Performance limitations in decentralized control

In decentralized control of multivariable systems, the system is decomposed into a number of subsystems and individual controllers are designed for each subsystem. Advantages of such decomposition include reduced modelling requirements and ease of implementation. However, a potential disadvantage is a reduction in achievable control performance due to restricted controller structure. In this paper we consider performance limitations from non-minimum phase transmission zeros in decentralized control. In particular, we derive conditions on when closing the loop around one subsystem moves transmission zeros of other subsystems across the imaginary axis. Such zero crossings may occur regardless of the existence of non-minimum phase behavior in the open-loop system, and may, therefore, represent performance limitations specific to the use of decentralized controllers.     

Decentralized blocking zeros and the decentralized strongstabilization problem

This paper is concerned with a new system theoretic concept, decentralized blocking zeros, and its applications in the design of decentralized controllers for linear time-invariant finite-dimensional systems. The concept of decentralized blocking zeros is a generalization of its centralized counterpart to multichannel systems under decentralized control. Decentralized blocking zeros are defined as the common blocking zeros of the main diagonal transfer matrices and various complementary transfer matrices of a given plant. As an application of this concept, we consider the decentralized strong stabilization problem (DSSP) where the objective is to stabilize a plant using a stable decentralized controller. It is shown that a parity interlacing property should be satisfied among the real unstable poles and real unstable decentralized blocking zeros of the plant for the DSSP to be solvable. That parity interlacing property is also sufficient for the solution of the DSSP for a large class of plants satisfying a certain connectivity condition. The DSSP is exploited in the solution of a special decentralized simultaneous stabilization problem, called the decentralized concurrent stabilization problem (DCSP). Various applications of the DCSP in the design of controllers for large-scale systems are also discussed     

Computation of the zeros of linear multivariable systems

The various subsets of the entire set of system zeros are unambiguously characterized in a manner which permits the definitive computation of the sets of centralized transmission and decoupling zeros by solving appropriate generalized eigenvalue problems using widely available ‘ expertly written ’ software embodying powerful QZ techniques, Furthermore, it is indicated that the present method is immediately applicable to the computation of the sets of decentralized fixed modes and decentralized transmission zeros with respect to any set of decentralized controllers.     

Fixed zeros of decentralized control systems

Considers the notion of decentralized fixed zeros for linear, time-invariant, finite-dimensional systems. For an N-channel plant that is free of unstable decentralized fixed modes, an unstable decentralized fixed zero of channel i (1⩽i⩽N) is defined as an element of the closed right half-plane, which remains as a blocking zero of that channel under the application of every set of N-1 controllers around the other channels, which make the resulting single-channel system stabilizable and detectable. The paper gives a complete characterization of unstable decentralized fixed zeros in terms of system-invariant zeros     

Fundamental limitation on achievable decentralized performance

A commonly accepted fact is that the diagonal structure of the decentralized controller poses fundamental limitations on the achievable performance, but few quantitative results are available for measuring these limitations. This paper provides a lower bound on the achievable quality of disturbance rejection using a decentralized controller for stable discrete time linear systems with time delays, which do not contain any finite zeros on or outside the unit circle. The proposed result is useful for assessing when full multivariable controllers can provide significantly improved performance, as compared to decentralized controllers. The results are also extended to the case, where the individual subcontrollers are restricted to be PID controllers.     

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.     

Two-delay robust digital control and its applications-avoiding theproblem on unstable limiting zeros

In the design of linear control systems, the existence of unstable zeros makes it difficult to construct many control systems. When the usual digital control scheme is used, unstable zeros appear in the discrete-time model due to the existence of limiting zeros even though the continuous-time plant is minimal phase. To avoid this unstable zero problem, two new digital control schemes, called two-delay output control and two-delay input control, are proposed. These control systems are proved to have no finite zeros. Asymptotic inverse systems, pole assignable unknown input observers, and output feedback controllers having the LTR (loop transfer recovery) property are developed using the two-delay output control. Zero assignable control systems and model matching control systems are developed using the two-delay input control     

Decentralized Resilient H∞ Load Frequency Control for Cyber-Physical Power Systems Under DoS Attacks

