Distributed plantwide control based on differential dissipativity

Modern chemical plants are becoming very complex, often consisting of a number of nonlinear process units (subsystems) with strong interactions due to material recycle and energy integration. The operation setpoint may need to be adjusted from time to time based on the market demand. To address the aforementioned challenges, a plantwide distributed nonlinear control scheme based on differential dissipativity is proposed in this paper, which can ensure plantwide incremental exponential stability and achieve bounded incremental L₂ gain performance. As a non‐unique property, the differential dissipativity of individual subsystem is shaped by a setpoint‐independent control structure – differential state feedback control. The dissipativity properties of subsystems and individual controllers are determined simultaneously as a large‐scale feasibility problem to ensure the plantwide stability and performance. It is converted into an LMI condition for plantwide supply rate planning and small‐scale sum‐of‐squares programming problems for individual subsystem dissipativity shaping, by using the alternating direction method of multipliers method. The proposed approach is illustrated using a chemical reactor network with a recycle stream. Copyright © 2016 John Wiley & Sons, Ltd.     

A pulp mill benchmark problem for control: application of plantwide control design

A heuristic for design of plantwide control strategies is introduced and applied to the millwide control of a previously presented pulp mill benchmark. Two control strategies (decentralized control and unit-based model predictive control) are compared according to their capacity to reduce the total error and maximize the operating profits. The control strategies are studied through closed-loop simulations of the process including several disturbances and setpoint changes in the digester, oxygen reactor, bleach plant, recausticizing plant and lime kiln.     

An industrial and academic perspective on plantwide control

The purpose of this paper is to stress the importance of selecting the right plantwide control structure and the need for a formalized approach that can encompass the many issues that arise in plantwide control design. Since the concept of process control design based on a holistic view of the process came about, the variety of procedures and approaches to the design problem has illustrated the difficulty of a unified approach. Using examples, the need and advantages of using a systematic approach based on considering the plant economics are highlighted. The examples deal with disturbance rejection, throughput maximization and economic optimization of plants consisting of parallel units.     

最优控制理论在磁轴承控制系统中的应用研究

建立了径向四自由度磁轴承系统状态方程, 介绍了采用最优控制理论中线性二次型方法设计磁轴承集中和分布参数控制器的方法和步骤, 并用MATLAB语言进行了仿真比较. 仿真和实验结果表明: 磁轴承转子在 60000rpm以下运行, 基于最优状态反馈控制理论设计的控制器, 忽略各自由度之间的耦合, 用分散控制策略设计的磁轴承控制系统, 基本满足磁轴承性能要求.     

Distributed control of plantwide chemical processes

Complex process plants increasingly appear in modern chemical industry. The wide use of material recycles and heat integration (with recycle and bypass streams) profoundly alters plantwide process dynamics and further increases their complexity. The interactions between process units may lead to poor performance of decentralized control systems. On the other hand, the complexity of plantwide systems prohibits the use of centralized controllers that reply on the complex model of the entire plantwide process. This paper addresses the plantwide chemical process control problem from a network perspective. The entire chemical plant is modeled as a network of process units linked by physical mass and energy flow and controlled by controllers that communicate with each other (i.e., distributed controllers). A two-port linear time-invariant representation is proposed to describe the dynamics of each process unit and its corresponding distributed controller. A two-step plantwide linear control design approach is developed. By using the dissipativity theory, the plantwide stability and control performance is translated into the closed-loop dissipativity condition that each distributed controller has to achieve. This allows the distributed controllers to be designed independently and to operate autonomously. The proposed approach is illustrated by a case study of a process network that consists of a reactor and a distillation column.     

Suboptimality of decentralized stochastic control and estimation

A stochastic version of suboptimal decentralized control is formulated to study the effects of interactions on performance of systems which are composed of locally optimal subsystems. Turning this approach the other way, we also investigate suboptimality of the decentralized control which arises from the globally optimal control of the overall interconnected system due to the loss of feedback control connections among the subsystems. Various characterizations of suboptimality are given in terms of interconnection and feedback gain matrices. By duality, we derive the suboptimality conditions for decentralized estimation. The separate solutions of control and estimation problems are used to provide a suboptimal decentralized design for incomplete state information. Additional conditions are obtained for robustness and reliability of the interconnected systems synthesized by a suboptimal decentralized control.     

A gradient flow approach to on-line robust pole assignment for synthesizing output feedback control systems

Pole assignment is a basic design method for synthesis of feedback control systems. In this paper, a gradient flow approach is presented for robust pole assignment in synthesizing output feedback control systems. The proposed approach is shown to be capable of synthesizing linear output feedback control systems via on-line robust pole assignment. Convergence of the gradient flow can be guaranteed. Moreover, with appropriate design parameters the gradient flow converges exponentially to an optimal solution to the robust pole assignment problem and the closed-loop control system based on the gradient flow is globally exponentially stable. These desired properties make it possible to apply the proposed approach to slowly time-varying linear control systems. Simulation results are shown to demonstrate the effectiveness and advantages of the proposed approach.     

