Linear periodic controller design for decentralized control systems

In the decentralized control of linear time-invariant (LTI) systems, a decentralized fixed mode (DFM) is a system mode which is immoveable using an LTI controller, while a quotient DFM (QDFM) is one which is immoveable using any form of nonlinear time-varying compensation. If a system has no unstable DFMs, there are well-known procedures for designing an LTI stabilizing controller; for systems which have unstable DFMs but no unstable QDFMs, we provide a simple design algorithm which yields a linear periodic sampled-data stabilizing controller.     

LMI optimization approach to robust decentralized controller design

A new approach for design of robust decentralized controllers for continuous linear time‐invariant systems is proposed using linear matrix inequalities (LMIs). The proposed method is based on closed‐loop diagonal dominance. Sufficient conditions for closed‐loop stability and closed‐loop block‐diagonal dominance are obtained. Satisfying the obtained conditions is formulated as an optimization problem with a system of LMI constraints. By adding an extra LMI constraint to the system of LMI constraints in the optimization problem, the robust control is addressed as well. Accordingly, the decentralized robust control problem for a multivariable system is reduced to an optimization problem for a system of LMI constraints to be feasible. An example is given to show the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

A model reference quantitative feedback design theory with application to turbomachinery

A new decentralized robust control design framework, model reference quantitative feedback design (MRQFD), is developed for the design of the MIMO parametric uncertain control systems. An internal model reference loop is proposed to obtain the achievement of generalized diagonal dominance (GDD) and the reduction of uncertainty in the resultant compensated internal loop system. Based on nonnegative matrix theory, a useful design guide is derived to achieve the GDD condition for the internal model reference loop. Then a sensitivity-based quantitative feedback design (QFD) method is developed and used to solve the resulting series of single-loop QFD problems. The MIMO quantitative specifications are guaranteed to be satisfied by the proposed design framework for largely uncertain systems. A successful application to the design of a robust multivariable controller for the Allison PD-514 aircraft turbine engine is presented to demonstrate the effectiveness of the methodology developed here.     

Fixed-structure robust controller synthesis via decentralized static output feedback

This paper describes and illustrates a unified methodology for robust, fixed-structure controller synthesis. The approach is based upon direct fixed-structure controller synthesis using a decentralized static output feedback formulation as a general framework for representing a large class of controller structures. Scaled Popov bounds for the real structured singular value are used to account for real parameter uncertainty and provide the means for optimizing a worst-case ℋ︁₂ cost bound with respect to the free parameters of the controller. Quasi-Newton optimization algorithms are used to solve the resulting numerical optimization problem. Initial stability multiplier and scaling matrices needed in scaled Popov synthesis are obtained by solving an LMI feasibility problem. Using both centralized and decentralized controller structures, numerical results are obtained for a 16th-order acoustic duct model with uncertain damped natural frequencies and for a two-dimensional beam-spring model with uncertain actuator locations. © 1998 John Wiley & Sons, Ltd.     

A power system nonlinear adaptive decentralized controller design

In this paper, a novel excitation control is designed for improvement of transient stability of power systems. The control algorithm is based on the adaptive backstepping method in a recursive way without linearizing the system model. Lyapunov function method is applied in designing the controller to ensure the convergence of the power angle, relative speed of the generator and the active electrical power delivered by the generator when a large fault occurs. Compared with the existing nonlinear decentralized control approaches, the proposed controller has no requirement for the bounds of interconnections in the power system. And the new approach does not need the existence of solution of a designed algebraic Riccati equation. Furthermore, the transient stability performance of power systems can also be improved by the designed control approach. The efficacy of the designed controller has been demonstrated in a multimachine power system. Simulation results show transient stability enhancement of a power system in the face of a large sudden fault.     

Effective transfer function method for decentralized control system design of multi-input multi-output processes

In terms of relative gain and relative frequency, the effective transfer function for independent controller design for multi-input multi-output processes is provided in this paper. Differing from existing equivalent transfer functions, the proposed effective transfer function provides both gain and phase information for decentralized controller design in a simple and straightforward manner. The interaction effects for a particular loop from all other closed loops are directly incorporated into the effective transfer functions in four ways. Consequently, the decentralized controllers can be independently designed by employing the single loop tuning techniques. This design method is simple, straightforward, easy to understand and implement by field engineers. Several multivariable industrial processes with different interaction modes are employed to demonstrate the effectiveness and simplicity of the method.     

