High-order Volterra Model Predictive Control and its application to a nonlinear polymerisation process

Model Predictive Control (MPC) has recently found wide acceptance in the process industry, but existing design and implementation methods are restricted to linear process models. A chemical process, however, involves severe nonlinearity which cannot be ignored in practice. This paper aims to solve this nonlinear control problem by extending MPC to accommodate nonlinear models. It develops an analytical framework for nonlinear model predictive control (NMPC). It also offers a third-order Volterra series based nonparametric nonlinear modelling technique for NMPC design, which relieves practising engineers from the need for deriving a physical-principles based model first. An on-line realisation technique for implementing NMPC is then developed and applied to a Mitsubishi Chemicals polymerisation reaction process. Results show that this nonlinear MPC technique is feasible and very effective. It considerably outperforms linear and low-order Volterra model based methods. The advantages of the developed approach lie not only in control performance superior to existing NMPC methods, but also in eliminating the need for converting an analytical model and then convert it to a Volterra model obtainable only up to the second order.     

基于在线最小二乘支持向量机的广义预测控制

This paper proposes a practical generalized predictive control(GPC)algorithm based on online least squares support vector machines(LS-SVM)which can deal with nonlinear systems effectively.At each sampling period the algorithm recursively modifies the model by adding a new data pair and deleting the least important one out of the consideration on realtime property.The data pair deleted is determined by the absolute value of lagrange multiplier from last sampling period.The paper gives the recursive algorithm of model parameters when adding a new data pair and deleting an existent one,respectively,and thus the inversion of a large matrix is avoided and the memory can be controlled by the algorithm entirely.The nonlinear LS-SVM model is applied in GPC algorithm at each sampling period.The experiments of generalized predictive control on pH neutralizing process show the effectiveness and practicality of the proposed algorithm.     

Synchronization of complex networks with coupling delays via adaptive pinning intermittent control

The problem of exponential synchronization for a class of general complex dynamical networks with nonlinear coupling delays by adaptive pinning periodically intermittent control is considered in this paper. We use the methods of the adaptive control, pinning control and periodically intermittent control. Based on the piecewise Lyapunov stability theory, some less conservative criteria are derived for the global exponential synchronization of the complex dynamical networks with coupling delays. And several corresponding adaptive pinning feedback synchronization controllers are designed. These controllers have strong robustness against the coupling strength and topological structure of the network. Using the delayed nonlinear system as the nodes of the networks, a numerical example of the complex dynamical networks with nonlinear coupling delays is given to demonstrate the effectiveness of the control strategy.     

Generalized Predictive Control with Online Least Squares Support Vector Machines

This paper proposes a practical generalized predictive control （GPC） algorithm based on online least squares support vector machines （LS-SVM） which can deal with nonlinear systems effectively. At each sampling period the algorithm recursively modifies the model by adding a new data pair and deleting the least important one out of the consideration on realtime property. The data pair deleted is determined by the absolute value of lagrange multiplier from last sampling period. The paper gives the recursive algorithm of model parameters when adding a new data pair and deleting an existent one, respectively, and thus the inversion of a large matrix is avoided and the memory can be controlled by the algorithm entirely. The nonlinear LS-SVM model is applied in GPC algorithm at each sampling period. The experiments of generalized predictive control on pH neutralizing process show the effectiveness and practicality of the proposed algorithm.     

Temperature prediction control based on least squares support vector machines

A prediction control algorithm is presented based on least squares support vector machines (LS-SVM) model for a class of complex systems with strong nonlinearity. The nonlinear off-line model of the controUed plant is built by LS-SVM with radial basis function (RBF) kernel. In the process of system running, the off-line model is linearized at each sampling instant, and the generalized prediction control (GPC) algorithm is employed to implement the prediction control for the controlled plant. The obtained algorithm is applied to a boiler temperature control system with complicated nonlinearity and large time delay. The results of the experiment verify the effectiveness and merit of the algorithm.     

Multi-model predictive control with local constraints based on model switching

Because model switching system is a typical form of Takagi-Sugeno（T-S） model which is an universal approximator of continuous nonlinear systems, we describe the model switching system as mixed logical dynamical （MLD） system and use it in model predictive control （MPC） in this paper. Considering that each local model is only valid in each local region,we add local constraints to local models. The stability of proposed multi-model predictive control （MMPC） algorithm is analyzed, and the performance of MMPC is also demonstrated on an inulti-multi-output（MIMO） simulated pH neutralization process.     