Decentralized control: Status and outlook

This paper reviews state of the art in the area of decentralized networked control systems with an emphasis on event-triggered approach. The models or agents with the dynamics of linear continuous-time time-invariant state-space systems are considered. They serve for the framework for network phenomena within two basic structures. The I/O-oriented systems as well as the interaction-oriented systems with disjoint subsystems are distinguished. The focus is laid on the presentation of recent decentralized control design and co-design methods which offer effective tools to overcome specific difficulties caused mainly by network imperfections. Such side-effects include communication constraints, variable sampling, time-varying transmission delays, packet dropouts, and quantizations. Decentralized time-triggered methods are briefly discussed. The review is deals mainly with decentralized event-triggered methods. Particularly, the stabilizing controller–observer event-based controller design as well as the decentralized state controller co-design are presented within the I/O-oriented structures of large scale complex systems. The sampling instants depend in this case only on a local information offered by the local feedback loops. Minimum sampling time conditions are discussed. Special attention is focused on interaction-oriented system architecture. Model-based approach combined with event-based state feedback controller design is presented, where the event thresholds are fully decentralized. Finally, several selected open decentralized control problems are briefly offered as recent research challenges.     

Adaptive fuzzy output feedback decentralized control of pure‐feedback nonlinear large‐scale systems

In this paper, an adaptive fuzzy decentralized output feedback control approach is presented for a class of uncertain nonlinear pure‐feedback large‐scale systems with immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the immeasurable states. On the basis of the adaptive backstepping recursive design technique, an adaptive fuzzy decentralized output feedback is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed‐loop system are semiglobally uniformly ultimately bounded (SUUB), and that the observer and tracking errors converge to a small neighborhood of the origin by appropriate choice of the design parameters. Simulation studies are included to illustrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimality of decentralized control for large-scale systems

A decentralized control scheme is given for the stabilization of large-scale linear systems composed of a number of controllable subsystems. A class of interconnection structures among subsystems is defined for which the overall system can always be stabilized by local state feedback which is optimal for a quadratic performance index. The resulting closed-loop system has robust stability properties against a wide range of variations in open-loop dynamics. Optimality of the decentralized control law is preserved for a modified performance index under perturbations in interconnections such that the strength of coupling does not increase. The class of decentrally stabilizable large-scale systems presented in this paper is the largest such class hitherto described by the structure of interconnections.     

多机电力系统分散最优励磁控制器研究

本文根据有控制结构约束的分散控制理论研究了电力系统分散最优励磁控制,并采用系统的性能指标确定反馈信号以及控制器安装顺序。为了验证所提控制方案对于抑制系统振荡及提高系统稳定性的效益,对一个三机系统做了动态物理模型实验及数字仿真。     

Two adaptive control structures of robot manipulators

This paper proposes two simple adaptive control schemes of robot manipulators. The first one is the state feedback control which consists of feedforward from the desired position trajectory, PD feedback from the actual trajectory, and an auxiliary input. The second one is the feedforward/feedback control which consists of a feedforward term from the desired position, velocity, and acceleration trajectory based on the inverse of robot dynamics. The feedforward, feedback, and auxiliary gains are adapted using simple equations derived from the decentralized adaptive control theory based on Lyapunov's direct method, and using only the local information of the corresponding joint. The proposed control schemes are computationally fast and do not require a priori knowledge of the detail parameters of the manipulator or the payload. Simulation results are presented in support of the proposed schemes. The results demonstrate that both controllers perform well with bounded adaptive gains.     

磁悬浮控制敏感陀螺转子偏转通道稳定控制方法

为克服强陀螺效应对高速磁悬浮控制敏感陀螺(MSCSG)转子偏转通道稳定性的影响,提出一种基于分散PID结合滤波交叉反馈的数字控制方案.根据洛伦兹力磁轴承支承的转子偏转系统结构特点,建立了MSCSG转子偏转动力学模型;利用所建立模型分析了两径向偏转自由度间的耦合特性,并提出在PID控制器的基础上,引入滤波交叉反馈来抑制径向偏转通道中的陀螺效应;搭建了以DSP和FPGA为核心的数字控制系统,并采用双线性变换将所提出的控制方法进行数字化实现.采用根轨迹法对所提出控制方法的稳定性进行了分析,通过实验比较了引入滤波交叉反馈控制前后转子偏转通道的稳定性.实验结果表明,分散PID控制条件下MSCSG转子在转速为3200 r/min时失稳,而引入滤波交叉反馈后,转子转速升至5000 r/min后仍可稳定运行.实验结果验证了所提出稳定控制方法对强陀螺效应的抑制作用.     