Equilibrium stability in decentralized design systems

The focus of this paper is on complex systems, and it presents a theoretical study of the design of complex engineering systems. More particularly, this paper studies the stability of equilibria in decentralized design environments. Indeed, the decentralization of decisions is often recommended in the design of complex systems, and the decomposition and coordination of decisions are a great challenge. The mechanisms behind this network of decentralized design decisions create difficult management and coordination issues. However, developing efficient design processes is paramount, especially with market pressures and customer expectations. Standard techniques to modelling and solving decentralized design problems typically fail to understand the underlying dynamics of the decentralized processes and therefore result in suboptimal solutions. This paper aims to model and understand the mechanisms and dynamics behind a decentralized set of decisions within a complex design process. Complex systems that are multidisciplinary and highly nonlinear in nature are the primary focus of this paper. Therefore, techniques such as response surface approximations and Game Theory are used to discuss and solve the issues related to multidisciplinary optimization. Nonlinear control theory is used in this paper as a new approach to study the stability of equilibrium points of the design space. Illustrations of the results are provided in the form of the study of the decentralized design of a pressure vessel.     

On the parametrization of all decentralized stabilizing controllers

A novel parametrization of all decentralized stabilizing controllers is provided in terms of a single parameter Q that is constrained to satisfy a finite number of quadratic equations. The results are presented in a general algebraic framework and apply to linear time-invariant systems. Implications of this parametrization for decentralized control system performance are also discussed.     

内模控制系统鲁棒跟踪控制器的参数化及优化

针对最常用的2自由度内模控制系统,利用基于传递函数互质分解的频域理论,推导了存在模型失配且参考输入和扰动为任意已知函数时,所有能实现稳态无差跟踪的前馈控制器和反馈滤波器的参数化表达式.所得结论同时适用干连续和离散时间系统,并可在参数化基础上实现频域的优化控制.     

Multi-loop design of multi-scale controllers for multivariable processes

Based on the recently proposed (SISO) multi-scale control scheme, a new approach is introduced to design multi-loop controllers for multivariable processes. The basic feature of the multi-scale control scheme is to decompose a given plant into a sum of basic modes. To achieve good nominal control performance and performance robustness, a set of sub-controllers are designed based on the plant modes in such a way that they are mutually enhanced with each other so as to optimize the overall control objective. It is shown that the designed multi-scale controller is equivalent to a conventional PID controller augmented with a filter. The multi-scale control scheme offers a systematic approach to designing multi-loop PID controllers augmented with filters. Numerical studies show that the proposed multi-loop multi-scale controllers provide improved nominal performance and performance robustness over some well-established multi-loop PID controller schemes.     

A generic approach to the design of decentralized linear output- feedback controllers

A sufficient condition for failure-tolerant performance stabilization in a desirable performance region under decentralized linear output-feedback is established. To exploit the flexibility in decentralized control beyond multivariable pole assignment, and to address the subsystem design objectives along with those of the overall system, a generic problem on decentralized linear output-feedback is then defined. The problem is reformulated in terms of a constrained nonlinear optimization problem. The proposed methodology results in the optimal reconciliation of failure-tolerant robust performance of the overall system, and (maximal) robustness, disturbance rejection, noninteractive performance, reliability and low actuator gains in the isolated subsystems in the face of unstructured perturbations in the controller and plant parameters. The effectiveness of the proposed approach is demonstrated by a numerical example.     

A decentralized model for scheduling independent tasks in Federated Grids

In this paper we present a decentralized model for scheduling independent tasks in Federated Grids. This model consists of a set of meta-schedulers on each of the grid infrastructures of the Federated Grid. Each meta-scheduler has to implement a mapping strategy in order to improve two of the most common objective functions of task scheduling problems: makespan and resource performance. We consider four possible algorithms that have to provide a simple, decoupled, and coarse-grained solution that could be deployed in any Grid. The main axis of the algorithms is that they consider the performance of the infrastructures forming the Federated Grid, not only their state.     

