Overlapping control design for multi-channel systems

This paper deals with the decentralized overlapping control of interconnected systems. The notion of a quotient overlapping fixed mode (QOFM) is first introduced and it is shown that a mode of an interconnected linear time-invariant system can be shifted by means of a general decentralized overlapping controller if and only if it is not a QOFM. It is then asserted that any interconnected system with no unstable QOFM can be stabilized by using an appropriate finite-dimensional linear time-varying controller. It is also shown how the existing results aiming at designing a decentralized controller of a certain type such as generalized sampled-data hold function, finite-dimensional linear time-varying, and sampled-data can be utilized to design a decentralized overlapping controller of a desired form, in order to achieve any design specification. The efficacy of the results is elucidated through two numerical examples.     

Decentralized adaptive iterative learning control for interconnected systems with uncertainties

In many applications,the system dynamics allows the decomposition into lower dimensional subsystems with interconnections among them.This decomposition is motivated by the ease and flexibility of the controller design for each subsystem.In this paper,a decentralized model reference adaptive iterative learning control scheme is developed for interconnected systems with model uncertainties.The interconnections in the dynamic equations of each subsystem are considered with unknown boundaries.The proposed controller of each subsystem depends only on local state variables without any information exchange with other subsystems.The adaptive parameters are updated along iteration axis to compensate the interconnections among subsystems.It is shown that by using the proposed decentralized controller,the states of the subsystems can track the desired reference model states iteratively.Simulation results demonstrate that,utilizing the proposed adaptive controller,the tracking error for each subsystem converges along the iteration axis.     

Design of a Robust Optimal Decentralized PI Controller Based on Nonlinear Constraint Optimization For Level Regulation: An Experimental Study

This paper presents the development of a new robust optimal decentralized PI controller based on nonlinear optimization for liquid level control in a coupled tank system. The proposed controller maximizes the closed-loop bandwidth for specified gain and phase margins, with constraints on the overshoot ratio to achieve both closed-loop performance and robustness. In the proposed work, a frequency response fitting model reduction technique is initially employed to obtain a first order plus dead time (FOPDT) model of each higher order subsystem. Furthermore, based on the reduced order model, a proposed controller is designed. The stability and performance of the proposed controller are verified by considering multiplicative input and output uncertainties. The performance of the proposed optimal robust decentralized control scheme has been compared with that of a decentralized PI controller. The proposed controller is implemented in real-time on a coupled tank system. From the obtained results, it is shown that the proposed optimal decentralized PI controller exhibits superior control performance to maintain the desired level, for both the nominal as well as the perturbed case as compared to a decentralized PI controller.      

Optimal decentralized control of large scale systems

This paper presents a new optimized decentralized controller design method for solving the tracking and disturbance rejection problems for large-scale linear time-invariant systems, using only low-order decentralized controllers. To illustrate the type of results which can be obtained using the new optimized decentralized control design method, the control of a large flexible space structure is studied and compared with the standard centralized LQR-observer controller. The order of the resultant decentralized controller is much smaller than that of the standard centralized LQR-observer controller. The proposed controller also has certain fail-safe properties and, in addition, it can be five orders of magnitude more robust than the standard LQR-observer controller based on their real stability radii. The new decentralized controller design method is applied to a large flexible space structure system with 5 inputs and 5 outputs and of order 24.     

An internal model approach to autonomous leader/follower trailing for non‐holonomic vehicles

The focus of this paper is on the design of a control architecture of decentralized type for controlling a leader/follower pair of autonomous non‐holonomic vehicles. A fundamental constraint in this trailing control requires that each agent employs local sensor information to process data on the relative position and velocity between its neighbouring vehicles, without relying on global communication with mission control. This constraint poses a challenge in the design of the control system because the reference trajectory to be tracked, which in the case considered in this paper is related to the motion of the leader, is not known a priori. It is shown in the paper that this specific control problem can be approached from the point of view of the internal model paradigm. In particular, once models of the autonomous dynamics of the leader are embedded in a decentralized dynamic controller, the design of the controller can be completed with a robust stabilizer, obtained by using ISS‐gain‐assignment techniques. It is shown that asymptotic convergence of the follower to an arbitrarily small neighbourhood of the desired steady‐state configuration is achieved, despite the presence of possibly large parameter uncertainties, while the motion of each agent remains confined into specified ‘sectors’ to avoid possible collision between neighbouring vehicles during transients. Simulation results are presented to illustrate the design methodology. Copyright © 2006 John Wiley & Sons, Ltd.     

