A novel tuning strategy for multivariable model predictive control

Model predictive control (MPC) has established itself as the most popular form of advanced multivariable control in the chemical process industry. However, the benefits of this technology cannot be realized unless the controller can be operated with desirable performance for an extended period of time. The objective of this work is to present an easy-to-use and reliable tuning strategy that enables the control practitioner to maintain MPC at peak performance with minimal effort. A novel analytical expression that computes the move suppression coefficients, guidelines to select the additional adjustable parameters, and their demonstration in an overall tuning strategy are some of the significant contributions of this work. The compact form for the analytical expression that computes the move suppression coefficients is derived as a function of a first order plus dead time (FOPDT) model approximation of the process dynamics. With tuning parameters computed. MPC is then implemented in the classical fashion using an internal model formulated from step response coefficients of the actual process. Just as a FOPDT model approximation has proved a valuable tool in tuning rules such as Cohen-Coon. ITAE and IAE for PID implementations, the tuning strategy presented here is significant because it offers an analogous approach for multivariable MPC.     

Distributed multiparametric model predictive control design for a quadruple tank process

Distributed control for plant wide control has received attention lately. In this paper, multiparametric quadratic programming based controllers have been developed for a benchmark quadruple tank problem. A centralized control strategy is developed by partitioning its six dimensional vector space based on constraint satisfaction, stability and optimality. Control design is simplified using its decentralized version after a relative gain array analysis of the benchmark. A cooperative game theory based distributed model predictive controller and decentralized proportional integral (PI) controller are also designed for the same system. A decoupling based cooperative distributed multiparametric model predictive controller (mpMPC) is proposed. The controllers are subjected to reference tracking and disturbance rejection and the performance measures are compared. Also, the robustness of cooperative mpMPC to parameter uncertainties is discussed. Distributed design approach is a natural fit for the vector space partitioning based mpMPC design. Simulations results are analyzed and the performance of the five controllers is discussed.     

DMC技术在聚合反应温度控制中的应用

针对聚乙烯生产装置的关键工艺参数——温度的控制要求，采用具有前馈一反馈结构的预测控制(DMC)方案对温度进行控制，并在DCS上实现，取得令人满意的效果。     

Multi-objective optimization for model predictive control

This paper presents a technique of multi-objective optimization for Model Predictive Control (MPC) where the optimization has three levels of the objective function, in order of priority: handling constraints, maximizing economics, and maintaining control. The greatest weights are assigned dynamically to control or constraint variables that are predicted to be out of their limits. The weights assigned for economics have to out-weigh those assigned for control objectives. Control variables (CV) can be controlled at fixed targets or within one- or two-sided ranges around the targets. Manipulated Variables (MV) can have assigned targets too, which may be predefined values or current actual values. This MV functionality is extremely useful when economic objectives are not defined for some or all the MVs. To achieve this complex operation, handle process outputs predicted to go out of limits, and have a guaranteed solution for any condition, the technique makes use of the priority structure, penalties on slack variables, and redefinition of the constraint and control model. An engineering implementation of this approach is shown in the MPC embedded in an industrial control system. The optimization and control of a distillation column, the standard Shell heavy oil fractionator (HOF) problem, is adequately achieved with this MPC.     

Design of a nuclear reactor controller using a model predictive control method

A model predictive controller is designed to control thermal power in a nuclear reactor. The basic concept of the model predictive control is to solve an optimization problem for finite future time steps at current time, to implement only the first optimal control input among the solved control inputs, and to repeat the procedure at each subsequent instant. A controller design model used for designing the model predictive controller is estimated every time step by applying a recursive parameter estimation algorithm. A 3-dimensional nuclear reactor analysis code, MASTER that was developed by Korea Atomic Energy Research Institute (KAERI), was used to verify the proposed controller for a nuclear reactor. It was known that the nuclear power controlled by the proposed controller well tracks the desired power level and the desired axial power distribution.     

Distributed model predictive control for constrained nonlinear systems with decoupled local dynamics

This paper considers the distributed model predictive control (MPC) of nonlinear large-scale systems with dynamically decoupled subsystems. According to the coupled state in the overall cost function of centralized MPC, the neighbors are confirmed and fixed for each subsystem, and the overall objective function is disassembled into each local optimization. In order to guarantee the closed-loop stability of distributed MPC algorithm, the overall compatibility constraint for centralized MPC algorithm is decomposed into each local controller. The communication between each subsystem and its neighbors is relatively low, only the current states before optimization and the optimized input variables after optimization are being transferred. For each local controller, the quasi-infinite horizon MPC algorithm is adopted, and the global closed-loop system is proven to be exponentially stable.     

Properties of extended predictive control

Many tuning strategies for model predictive control algorithms have been proposed in the literature depending on the conditionality of the system matrix and the choice of its cost function. In this paper, the properties of a new predictive controller termed extended predictive control (EPC) are investigated and presented. These properties are important to the understanding of the unique tuning strategy of EPC. EPC is based on the assumption of infinite horizon which is preferable to guarantee stability. The EPC properties are derived using a second order plant with relatively large dead time and is applicable to any open-loop stable system. The tuning strategy of EPC was applied to generalized predictive control with good results.     

