desired conversion and molecular chain length were obtained at different initiator concentrations by applying the optimal control theory which is based on the Hamiltonian principle. The polynomial Nonlinear auto Regressive Integrated Moving Average with external input (NARIMAX) model is used to relate the reactor temperature with heat input for nonlinear control algorithm. The linear (ARIMAX) and nonlinear (NARIMAX) models are utilized in the GPC algorithm for comparison. A Pseudo Random Binary Sequence (PRBS) signal was employed to operate the system. The model parameters are evaluated by using Levenberg Marquart Method. The NLGPC, Linear Generalized Predictive Control (LGPC) and standard PID controllers are applied experimentally to the polymerization reactor by using on-line computer control system. The performance of NLGPC control system was compared with LGPC and standard PID controller. It is concluded that the NLGPC control gives much better performance than the other.     

MULTIVARIABLE PROCESS IDENTIFICATION AND CONTROL OF CONTINUOUS FLUIDIZED BED DRYERS

Dynamic models that rigorously describe fluidized bed dryers based on the fundamental principles of the process are usually so complex to be employed in control system design. To obtain simple reduced-order models for such systems, a sequence of step changes in the manipulated and load variables is introduced into the rigorous model. The obtained input-output dynamic response data are used for off-line model identification. Different types of linear models are generated, which are shown to be adequately representing the fluidized bed drying dynamics. The derived models are useful to develop model-based control algorithms such as Internal Model Control (IMC) and Model Predictive Control (MPC). Performance and robustness properties of these controllers are analyzed. Simulation results demonstrate a good performance in terms of tracking and load rejection capabilities.     

Learning control of fermentation process with an improved DHP algorithm☆

Control of the fed-batch ethanol fermentation processes to produce maximum product ethanol is one of the key issues in the bioreactor system. However, ethanol fermentation processes exhibit complex behavior and nonlinear dynamics with respect to the cel mass, substrate, feed-rate, etc. An improved dual heuristic program-ming algorithm based on the least squares temporal difference with gradient correction (LSTDC) algorithm (LSTDC-DHP) is proposed to solve the learning control problem of a fed-batch ethanol fermentation process. As a new algorithm of adaptive critic designs, LSTDC-DHP is used to realize online learning control of chemical dynamical plants, where LSTDC is commonly employed to approximate the value functions. Application of the LSTDC-DHP algorithm to ethanol fermentation process can realize efficient online learning control in continuous spaces. Simulation results demonstrate the effectiveness of LSTDC-DHP, and show that LSTDC-DHP can obtain the near-optimal feed rate trajectory faster than other-based algorithms.     

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.     

Extended Linear QDMC of a Gibbsite Crystalliser: A Simulation Study

An extended linear quadratic dynamic matrix control (EQDMC) of a gibbsite crystallisation system is presented. The process model of the crystalliser is based on the conservation principles of mass and population balances, and kinetic relations including nucleation, growth, and agglomeration correlations. It is shown that the process is non‐linear with constraints and possesses interaction among its process variables. Practical concerns in crysallisation plants such as low flow rates and high magma densities that may lead to solids deposition and eventual line blocking are considered as the system's constraints. The controller is developed by combining extended linear dynamic matrix control (EDMC) and quadratic dynamic matrix control (QDMC) algorithms. Two types of control outputs are considered: controlled and associated variables. The capability of the controller in bringing the controlled variables to their setpoints while maintaining all process constraints within their limits is demonstrated via simulation. It is shown that increasing prediction horizon improves the control performance.     

IDENTIFICATION AND NON LINEAR POLE PLACEMENT SELF TUNING PID CONTROL OF A JACKETED WELL MIXED REACTOR

This paper describes the application of Non Linear Self Tuning PID (NLSTPID) system with the intention of controlling the temperature of a cooling jacketed polymer reactor containing toluene and styrene mixture. The use of polynomial Nonlinear AutoRegressive Moving Average with eXternal input (NARMAX) model related with tank temperature and heat input for nonlinear control was emphasised. The first part of the paper presents an identification algorithm for the construction of polynomial NARMAX and AutoRegressive Moving Average with external input (ARMAX) models. A Pseudo Random Binary Sequence (P.R.B.S) signal was utilised as a forcing function in order to determine the parameters of the models. Levenberg Marquardt algorithm was used to estimate the relevant parameters of NARMAX model. Similar work was carried out for ARMAX model using Bierman, Kalman and Least Square Estimation algorithms. The time response of the tank temperature obtained from computer simulation, identified models and experimental data to a unit step change in manipulated variable were compared. Next, linear and non linear models were used with STPID algorithm to demonstrate the performance of the available control in response to disturbances. All theoretical works were compared with experimental data.