This paper designs a decentralized resilient H_∞ load frequency control (LFC) scheme for multi-area cyber-physical power systems (CPPSs). Under the network-based control framework, the sampled measurements are transmitted through the communication networks, which may be attacked by energy-limited denial-of-service (DoS) attacks with a characterization of the maximum count of continuous data losses (resilience index). Each area is controlled in a decentralized mode, and the impacts on one area from other areas via their interconnections are regarded as the additional load disturbance of this area. Then, the closed-loop LFC system of each area under DoS attacks is modeled as an aperiodic sampled-data control system with external disturbances. Under this modeling, a decentralized resilient H_∞ scheme is presented to design the state-feedback controllers with guaranteed H_∞ performance and resilience index based on a novel transmission interval-dependent loop functional method. When given the controllers, the proposed scheme can obtain a less conservative H_∞ performance and resilience index that the LFC system can tolerate. The effectiveness of the proposed LFC scheme is evaluated on a one-area CPPS and two three-area CPPSs under DoS attacks.      

Adaptive minimum-variance and model-reference control for non-minimum phase systems

The well known minimum-variance adaptive controller and model-reference controller have been extended to include non-minimum phase systems. The simplicity of the original controllers is maintained. By allowing the intersample control signal to have two values, rather than one, the system zeros can be allocated to some prespecified locations. The stability issue related to both controllers for non-minimum phase systems is thus resolved.     

Decomposition and decentralized control of systems with multi-overlapping structure

This paper considers decomposition and decentralized control of systems with multi-overlapping structure. It is demonstrated, using the inclusion principle, how the systems with longitudinal, loop and radial topologies can be expanded, and how the results can be used for designing controllers under information structure constraints. The proposed methodology is applied to automatic generation control (AGC) of an electric power system.     

On the periodic coordination of linear stochastic systems

The decentralized stochastic control of a linear dynamic system consisting of several subsystems is considered. A two-level approach is used by the introduction of a coordinator who collects measurements from the local controllers periodically and in return transmits coordinating parameters. Two types of coordination are considered: open-loop feedback and closed loop. The resulting control laws are found to be intuitively attractive.     

Stability conditions for the sequential design of non-diagonal multivariable feedback controllers

Sufficient conditions to guarantee closed-loop internal stability for sequentially designed multivariable feedback control systems are developed in this paper. The class of MIMO systems considered have transfer function matrices that are square and invertible. The contributions of these stability conditions to the knowledge base of sequential loop design are two-fold. First, unstable Smith-McMillan pole-zero cancellations in the feedback loop are explicitly considered, thus ensuring internal closed-loop stability. Second, the class of systems addressed is expanded to include MIMO systems with non-minimum phase Smith-McMillan zeros. An important feature of the proposed stability conditions is that the elements of the controller matrix which must be non-zero to achieve internal stability are transparently displayed. As a result, only those off-diagonal controllers needed to achieve the pre-specified stability objectives are used, thus reducing implementation complexity. The application of the stability criteria is demonstrated in a design example for an unstable, non-minimum phase (2 2 2) system.     

Time-varying feedback laws for decentralized control

Decentralized control schemes are considered for time-invariant, finite dimensional, linear systems with know state equations. It is assumed that the systems are reachable and observable at a fictitious centralized control station, and that there is strong connectivity between the decentralized control stations via the system where necessary. It is shown that whether or not there are decentralized fixed modes in the open-loop system, periodically varying feedback gains at all but one of the control stations permit the remaining control station to observe and control the system given knowledge of the control laws implemented at the other control stations. Certain time-invariant systems which cannot be stabilized by decentralized time-invariant controllers, namely those with unstable decentralized fixed modes, can thus be stabilized by decentralized time-varying controllers.     

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.     

On the quantitative characterization of approximate decentralized fixed modes using transmission zeros

The spectrum of a linear time-invariant multivariable system, using decentralized linear time-invariant controllers, can only be assigned to a symmetric set of complex numbers that include the decentralized fixed modes (DFM). Hence only systems with stable DFM can be stabilized. Although the concept of DFM characterizes when a decentralized controller can stabilize a system, it gives no indication of howhard it is to effect such a stabilization. A system is considered hard to stabilize if large controller gains are required. Modes that are hard to shift are termedapproximate decentralized fixed modes. In this paper two new assignability measures which quantify the difficulty of shifting a mode are derived. The first is coordinate invariant and is based on the distance between a mode and a set of transmission zeros. The second is coordinate dependent and is based on the minimum singular value of a set of transmission zero matrices. This work has been supported by the Natural Sciences are Engineering Research Council of Canada under Grant No. A4396.     