基于Backstepping方法的MIMO过程分散PID控制器设计

A novel decentralized PID controller design procedure based on backstepping principles is presented to operate multiple-input multiple-output (MIMO) dynamic processes. The first key feature of the design procedure is that a whole MIMO control system is decomposed into multiple control loops, therefore the sub-controllers can be efficiently flexibly designed in parallel prototype. The second key feature is that the decentralized controller has equivalency to those designed by backstepping approach. As a complementary support to the design procedure, the sufficient condition of the whole closed-loop system stability is analyzed via the small gain theorem and it can be proven that the process tracking performance is improved. The simulation results of the Shell benchmark control problem are provided to verify the effectiveness and practicality of the proposed decentralized PID control.     

Interconnection-based performance analysis for a class of decentralized controllers

This paper is concerned with decentralized controller design for large-scale interconnected systems of pseudo-hierarchical structure. Given such a system, one can use existing techniques to design a decentralized controller for the reference hierarchical model, obtained by eliminating certain weak interconnections of the original system. Although this indirect controller design is appealing as far as the computational complexity is concerned, it does not necessarily result in satisfactory performance for the original pseudo-hierarchical system. An LQ cost function is defined in order to evaluate the performance discrepancy between the pseudo-hierarchical system and its reference hierarchical model under the designed decentralized controller. A discrete Lyapunov equation is then solved to compute this performance index. However, due to the large-scale nature of the system, this equation cannot be handled efficiently in many real-world systems. Thus, attaining an upper bound on this cost function can be more desirable than finding its exact value, in practice. For this purpose, a novel technique is proposed which only requires solving a simple LMI optimization problem with three variables. The problem is then reduced to a scalar optimization problem, for which an explicit solution is provided. It is also shown that when the original model is exactly hierarchical, then the upper bounds obtained from the LMI and scalar optimization problems will both be equal to zero.     

Backstepping-based Decentralized PID Controller Design for MIMO Processes

A novel decentralized PID controller design procedure based on backstepping principles is presented to operate multiple-input multiple-output(MIMO)dynamic processes.The first key feature of the design procedure is that a whole MIMO control system is decomposed into multiple control loops,therefore the sub-controllers can be efficiently flexibly designed in parallel prototype. The second key feature is that the decentralized controller has equivalency to those designed by backstepping approach.As a complementary support to the design procedure,the sufficient condition of the whole closed-loop system stability is analyzed via the small gain theorem and it can be proven that the process tracking performance is improved.The simulation results of the Shell benchmark control problem are provided to verify the effectiveness and practicality of the proposed decentralized PID control.     

Decentralized adaptive controller design of large-scale uncertain robotic systems

In this paper, we develop a decentralized neural network control design for robotic systems. Using this design, it is not necessary to derive the robotic dynamical system (robotic model) for the control of each of the robotic components, as in traditional robot control. The advantage of the proposed neural network controller is that, under a mild assumption, unknown nonlinear dynamics such as inertia matrix and Coriolis/centripetal matrix and friction, as well as interconnections with arbitrary nonlinear bounds can be accommodated with on-line learning.     