Sliding mode-based adaptive tube model predictive control for robotic manipulators with model uncertainty and state constraints

In this paper, the optimal tracking control for robotic manipulatorswith state constraints and uncertain dynamics is investigated, and a sliding mode-based adaptive tube model predictive control method is proposed. First, utilizing the high-order fully actuated system approach, the nominal model of the robotic manipulator is constructed as the predictive model. Based on the nominal model, a nominal model predictive controller with the sliding mode is designed, which relaxes the terminal constraints, and realizes the accurate and stable tracking of the desired trajectory by the nominal system. Then, an auxiliary controller based on the node-adaptive neural networks is constructed to dynamically compensate nonlinear uncertain dynamics of the robotic manipulator. Furthermore, the estimation deviation between the nominal and actual states is limited to the tube invariant sets. At the same time, the recursive feasibility of nominal model predictive control is verified, and the ultimately uniformly boundedness of all variables is proved according to the Lyapunov theorem. Finally, experiments show that the robotic manipulator can achieve fast and efficient trajectory tracking under the action of the proposed method.     

Recent advances on micro-control for near-critical complex systems

Near-critical systems are a class of complex systems that are “close” to criticality and possess potentials to be induced or manipulated to become critical [1,2]. Such systems demonstrate advantages in multi-disciplinary application scenarios. For example, when a biological predator-prey system is near critical, the escape probability of the prey is the highest and the whole system possesses a highly dynamical and flexible structure [3]. When a real-time computing network is near critical, it can perform complex computations on time series [4]. Actually, dynamical systems that are capable of fulfilling complex computational tasks often operate near the edge of chaos. To fully take advantage of near criticality, how to estimate and control of near-critical complex systems becomes a pressing issue. Classical control theory, whichmainly includes linear systems theory, sampled-data control theory, stochastic control theory, nonlinear systems theory and so on, concentrates on various topics such as stability of dynamical systems, time-domain and frequency-domain analysis, synthesis and compensation of controllers. However, most of them are inapplicable to the control of complex systems, mainly due to the following reasons. The classical control theory is model based, whereas in most case, we cannot obtain a mathematical model of a complex system, let alone an accurate one, since such a complex system is mostly featured with highly nonlinear dynamics, emergent properties, self-adaption and self-organization. For example, the classical frequency-domain methods, such as frequency response analysis and root locus methods, are inapplicable without a model. The control for complex systems is usually considered on a case by case basis and realized by inputting noise [5] and micro-control by constructing weak feedback loop [6] in some scenerios, as opposed to the model-based control theory for general linear or nonlinear dynamical systems....     

Prediction method for energy consumption per ton of fused magnesium furnaces using data driven and mechanism model

This paper gives an overview of early development of nonlinear disturbance observer design technique and the disturbance observer based control (DOBC) design. Some critical points raised in the development of the methods have been reviewed and discussed which are still relevant for many researchers or practitioners who are interested in this method. The review is followed by the development of a new type of nonlinear PID controller for a robotic manipulator and its experimental tests. It is shown that, under a number of assumptions, the DOBC consisting of a predictive control method and a nonlinear disturbance observer could reduce to a nonlinear PID with special features. Experimental results show that, compared with the predictive control method, the developed controller significantly improves performance robustness against uncertainty and friction. This paper may trigger further research and interests in the development of DOBC and related methods, and building up more understanding between this group of control methods with comparable ones (particularly control methods with integral action).     

基于关联存储网络的非线性约束监督预测控制

设定值优化是复杂工业过程中一种有效的优化控制手段,通过在通常的校正级上面加一层监督级而实现.模型预测控制已广泛应用于工业过程控制,但约束优化的实现是一个难题.鉴于此,建立了非线性监督预测控制的模糊神经网络模型,由此推导出监督预测控制的可行解,并用于燃气轮机系统转速和功率的控制.仿真结果表明了该方法的优越性.     

广义预测控制器系数直接算法

为了简化广义预测控制算法的分析与设计，提出了广义预测控制器系数直接计算方法．该方法利用过程模型直接递推，把广义预测控制律表达成控制器系数与参考轨迹及过程历史信息乘积的形式．其控制器系数计算只与模型参数及设计参数有关，避免了在线求解Diophantine方程、输出预测表达式及自由响应项，简化了设计思路，减少了在线运算量．在一个DCS控制的非线性液位装置上得到的对比实验结果表明该方法是可行和有效的．     

基于SVM的PVC汽提过程预测控制方法

针对汽提塔温度控制系统的非线性和参数时变的特性,采用支持向量机对汽提塔温度进行建模,结合非线性模型的实时线性化和广义预测控制隐式算法,提出了基于支持向量预测模型的广义预测控制算法.同时将该算法应用到聚氯乙烯汽提生产过程当中,并将模型在线校正和误差反馈校正相结合,根据实际情况进行了多种情况下的仿真,仿真结果表明了方法的有效性.     

Generalized predictive control using recurrent fuzzy neural networks for industrial processes

This paper presents a design methodology for predictive control of industrial processes via recurrent fuzzy neural networks (RFNNs). A discrete-time mathematical model using RFNN is constructed and a learning algorithm adopting a recursive least squares (RLS) approach is employed to identify the unknown parameters in the model. A generalized predictive control (GPC) law with integral action is derived based on the minimization of a modified predictive performance criterion. The stability and steady-state performance of the resulting control system are studied as well. Two examples including the control of a nonlinear process and the control of a physical variable-frequency oil-cooling machine are used to demonstrate the effectiveness of the proposed method. Both results from numerical simulations and experiments show that the proposed method is capable of controlling industrial processes with satisfactory performance under setpoint and load changes.     

