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.     

Dissipativity-based distributed fault diagnosis for plantwide chemical processes

Most modern chemical processes consist of a number of process units interconnected with mass and energy flows, often with energy integration and materials recycle loops. As such, faults (process faults, actuator faults, or sensor faults) often propagate to multiple process units (subsystems), causing significant difficulties in fault diagnosis for plantwide systems. In this paper, a general distributed fault diagnosis approach is proposed for plantwide chemical processes, which takes into account the interactions among process units. The distributed fault diagnostic observers are designed to be sensitive to the local faults (local sensitivity) and insensitive to faults in other process units (remote faults insensitivity) and disturbances. The above requirements are formulated as plantwide dissipativity conditions and the gains for the distributed estimators and residual generators are obtained offline by solving a set of linear matrix inequalities. A case study of heat exchanger network is presented to demonstrate the effectiveness of the proposed approach.     

A hybrid model predictive control strategy for nonlinear plant-wide control

A plant-wide control strategy based on integrating linear model predictive control (LMPC) and nonlinear model predictive control (NMPC) is proposed. The hybrid method is applicable to plants that can be decomposed into approximately linear subsystems and highly nonlinear subsystems that interact via mass and energy flows. LMPC is applied to the linear subsystems and NMPC is applied to the nonlinear subsystems. A simple controller coordination strategy that counteracts interaction effects is proposed for the case of one linear subsystem and one nonlinear subsystem. A reactor/separator process with recycle is used to compare the hybrid method to conventional LMPC and NMPC techniques.     

Robust adaptive boundary control of semilinear PDE systems using a dyadic controller

In this paper, we describe a dyadic adaptive control framework for output tracking in a class of semilinear systems of partial differential equations with boundary actuation and unknown distributed nonlinearities. The dyadic adaptive control framework uses the linear terms in the system to split the plant into 2 virtual subsystems, one of which contains the nonlinearities, whereas the other contains the control input. Full‐plant‐state feedback is used to estimate the unmeasured individual states of the 2 subsystems as well as the nonlinearities. The control signal is designed to ensure that the controlled subsystem tracks a suitably modified reference signal. We prove the well posedness of the closed‐loop system rigorously and derive conditions for closed‐loop stability and robustness using finite‐gain stability theory.     

Observer‐based adaptive neural control for a class of nonlinear singular systems

The problem of observer‐based adaptive neural control via output feedback for a class of uncertain nonlinear singular systems is studied in this article. The nonlinear singular systems can be regarded as two subsystems that are coupled with each other: differential subsystem and algebraic subsystem. The differential systems can be nonstrict feedback structures. To guarantee that the singular system is regular and impulse‐free, two new conditions are proposed. By the conditions, the linear controller and observer, which are used to estimate the immeasurable state variables, are obtained. Then, an output feedback scheme through adaptive neural backstepping is proposed to ensure that all states of the closed‐loop system are semiglobally uniformly ultimately bounded and converge to a small neighborhood of the origin. Simulation examples illustrate the effectiveness of the presented method.     

Dissipativity and dissipative control for positive switched systems: A multiple linear copositive storage function method

In this article, the problems of dissipativity analysis and dissipative control are investigated for positive switched linear systems in both continuous and discrete‐time domains. We aim at solving the problems via employing a multiple linear copositive storage function scheme. The solvability of the problems for individual subsystem is only on their active regions. Switching laws and a set of feedback controllers are jointly devised such that the associated closed‐loop switched systems are not only positive but also dissipative, which is from the exogenous input to the output. Asymptotic stability is derived if all subsystems are zero‐state detectable. Moreover, sufficient conditions guaranteeing dissipativity with positivity constraint are presented, which can be easily examined on the grounds of linear programming approach. Finally, an example is offered, illustrating that the proposed control strategy is successful.     

Geometrically (Q,S, R)‐Incremental Dissipativity and Incremental Stability for Switched Time‐Varying Nonlinear Discrete‐Time Systems

This paper investigates geometrically (Q,S,R)‐incremental dissipativity and incremental stability for switched time‐varying nonlinear discrete‐time systems. A geometrically (Q,S,R)‐incremental dissipativity concept is proposed for switched nonlinear discrete‐time systems by using multiple storage functions and multiple incremental supply rate. Furthermore, the sufficient conditions of geometrically (Q,S,R)‐incremental dissipativity are given under the design of state‐dependent switching law. The incremental stability conditions are derived for geometrically (Q,S,R)‐incrementally dissipative switched systems. By designing of a composite state‐dependent switching law, the feedback interconnected switched systems are ensured to be geometrically (Q,S,R)‐incrementally dissipative. A numerical example is given to illustrate the validity of the proposed approach.     