Special decentralized control problems in discrete-time interconnected systems composed of two subsystems

In this paper, some special decentralized control problems are addressed for discrete-time interconnected systems. First it is pointed out that some subsystems must be unstable to ensure stability of the overall system in some special cases. Then a special kind of decentralized control problem is studied. This kind of problem can be viewed as harmonic control among independent subsystems. Research results show that two unstable systems can generate a stable system through some effective cooperations. In addition, a decentralized controller design method based on linear matrix inequality is also given by using parameter-dependent Lyapunov function method developed for the study of robust stability. A special linear star coupled dynamical network is also considered. The central subsystem must be unstable to stabilize the whole network under a special coupling. Several examples are given to illustrate the results.     

Decentralized model predictive control of a multi-evaporator air conditioning system

Temperature control of multiple zones with a multi-evaporator vapor compression system is a common problem in modern air conditioning. Due to the coupled system dynamics, standard decoupled controllers can interfere with each unit′s performance. This paper proposes an architecture that is decentralized and modular, avoiding competing controllers and the practical difficulty of implementing a centralized controller. A model predictive control (MPC) supervisor calculates evaporator cooling and pressure setpoints for each zone, balancing temperature regulation with energy efficiency; these setpoints are tracked by local level controllers, which rely upon MPC's ability to respect constraints in order to maintain safe, efficient operation.     

Decentralized switching control for hierarchical systems

In this paper, a decentralized switching scheme is introduced for uncertain interconnected systems with a structure which is “approximately hierarchical”, and where the switching controller acts on the control agents independently of each other. In this problem, it is assumed that the plant at any point of time can be described by a finite set of linear time-invariant (LTI) finite-dimensional models, but that the switching controller does not require any knowledge of these plant models; the only requirement made is that there exists a known finite set of decentralized controllers, containing at least one controller which can stabilize and regulate the actual physical plant at any time. Simulation results obtained for the proposed decentralized switching controller are given.     

Discrete-time control of continuous systems with approximate decentralized fixed modes

In this paper, the discrete-time control of decentralized continuous-time systems, which have approximate decentralized fixed modes, is studied. It is shown that under certain conditions, discrete-time controllers can improve the overall performance of the decentralized control system, when a linear time-invariant continuous-time controller is ineffective. In order to obtain these conditions, a quantitative measure for different types of approximate fixed modes in a decentralized system is given. In this case, it is shown that discrete-time zero-order hold (ZOH) controllers, and in particular, that generalized sampled-data hold functions (GSHF), can significantly improve the overall performance of the resultant closed-loop system. The proposed sampled-data controller is, in fact, a linear time-varying controller for the continuous-time system.     

H∞ decentralized fuzzy model reference tracking controldesign for nonlinear interconnected systems

In general, due to the interactions among subsystems, it is difficult to design an H_∞ decentralized controller for nonlinear interconnected systems. The model reference tracking control problem of nonlinear interconnected systems is studied via H_∞ decentralized fuzzy control method. First, the nonlinear interconnected system is represented by an equivalent Takagi-Sugeno type fuzzy model. A state feedback decentralized fuzzy control scheme is developed to override the external disturbances such that the H∞ model reference tracking performance is achieved. Furthermore, the stability of the nonlinear interconnected systems is also guaranteed. If states are not all available, a decentralized fuzzy observer is proposed to estimate the states of each subsystem for decentralized control. Consequently, a fuzzy observer-based state feedback decentralized fuzzy controller is proposed to solve the H_∞ tracking control design problem for nonlinear interconnected systems. The problem of H _∞ decentralized fuzzy tracking control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem (EVP). The EVP can be solved very efficiently using convex optimization techniques. Finally, simulation examples are given to illustrate the tracking performance of the proposed methods     

Decentralized global robust stabilization of a class of interconnected minimum-phase nonlinear systems

This paper focuses on a class of large-scale interconnected minimum-phase nonlinear systems with parameter uncertainty and nonlinear interconnections. The uncertain parameters are allowed to be time-varying and enter the systems nonlinearly. The interconnections are bounded by nonlinear functions of states. The problem we address is to design a decentralized robust controller such that the closed-loop large-scale interconnected nonlinear system is globally asymptotically stable for all admissible uncertain parameters and interconnections. It is shown that decentralized global robust stabilization of the system can be achieved using a control law obtained by a recursive design method together with an appropriate Lyapunov function.     