Online elicitation of Mamdani-type fuzzy rules via TSK-based generalized predictive control

Many synergies have been proposed between soft-computing techniques, such as neural networks (NNs), fuzzy logic (FL), and genetic algorithms (GAs), which have shown that such hybrid structures can work well and also add more robustness to the control system design. In this paper, a new control architecture is proposed whereby the on-line generated fuzzy rules relating to the self-organizing fuzzy logic controller (SOFLC) are obtained via integration with the popular generalized predictive control (GPC) algorithm using a Takagi-Sugeno-Kang (TSK)-based controlled autoregressive integrated moving average (CARIMA) model structure. In this approach, GPC replaces the performance index (PI) table which, as an incremental model, is traditionally used to discover, amend, and delete the rules. Because the GPC sequence is computed using predicted future outputs, the new hybrid approach rewards the time-delay very well. The new generic approach, named generalized predictive self-organizing fuzzy logic control (GPSOFLC), is simulated on a well-known nonlinear chemical process, the distillation column, and is shown to produce an effective fuzzy rule-base in both qualitative (minimum number of generated rules) and quantitative (good rules) terms.     

一种基于最小二乘支持向量机的预测控制算法

针对工业过程中普遍存在的非线性被控对象，提出一种基于最小二乘支持向量机建模的预测控制算法．首先，用具有RBF核函数的LS-SVM离线建立被控对象的非线性模型；然后，在系统运行过程中，将离线模型在每一个采样周期关于当前采样点进行线性化，并用广义预测算法实现对被控系统的预测控制．仿真结果表明了该算法的有效性和优越性．     

Predictive LPV control of a liquid–gas separation process

The problem of controlling a liquid–gas separation process is approached by using LPV control techniques. An LPV model is derived from a nonlinear model of the process using differential inclusion techniques. Once an LPV model is available, an LPV controller can be synthesized. The authors present a predictive LPV controller based on the GPC controller [Clarke D, Mohtadi C, Tuffs P. Generalized predictive control – Part I. Automatica 1987;23(2):137–48; Clarke D, Mohtadi C, Tuffs P. Generalized predictive control – Part II. Extensions and interpretations. Automatica 1987;23(2):149–60]. The resulting controller is denoted as GPC–LPV. This one shows the same structure as a general LPV controller [El Gahoui L, Scorletti G. Control of rational systems using linear-fractional representations and linear matrix inequalities. Automatica 1996;32(9):1273–84; Scorletti G, El Ghaoui L. Improved LMI conditions for gain scheduling and related control problems. International Journal of Robust Nonlinear Control 1998;8:845–77; Apkarian P, Tuan HD. Parametrized LMIs in control theory. In: Proceedings of the 37th IEEE conference on decision and control; 1998. p. 152–7; Scherer CW. LPV control and full block multipliers. Automatica 2001;37:361–75], which presents a linear fractional dependence on the process signal measurements. Therefore, this controller has the ability of modifying its dynamics depending on measurements leading to a possibly nonlinear controller. That controller is designed in two steps. First, for a given steady state point is obtained a linear GPC using a linear local model of the nonlinear system around that operating point. And second, using bilinear and linear matrix inequalities (BMIs/LMIs) the remaining matrices of GPC–LPV are selected in order to achieve some closed loop properties: stability in some operation zone, norm bounding of some input/output channels, maximum settling time, maximum overshoot, etc., given some LPV model for the nonlinear system. As an application, a GPC–LPV is designed for the derived LPV model of the liquid–gas separation process. This methodology can be applied to any nonlinear system which can be embedded in an LPV system using differential inclusion techniques.     

采用遗传算法训练对角递归神经网络预测控制器

本文提出了一种基于广义预测控制的神经网络预测控制方案．预测控制器由对角递归 神经网络预测控制器和前向神经网络静态补偿器组成．两种神经网络均采用遗传算法进行训 练．仿真实验表明,对于带纯时延的非线性被控对象,采用遗传算法设计的对角递归神经网 络预测控制器具有令人满意的控制性能．     

基于神经网络的时滞非线性系统的广义预测控制

针对一类时滞非线性被控对象,提出一种基于RBF神经网络的广义预测自校正控制方案,在广义预测控制中,采用RBF神经网络建立被控对象的多步预测模型,并不断修正预测输出,提高预测输出的精度.控制器则采用GPC隐式修正算法,不用辨识对象的模型参数,大大减少了计算量.经过仿真研究,与常规的PID自适应控制方法相比较,证明了该方法的优越性,预测控制误差小,实时性好,动态响应快.