Decentralized adaptive consensus control for discrete‐time heterogeneous semiparametric multiagent systems

Different from the consensus control of traditional multiagent systems, this paper studies the decentralized adaptive consensus control for discrete‐time heterogeneous hidden leader‐following semiparametric multiagent system, in which the dynamic equation of each agent has both parametric uncertainties and nonparametric uncertainties. In the considered system, there is a hidden leader agent who can receive the reference signal, but it can only affect the states of those agents who are in its neighborhood. For other following agents, they do not know the leader's existence or the reference signal, and they can only receive information from their neighbors. Our goal is to design decentralized adaptive controllers to make sure that all agents can track the reference signal, and the closed‐loop system achieves consensus in the presence of mutual coupling relations. Due to the existence of both parametric and nonparametric uncertainties in the system, we need to estimate them separately. For the parametric part, we propose a novel dead zone with threshold converging to zero to modify the traditional gradient update law, while for the nonparametric part, we introduce an auxiliary variable including both two uncertainties to facilitate the nonparametric uncertainties compensation. Based on the certainty equivalence principle in adaptive control theory, the decentralized adaptive controller is designed for each agent to make sure that all of them can track the reference signal. Finally, under the proposed control protocol, strict mathematical proofs are given by using Lyapunov theory; then, simulation results are provided to demonstrate the effectiveness of proposed decentralized adaptive controllers.     

The Mimo Predictive Pid Controller Design

This paper is concerned with the design of Multi‐Inputs and Multi‐Outputs (MIMO) predictive PID controllers, which have similar performance to that obtainable from model‐based predictive controllers. A new PID control structure is defined which incorporates the prediction of future outputs and uses future set point. A method is proposed to calculate the optimal values of the PID gains from generalised predictive control results. A decentralized version of the predictive PID controllers is presented and the stability of the closed loop system is studied. Simulation studies demonstrate the superior performance of the proposed controller compared with a conventional PID controller. The results are also compared with generalised predictive control solutions.     

OPTIMIZATION OF DECENTRALIZED PI/PID CONTROLLERS BASED ON GENETIC ALGORITHM

In this paper, an optimization method of tuning decentralized PI/PID controllers based on genetic algorithms is presented. First, the existence of decentralized PI controllers with integrity is examined. Then, stable regions of each PI/PID controller parameters are calculated as the feasible area to be exploited, and the optimal PI/PID controllers are obtained by using a real‐coded genetic algorithm with elitist strategy, to meet the design specifications for the whole control system. The proposed method is applied to six examples from literature. Simulation results demonstrate that the proposed decentralized PI control is compatible to the referenced method while the decentralized PID control is better than the referenced method, and the proposed method is feasible for more complicated control systems optimizations.     

Independent design of robust partially decentralized controllers

An independent design method for robust partially decentralized controllers is developed. In the proposed design method, the partially decentralized control system is first expanded to the nonsquare decentralized structure. Using the Internal Model Control parametrization, the independent design procedure for robust nonsquare decentralized controllers can then be applied directly to the expanded system. Two examples, including a nonlinear stirred mixing tank, are used to illustrate the developed design method and a comparison to a decentralized controller is made.     

Controller synthesis for sign-invariant impulse response

In this paper, we consider the problem of designing controllers for discrete-time linear time-invariant (LTI) plants that render the closed-loop impulse response nonnegative. Such systems have a non-undershooting and non-overshooting step response. We first show that the impulse response of any discrete-time LTI system changes sign at least "r" times if it has "r" real, positive zeros outside a circular disk centered at the origin and containing all its poles. We then show that a necessary and sufficient condition on the plant for the existence of a compensator that makes the closed loop impulse response sign invariant is that there be no real, positive, nonminimum phase plant zeros. Finally, we show, by construction, how such a compensator may be synthesized when the plant does satisfy the existence condition.