Sequential stability and optimization of large scale decentralized systems

The notion of sequential stability in the synthesis of decentralized control for large scale systems is introduced in this paper. This notion is concerned with the property of a synthesis technique which allows the decentralized controllers of a large scale system to be connected to the systems one at a time (in a sequential way) such that the controlled system remains stable at all times. The motivation for introducing this constraint is that in practical terms, it is generally impossible to connect all decentralized controllers to a system simultaneously (due to the difficulties of communication etc.). A practical design procedure for the synthesis of a decentralized robust regulator for the servomechanism problem, based on a sequential approach to system design, is then given. The design procedure proceeds in two stages: (1) decentralized controllers are initially connected to the system in a sequential way to guarantee stability; (2) the parameters of the decentralized controllers are then sequentially adjusted, in a way to guarantee stability, so as to optimize a given performance index for the system. Applications of the above procedure are then made to the synthesis of centralized multivariable controllers and to the decentralized robust control of unknown systems.A simple example is given to illustrate the design synthesis.     

Design of decentralized robust load-frequency controller based on SVD method

A decentralized robust control scheme is presented for the load-frequency control of interconnected power systems with uncertain parameters. A singular value decomposition (SVD) technique and Lyapunov stability theory are adopted to implement a decentralized robust controller. The stability analysis of the closed-loop interconnected systems for all admissible uncertainties is discussed. The performance robustness of the proposed decentralized robust control scheme has been verified through simulation studies on a two-area power system model. The effectiveness of the decentralized control algorithm is compared to that of a centralized robust one. It has been found that both control schemes have almost the same performance with integral control action in the presence of parametric uncertainty in the plant.     

Characterizations of decentralized fixed modes for interconnected systems

A study of the characterization of decentralized fixed modes for large-scale interconnected systems is made. This is done by obtaining a recursive characterization of decentralized fixed modes, in which the existence of fixed modes of a ν-control agent system is expressed in terms of the existence of fixed modes of ν ? 1 control agent systems. An interpretation of these conditions is then made in the frequency domain. Simple conditions, in terms of the controllability of the system's subsystems, are then found for a composite system consisting of ν interconnected subsystems to have no decentralized fixed modes. This result clarifies some recent discussion on the fixed modes of interconnected systems; in particular, it proves that Fessas's conjecture is true for systems with two control agents, but false for systems with more than two control agents.     

Stabilizing decentralized model predictive control of nonlinear systems

This note presents a stabilizing decentralized model predictive control (MPC) algorithm for nonlinear discrete time systems. No information is assumed to be exchanged between local control laws. The stability proof relies on the inclusion of a contractive constraint in the formulation of the MPC problem.     

一类模糊P I D 控制器的鲁棒优化设计

研究一类模糊 PID控制器的鲁棒设计。以小增益定理分析得到该模糊 PID控制系统稳定性条件。针对参数摄动系统的“最坏点”,用该稳定性条件作为约束 ,采用遗传算法对标称系统的性能进行优化 ,求得优化鲁棒控制器。以倒立摆为例进行鲁棒模糊 PID控制器的设计 ,实验结果表明了该方法的有效性     

Fractional IMC-PID-filter controllers design for non integer order systems

Fractional order controller design with a small number of tuning parameters is very attractive. Few attempts have been done recently for some limited cases of models. In this paper, a new approach is developed to design simple fractional-order controllers to handle fractional order processes. The fractional property is not especially imposed by the controller structure but by the closed-loop reference model. The resulting controller is fractional but it has a very interesting structure for its implementation. Indeed, the controller can be decomposed into two transfer functions: a PI^υD^μ-controller and a simple fractional filter. The new structure is named PI^υD^μ-FOF-controller. The design method is based on the internal model control (IMC) paradigm.     

The design of robust feedback controllers in the time domain

In this new approach to designing multivariable feedback controllers in the time domain the model uncertainties are dealt with in the sense of unknown-but-bounded uncertainties. They are described by multi-input multi-output comparison systems. Thus, the character of the plant as a multi variable dynamical system is preserved even in the considerations of the uncertainties. The controller parameters are selected by means of well-known design algorithms. The robustness of the controller is investigated on the basis of a stability condition and an estimate of the input-output behaviour of the incompletely known closed-loop original system. The results are illustrated by a practical design example.