Vector dissipativity theory and stability of feedback interconnections for large-scale non-linear dynamical systems

Recent technological demands have required the analysis and control design of increasingly complex, large-scale non-linear dynamical systems. In analysing these large-scale systems, it is often desirable to treat the overall system as a collection of interconnected subsystems. Solution properties of the large-scale system are then deduced from the solution properties of the individual subsystems and the nature of the system interconnections. In this paper we develop an analysis framework for large-scale dynamical systems based on vector dissipativity notions. Specifically, using vector storage functions and vector supply rates, dissipativity properties of the composite large-scale system are shown to be determined from the dissipativity properties of the subsystems and their interconnections. Furthermore, extended Kalman–Yakubovich–Popov conditions, in terms of the subsystem dynamics and interconnection constraints, characterizing vector dissipativeness via vector system storage functions are derived. Finally, these results are used to develop feedback interconnection stability results for large-scale non-linear dynamical systems using vector Lyapunov functions.     

Exponentially incremental dissipativity for nonlinear stochastic switched systems

ABSTRACT

In this paper, we investigate the exponentially incremental dissipativity for nonlinear stochastic switched systems by using the designed state-dependent switching law and multiple Lyapunov functions approach. Specifically, using incremental supply rate as well as a state dissipation inequality in expectation, a stochastic version of exponentially incremental dissipativity is presented. The sufficient conditions for nonlinear stochastic switched systems to be exponentially incrementally dissipative are given by the designed state-dependent switching law. Furthermore, the extended Kalman–Yakubovich–Popov conditions are derived by using two times continuously differentiable storage functions. Moreover, the incremental stability conditions in probability for nonlinear stochastic switched systems are derived based on exponentially incremental dissipativity. The exponentially incremental dissipativity is preserved for the feedback-interconnected nonlinear stochastic switched systems with the composite state-dependent switching law; meanwhile, the incremental stability in probability is preserved under some certain conditions. A numerical example is given to illustrate the validity of our results.     

Operability analysis of nonlinear processes based on incremental dissipativity

Process operability can be defined as the ability of a process to reject disturbances at a specified operating point and/or to move quickly and smoothly from one operating point to another operating point using a feedback control system. Unlike linear processes, the properties of nonlinear processes (e.g., stability, minimum phase condition, etc.) are different around different equilibria. Most existing operability analysis for nonlinear systems focuses on one particular operating point of interest. This paper addresses the issues of dynamic process operability at various operating points, including the reachability of all equilibrium points or output trajectories in an operating region, regardless of initial conditions. In this work, a nonlinear analysis approach is developed based on the concept of incremental stability. Conditions for incremental stability are derived based on incremental dissipativity. The links between input and output multiplicities and incremental dissipativity are explored. The dynamic control performance achievable in terms of the speed of the response of the closed-loop system and offset minimization is studied. A method for determination of incremental dissipativity using Linear Differential Inclusion (LDI) is also presented, to facilitate the dissipativity based operability analysis.     

Dissipativity reinforcement in feedback systems and its application to expanding power systems

This paper focuses on the performance analysis and improvement of interconnected passive systems. We assume that each subsystem has a special passivity property that is characterized by 2 parameters. The parameters are also utilized for evaluating the dissipation performance as the L₂‐gain. Then, the feedback system composed of passive subsystems inherits the parameter‐dependent passivity, and the parameter transition is given. In addition, it is shown that the dissipation performance of the feedback system is strictly improved as compared with that of the subsystems, which is called dissipativity reinforcement in this paper. Furthermore, we expand the feedback system to a larger‐scale system via the iterative feedback connection of the passive subsystems. Then, the performance of the entire system is gradually reinforced with the increase in the number of subsystems. Subsequently, we extend the class of parameter‐dependent passivity to a frequency‐dependent one. Finally, dissipativity reinforcement via an iterative feedback connection is applied to a power system that involves a large number of renewable energy generators. In particular, we propose a strategy for designing the power system, such that the dissipation performance of the entire system is gradually reinforced via scale expansion, ie, with the increase in the amount of energy generators installed.     

Decentralized event‐triggered control of large‐scale nonlinear systems

This paper studies the decentralized event‐triggered control of large‐scale nonlinear systems. We consider a class of decentralized control systems that are transformable into an interconnection of input‐to‐state stable subsystems with the sampling errors as the inputs. The sampling events for each subsystem are triggered by a threshold signal, and the threshold signals for the subsystems are independent with each other for the decentralized implementation. By appropriately designing the event‐triggering mechanisms, it is shown that infinitely fast sampling can be avoided for each subsystem and asymptotic regulation is achievable for the large‐scale system. The proposed design is based on the ISS small‐gain arguments, and is validated by a benchmark example of controlling two coupled inverted pendulums.     