An improved decentralized control method for Bank‐to‐Turn missile autopilot design

In this paper, an improved decentralized control method is proposed to design a bank‐to‐turn (BTT) missile autopilot. Compared to the general diagonal blocked Lyapunov function method, the improved decentralized control method by considering the coupling terms as the structured uncertainty can provide a simpler design, tolerate more types of uncertainties and yield a better dynamic performance. Moreover, this method can be extended to multi‐model systems expediently. Due to the structural constraints, the decentralized controller may not realize the tracking control target under some conditions, and this paper also provides such a condition. The decentralized controller design is formulated in terms of linear matrix inequality (LMI) optimization, and the simulation results demonstrate the effectiveness of the proposed method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

一种具有非线性观测器的分散式自适应鲁棒机器人控制新方案

本文提出一种新型的分散式自适应鲁棒机器人控制方案。它主要解决以下诸方面的问题:1)减少在线计算量;2)通过设置一个非线性观测器来及时修正模型信息,以适应负载及其他因素变化的需要,进而有效地减少所需控制值(尤其当系统处于平稳工作状态时,效果更加明显),相应地,也就减少了系统工作时的动能损耗。这一点对[1]中提出的机器人分散式变结构控制算法有较大改进;3)对系统的不确定性和扰动作用具有鲁棒性。     

High-performance decentralized control design for general interconnected systems with applications in cooperative control

This paper deals with the decentralized control of an interconnected system, where each subsystem has models of all other subsystems (subject to uncertainty). A decentralized controller is constructed based on a reference centralized controller. It is shown that when a priori knowledge of each subsystem about the other subsystems’ models is exact, then the decentralized closed-loop system can perform exactly the same as its centralized counterpart. An easy-to-check necessary and sufficient condition for the internal stability of the decentralized closed-loop system is obtained. Moreover, the stability of the closed-loop system in the presence of the perturbation in the parameters of the system is investigated, and it is shown that the decentralized control system is probably more robust than its centralized counterpart. A proper cost function is then defined to evaluate the closeness of the decentralized closed-loop system to the corresponding centralized control system. This enables the designer to obtain the maximum allowable standard deviation for the modelling errors of the subsystems to achieve a satisfactorily small relative performance deviation with a sufficiently high probability. Finally, the proposed method is exploited to design a near-optimal decentralized control law with respect to a quadratic cost function, whose performance can, under certain conditions, be equal to the minimum achievable performance index corresponding to the centralized LQR control law. The effectiveness of the proposed method is demonstrated in three numerical examples.     

An optimal control based approach to designing plantwide control system architectures

An approach to designing decentralized plantwide control system architectures is presented. The approach is based on splitting the optimal controller gain matrix that results from solving an output optimal control problem into feedback and feedforward parts. These two parts are then used to design and evaluate decentralized control systems. Results for the application of the methodology to a realistic, 4 by 4 reactor with recycle process are given. For this system, the optimal control based approach suggests feedback pairings that are significantly different than those suggested by the steady state RGA. The approach presented can give an indication if MPC is preferred over a decentralized approach to plantwide control. Comparison of the results produced by the best decentralized plantwide system and a model predictive control system are presented.     

Decentralized adaptive control for large-scale time-delay systems with dead-zone input

In this paper, a decentralized adaptive control scheme is proposed to address output tracking of a class of interconnected time-delay subsystems with the input of each loop preceded by an unknown dead-zone. Each local controller is designed using the backstepping technique and consists of a new robust control law and new updating laws. Unknown time-varying delays are compensated by using appropriate Lyapunov-Krasovskii functionals. Furthermore, by introducing a new smooth dead-zone inverse, the proposed backstepping design is able to eliminate the effects resulting from dead-zone nonlinearities in the input. It is shown that the proposed controller can guarantee not only stability, but also good transient performance.