Output feedback model predictive control of hydraulic systems with disturbances compensation

Enhancing the robustness of output feedback control has always been an important issue in hydraulic servo systems. In this paper, an output feedback model predictive controller (MPC) with the integration of an extended state observer (ESO) is proposed for hydraulic systems. The ESO was designed to estimate not only the unmeasured system states but also the disturbances, which will be synthesized into the design of the output prediction equation. Based on the mechanism of receding horizon and repeating optimization of MPC, the output prediction equation will be updated in real time and the future behavior of the system will be accurately predicted since the disturbances are compensated effectively. Hence, the ability of the traditional MPC to suppress disturbances will be improved evidently. The experiment results show that the proposed controller has high-performance nature and strong robustness against various model uncertainties, which verifies the effectiveness of the proposed control strategy.     

不可靠WSN时钟同步网络化输出反馈MPC量化分析

在Cyber-Physical环境下,时钟同步双向信息交换过程中,包含时钟信息的数据包丢失将对时钟同步性能产生影响。讨论了现代控制理论状态空间模型的输出反馈Tubes-MPC时钟同步方法。由分离原理,设计了本地化的状态估计器与控制器,实现了输出反馈Tubes-MPC时钟同步的指数稳定。以不完全量测下的观测模型为基础,定量分析了统计意义下的同步误差方差上界与下界,并采用MPC中Set-Theory-in-Control方法,将完全量测下的干扰误差集合运算于由丢包所引入的附加的估计误差集合,建立了集合约束下的模型预测优化模型。已构建的统一框架下的输出反馈Tubes-MPC时钟同步系统化方法,综合考量了控制理论在线计算复杂度与网络控制观点应用的可行性,对无线网络的不可靠性、网络规模、收敛性能具有鲁棒性,进一步容易扩展为网络级绝对时钟状态空间模型。     

A neural network model based predictive control approach: application to a semi-batch reactor

Neural networks can be considered to be new modelling tools in process control and especially in non-linear dynamical systems cases. Their ability to approximate non-linear functions has been very often demonstrated and tested by simulation and experimental studies. In this paper, a predictive control strategy of a semi-batch reactor based on neural network models is proposed. Results of a non-linear control of the reactant temperature of a semi-batch reactor are presented. The process identification is composed of an off-line phase that consists in training the network, and of an on-line phase that corresponds to the neural model adaptation so that it fits any modification of the process dynamics. Experimental results when using this method to control a semi-batch reactor are reported and show the great potential of this strategy in controlling non-linear processes.     

多变量DMC预测控制在MGT-CCHP系统中应用

MGT-CCHP系统可以减少温室气体排放,具有节能、环保和高安全性等优势,是提供清洁、可靠、高质量、多用途的小型分布式能源的最佳方式之一。将MGT-CCHP系统作为研究对象,通过多变量动态矩阵(DMC)进行预测控制,结合S函数,用Simulink仿真模型,合理选取控制参数,可有效地控制MGT-CCHP模型,较快地跟踪期望值,达到预期的控制效果。     

多变量非自衡系统的预测控制研究

该文研究了多变量非自衡对象的特点及控制问题，推导了一种适用于非自衡系统的多变量预测控制算法，通过对环境试验设备温度湿度控制系统的仿真实验，证实了此算法的有效性和实用性。     

基于不同建模周期的多变量预测控制研究

文中对各通道特性差异比较大的多变量系统采用了不同建模周期的预测建模方法及预测控制算法，并给出了算法推导和仿真实例。     

Parameterized data-driven fuzzy model based optimal control of a semi-batch reactor

A parameterized data-driven fuzzy (PDDF) model structure is proposed for semi-batch processes, and its application for optimal control is illustrated. The orthonormally parameterized input trajectories, initial states and process parameters are the inputs to the model, which predicts the output trajectories in terms of Fourier coefficients. Fuzzy rules are formulated based on the signs of a linear data-driven model, while the defuzzification step incorporates a linear regression model to shift the domain from input to output domain. The fuzzy model is employed to formulate an optimal control problem for single rate as well as multi-rate systems. Simulation study on a multivariable semi-batch reactor system reveals that the proposed PDDF modeling approach is capable of capturing the nonlinear and time-varying behavior inherent in the semi-batch system fairly accurately, and the results of operating trajectory optimization using the proposed model are found to be comparable to the results obtained using the exact first principles model, and are also found to be comparable to or better than parameterized data-driven artificial neural network model based optimization results.     