Modeling and vibration control for a flexible pendulum inverted system based on a PDE observer

This study addresses the problem of trajectory control of a flexible pendulum inverted system on the basis of the partial differential equation (PDE) and ordinary differential equation (ODE) dynamic model. One of the key contributions of this study is that a new model is proposed to simplify the complex system. In addition, this study proposed a nonlinear PDE observer to estimate distributed positions and velocities along flexible pendulum. Singular perturbation method is proposed to solve the coupling system of nonlinear PDE observer. The nonlinear PDE observer is divided into a fast subsystem and a slow subsystem by the use of the singular perturbation method. To stabilise this fast subsystem, a boundary controller is proposed at the free end of the beam. The sliding-mode control method is proposed to design controller for slow subsystems. The asymptotic stability of both the proposed nonlinear PDE observer and controller is validated by theoretical analysis. The results are illustrated by simulation.     

Distributed adaptive high‐gain extended Kalman filtering for nonlinear systems

In this work, we propose a distributed adaptive high‐gain extended Kalman filtering approach for nonlinear systems. Specifically, we consider a class of nonlinear systems that are composed of several subsystems interacting with each other via their states. In the proposed approach, an adaptive high‐gain extended Kalman filter is designed for each subsystem. The distributed Kalman filters communicate with each other to exchange estimated subsystem state information. First, assuming continuous communication among the distributed filters within deterministic form of subsystems, an implementation strategy that specifies how the distributed filters should communicate is designed and the detailed design of the subsystem filter is described. Second, we consider the case of stochastic subsystems for which the designed subsystem filters communicate to exchange information at discrete‐time instants. A state predictor in each subsystem filter is used to provide predictions of states of other subsystems. The stability properties of the proposed distributed estimation schemes with both continuous and discrete communications are analyzed. Finally, the effectiveness and applicability of the proposed schemes are illustrated via the application to a chemical process example. Copyright © 2017 John Wiley & Sons, Ltd.     

带有界扰动的一类大型互联非线性系统的鲁棒分散控制

研究带有界扰动的一类大型互联非线性系统的鲁棒分散控制问题, 该系统的第i个子系统的标称模型具有相对阶r_i及指数稳定的零动态, 且每个子系统的互联项满足匹配条件. 通过子系统状态的线性变换得到鲁棒分散状态反馈控制器, 当该控制律作用于系统时, 系统的状态能够收敛到原点的一个小邻域内, 并给出仿真算例说明该结论的可行性和有效性.     

Exponential quasi‐(Q,S,R)‐dissipativity and practical stability for switched nonlinear systems

In this paper, the problems of exponential quasi‐(Q,S,R)‐dissipativity and practical stability analysis for a switched nonlinear system are addressed. First, the concept of exponential quasi‐(Q,S,R)‐dissipativity for switched nonlinear systems without requiring the exponential quasi‐(Q,S,R)‐dissipativity property of each subsystem is proposed. Then, we show that an exponentially quasi‐(Q,S,R)‐dissipative switched nonlinear system is practically stable. Second, this exponential quasi‐(Q,S,R)‐ dissipativity property for a switched nonlinear system is obtained by the design of a state‐dependent switching law. Third, a composite state‐dependent switching law is designed to render the feedback interconnection of switched nonlinear systems exponentially quasi‐(Q,S,R)‐dissipative. This switching law allows interconnected switched nonlinear systems to switch asynchronously. Finally, the effectiveness of the results is verified by a numerical example.     

Adaptive fuzzy semi‐decentralized control for a class of large‐scale nonlinear systems with unknown interconnections

In this paper, a general method is developed to generate a stable adaptive fuzzy semi‐decentralized control for a class of large‐scale interconnected nonlinear systems with unknown nonlinear subsystems and unknown nonlinear interconnections. In the developed control algorithms, fuzzy logic systems, using fuzzy basis functions (FBF), are employed to approximate the unknown subsystems and interconnection functions without imposing any constraints or assumptions about the interconnections. The proposed controller consists of primary and auxiliary parts, where both direct and indirect adaptive approaches for the primary control part are aiming to maintain the closed‐loop stability, whereas the auxiliary control part is designed to attenuate the fuzzy approximation errors. By using Lyapunov stability method, the proposed semi‐decentralized adaptive fuzzy control system is proved to be globally stable, with converging tracking errors to a desired performance. Simulation examples are presented to illustrate the effectiveness of the proposed controller. Copyright © 2006 John Wiley & Sons, Ltd.     

分散模型参考自适应控制

本文针对由参数未知、存在有界扰动和非线性关联的子系统组成的大规模互联系统,提出 了一种新的分散模型参考自适应控制法.它适用于孤立子系统传递函数的相对阶次n*i为任 意值的情况.根据李雅普诺夫稳定性理论,文中证明了这种分散自适应控制系统全局稳定的 充分条件.与有关文献所介绍的方法相比,本文的方法可用于n*i>2的场合,因而它更具有 一般性和实用性.     

非线性相似组合系统的渐近稳定

本文对一类具有相似性的不确定非线性组合系统设计了鲁棒控制器．对不确定性只要 求一个已知的可能函数界,互联的强度由非减函数限制,减弱了对互联项的要求．我们利用系 统本身的相似性,简化了设计过程．所得控制器保证系统的渐近稳定性．