基于误差系统的信息融合最优预见跟踪控制

针对期望轨迹和干扰可预见的最优跟踪问题, 提出了一种基于误差系统的信息融合最优控制方法. 将线性伺服系统转化为误差系统; 利用信息融合估计方法, 通过融合期望轨迹、干扰输入、误差系统状态等信息, 获得误差系统协状态以及控制增量的最优估计. 构建了由积分项、状态反馈控制项和预见前馈补偿项组成的最优预见控制系统. 线性直流电机系统的控制仿真结果表明, 信息融合最优预见控制下的位置跟踪精度比传统最优预见控制下的要高.     

Performance assessment of decentralized control systems: An iterative approach

In this work, an efficient approach for performance assessment of decentralized control systems based on a general quadratic performance index involving both system states and inputs is proposed. The performance assessment problem is formulated as an optimization problem subject to constraints in the form of linear/bilinear matrix inequalities which explicitly take the block-diagonal structural constraint on decentralized control systems into account. In order to solve the optimization problem efficiently, an iterative approach based on the original optimization problem and an equivalent transformation of the original one is proposed. Specifically, the proposed approach under the assumption that the full state feedback is available is first presented; and then the approach is extended to the case that only output feedback is available. The proposed approach solves for both the best achievable performance and the corresponding controller (and observer) gains. The application of the proposed approach to two examples including a reactor–separator chemical process example illustrates the applicability and effectiveness of the proposed approach.     

Adaptive fuzzy decentralized output feedback control for stochastic nonlinear large‐scale systems using DSC technique

In this paper, an adaptive fuzzy decentralized backstepping output feedback control approach is proposed for a class of uncertain large‐scale stochastic nonlinear systems without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. Using the designed fuzzy state observer, and by combining the adaptive backstepping technique with dynamic surface control technique, an adaptive fuzzy decentralized output feedback control approach is developed. It is shown that the proposed control approach can guarantee that all the signals of the resulting closed‐loop system are semi‐globally uniformly ultimately bounded in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by choosing appropriate design parameters. A simulation example is provided to show the effectiveness of the proposed approaches. Copyright © 2011 John Wiley & Sons, Ltd.     

参数不确定广义大系统的保性能分散控制

对一类范数有界时不变参数不确定的连续广义大系统和一个二次型性能指标,研究了其保性能分散控制问题.目的是设计一状态反馈分散控制器,使得对所有容许的不确定性,闭环系统不仅是鲁棒稳定的,而且性能指标有一上界.应用线性矩阵不等式方法,给出了一个用线性矩阵不等式表达的保性能分散控制器存在的充分条件;在此条件可解时,给出了保性能分散控制律的表达式.最后,举例说明了该方法的应用.     

不确定广义大系统有限时间鲁棒分散控制

研究不确定连续广义大系统的有限时间鲁棒分散控制问题,设计系统的有限时间鲁棒分散状态反馈控制器.首先应用广义Lyapunov 函数法,给出不确定广义大系统有限时间鲁棒稳定的充分条件;其次,给出不确定广义大系统应用分散状态反馈控制器鲁棒镇定的充分条件和有限时间鲁棒分散控制器的设计方法;最后,通过仿真例子验证所提出方法的有效性.     

Decentralized tube‐based model predictive control of uncertain nonlinear multiagent systems

This paper addresses the problem of decentralized tube‐based nonlinear model predictive control (NMPC) for a general class of uncertain nonlinear continuous‐time multiagent systems with additive and bounded disturbance. In particular, the problem of robust navigation of a multiagent system to predefined states of the workspace while using only local information is addressed under certain distance and control input constraints. We propose a decentralized feedback control protocol that consists of two terms: a nominal control input, which is computed online and is the outcome of a decentralized finite horizon optimal control problem that each agent solves at every sampling time, for its nominal system dynamics; and an additive state‐feedback law which is computed offline and guarantees that the real trajectories of each agent will belong to a hypertube centered along the nominal trajectory, for all times. The volume of the hypertube depends on the upper bound of the disturbances as well as the bounds of the derivatives of the dynamics. In addition, by introducing certain distance constraints, the proposed scheme guarantees that the initially connected agents remain connected for all times. Under standard assumptions that arise in nominal NMPC schemes, controllability assumptions, communication capabilities between the agents, it is guaranteed that the multiagent system is input‐to‐state stable with respect to the disturbances, for all initial conditions satisfying the state constraints. Simulation results verify the correctness of the proposed framework.     

跳变双线性随机离散组合系统的保成本分散控制

研究一类跳变双线性随机离散组合系统的保成本分散控制问题．首先给出问题可解的充分条件,然后基于线性矩阵不等式方法设计保成本分散状态反馈控制律．理想的保成本分散状态反馈控制器可通过应用现有的软件,求解一组线性矩阵不等式而得到．仿真例子说明了该方法的有效性.