T–S fuzzy model predictive speed control of electrical vehicles

This paper proposes a novel nonlinear model predictive controller (MPC) in terms of linear matrix inequalities (LMIs). The proposed MPC is based on Takagi–Sugeno (TS) fuzzy model, a non-parallel distributed compensation (non-PDC) fuzzy controller and a non-quadratic Lyapunov function (NQLF). Utilizing the non-PDC controller together with the Lyapunov theorem guarantees the stabilization issue of this MPC. In this approach, at each sampling time a quadratic cost function with an infinite prediction and control horizon is minimized such that constraints on the control input Euclidean norm are satisfied. To show the merits of the proposed approach, a nonlinear electric vehicle (EV) system with parameter uncertainty is considered as a case study. Indeed, the main goal of this study is to force the speed of EV to track a desired value. The experimental data, a new European driving cycle (NEDC), is used in order to examine the performance of the proposed controller. First, the equivalent TS model of the original nonlinear system is derived. After that, in order to evaluate the proficiency of the proposed controller, the achieved results of the proposed approach are compared with those of the conventional MPC controller and the optimal Fuzzy PI controller (OFPI), which are the latest research on the problem in hand.     

Nonlinear predictive control of a boiler-turbine unit: A state-space approach with successive on-line model linearisation and quadratic optimisation

This paper details development of a Model Predictive Control (MPC) algorithm for a boiler-turbine unit, which is a nonlinear multiple-input multiple-output process. The control objective is to follow set-point changes imposed on two state (output) variables and to satisfy constraints imposed on three inputs and one output. In order to obtain a computationally efficient control scheme, the state-space model is successively linearised on-line for the current operating point and used for prediction. In consequence, the future control policy is easily calculated from a quadratic optimisation problem. For state estimation the extended Kalman filter is used. It is demonstrated that the MPC strategy based on constant linear models does not work satisfactorily for the boiler-turbine unit whereas the discussed algorithm with on-line successive model linearisation gives practically the same trajectories as the truly nonlinear MPC controller with nonlinear optimisation repeated at each sampling instant.     

Well-conditioned model predictive control

Model-based predictive control is an advanced control strategy that uses a move suppression factor or constrained optimization methods for achieving satisfactory closed-loop dynamic responses of complex systems. While these approaches are suitable for many processes, they are formulated on the selection of certain parameters that are ambiguous and also computationally demanding which makes them less suited for tight control of fast processes. In this paper, a new dynamic matrix control (DMC) algorithm is proposed that reduces inherent ill-conditioning by allowing the process prediction time step to exceed the control time step. The main feature, that stands in contrast with current DMC approaches, is that the original open-loop data are used to evaluate a "shifting factor" m in the controller matrix where m replaces the move suppression coefficient. The new control algorithm is practically demonstrated on a fast reacting process with better control being realized in comparison with DMC using move suppression. The algorithm also gives improved closed-loop responses for control simulations on a multivariable nonlinear process having variable dead-time, and on other models found in the literature. The shifting factor m is generic and can be effectively applied for any control horizon.     

Improved finite-control-set model predictive control for active front-end rectifiers with simplified computational approach and on-line parameter identification

In this paper, an improved finite-control-set model predictive control method is proposed for active front-end rectifiers where the computational effort and parameter mismatch problems are taken into account simultaneously. Specifically, a desired voltage vector which only requires one exploration is directly selected by using a single cost function, and the process of selection of the desired voltage vector is optimized by using a sector distribution method. Meanwhile, a model reference adaptive system-based online parameter identification approach is presented to alleviate the parameter mismatch problem. The advantages of the proposed method summarized as follows: First, the proposed algorithm reduces the eight possible voltage vectors to one. The exhaustive exploration can be avoided while the control performance is not deteriorated. Second, the proposed controller can mitigate performance degradation caused by the model parameter mismatch. Simulation results under various parameters operating conditions are presented to demonstrate the efficacy of the proposed method.     

Fuzzy model predictive control of non-linear processes using convolution models and foraging algorithms

In this paper, a fuzzy model predictive control (FMPC) approach is introduced to design a control system for nonlinear processes. The proposed control strategy has been successfully employed for representative, benchmark chemical processes. Each nonlinear process system is described by fuzzy convolution models, which comprise a number of quasi-linear fuzzy implications (FIs). Each FI is employed to describe a fuzzy-set based relation between control input and model output. A quadratic optimization problem is then formulated, which minimizes the difference between the model predictions and the desired trajectory over a predefined predictive horizon and the requirement of control energy over a shorter control horizon. The present work proposes to solve this optimization problem by employing a contemporary population-based evolutionary optimization strategy, called the Bacterial Foraging Optimization (BFO) algorithm. The solution of this optimization problem is utilized to determine optimal controller parameters. The utility of the proposed controller is demonstrated by applying it to two non-linear chemical processes, where this controller could achieve better performances than those achieved by similar competing controller, under various operating conditions and design considerations. Further comparisons between various stochastic optimization algorithms have been reported and the efficacy of the proposed approach over similar optimization based algorithms has been concluded employing suitable performance indices.     

An approach to predictive control of multivariable time-delayed plant: stability and design issues

In this paper, a new method of multivariable predictive control is presented. The main advantage of a predictive approach is that multivariable plants with time delays can be easily handled. The proposed control algorithm also introduces a compact and simple design in the case of higher-order and nonminimal phase plants, but it is limited to open-loop stable plants. The algorithm of the proposed multivariable predictive control is developed, designed, and implemented on an air-conditioned system. The stability of the proposed control law is discussed.