Reduced-order Dynamic Compensation Research Articles

Leader-Following Output Consensus for High-Order Nonlinear Multiagent Systems

This technical note focuses on the leader-following output consensus problem for a class of high-order nonlinear multiagent systems under a fixed directed graph. To obtain the global result of output feedback control for the system with the less conservative condition on nonlinear terms than traditional Lipschitz one, the novel reduced-order dynamic compensator is constructed. By introducing an appropriate state transformation, a new fully distributed output feedback control method is proposed, which greatly simplifies the design procedure compared with the backstepping method. The distributed linear-like controller with a dynamic gain is designed for each agent based only on the relative output measurements of neighboring agents. The condition that the orders of all agents should be the same is not needed anymore with the proposed method; thus, the novel result will have extensive applications. Finally, the theoretical results are supported by a numerical simulation.

Stabilization of linear systems with simultaneous state, actuation, and measurement delays

This paper considers the problem of stabilizing continuous-time linear systems with time delays. Specifically, a fixedorder (i.e. full- and reduced-order) dynamic compensation problem is addressed for systems with simultaneous state, input, and output delays. The principal result involves sufficient conditions for characterizing fixed-order dynamic controllers for delay systems via a system of modified coupled Riccati equations. The controllers obtained are delay independent and hence apply to systems with arbitrary unknown delay.

A periodic fixed-structure approach to multirate control

We develop an approach to designing reduced-order multirate controllers. A discrete-time model that accounts for the multirate timing sequence of measurements is presented and is shown to have periodically time-varying dynamics. Using discrete-time stability theory, the optimal projection approach to fixed-order (i.e. full- and reduced-order) dynamic compensation is generalized to obtain reduced-order periodic controllers that account for the multirate architecture. It is shown that the optimal reduced-order controller is characterized by means of a periodically time-varying system of equations consisting of coupled Riccati and Lyapunov equations. In addition, the multirate static output-feedback control problem is considered. For both problems, the design equations are presented in a concise, unified manner to facilitate their accessibility for developing numerical algorithms for practical applications. >

Optimal dynamic output feedback for nonzero set point regulation: the discrete-time case

Standard discrete-time LQG theory is generalized to a regulation problem involving a priori specified nonzero set points for the state and control variables and nonzero-mean disturbances. The optimal control law consists of a closed loop component feeding back measurements and a constant open-loop component which accounts for the nonzero set point and the nonzero mean disturbance. For generality, the results are obtained for the problem of fixed-order (i.e., full- and reduced-order) dynamic compensation. It is shown that the closed-loop controller can be designed independently of the open-loop control.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Stability robustness bounds for discrete-time linear regulators

Stability robustness analysis and design for linear multivariable discrete-time systems with bounded uncertainties are discussed. Robust stability of the full-state feedback linear quadratic (LQ) regulator in the presence of perturbations (modelling errors) of the system matrices is investigated. These results are based on a recently developed bound on elemental (structured) time-varying perturbations of an asymptotically stable linear time-invariant discrete-time system. Lyapunov theory and singular value decomposition techniques are employed in deriving these bounds. Extensions of these results to linear stochastic systems with the Kalman filter as the stale estimator (LQG regulators) and to reduced-order dynamic compensator feedback are described. A state feedback control design method is presented for LQ regulators, using a quantitative measure called the Stability Robustness Index. Simple examples illustrate these new results.

Reduced-order dynamic compensator design for stability robustness of linear discrete-time systems

A reduced-order dynamic compensator design is presented with stability robustness for linear discrete systems, by including a stability robustness component in addition to the standard quadratic state and control terms in the performance criterion. The robustness component is based on an unstructured perturbation stability bound for time varying perturbations. The controller design is developed by the parameter optimization technique and involves the solution of five algebraic matrix equations, four of which are discrete-time Lyapunov matrix equations. >

Robust H∞ control design for systems with structured parameter uncertainty

In a recent paper a unification of the H 2 (LQG) and H ∞ control-design problems was obtained in terms of modified algebraic Riccati equations. In the present paper these results are extended to guarantee robust H 2 and H ∞ performance in the presence of structured real-valued parameter variiations ( ΔA, ΔB, ΔC) in the state space model. For design flexibility the paper considers two distinct types of uncertainty bounds for both full- and reduced-order dynamic compensation. An important special case of these results generates H 2/ H ∞ controller designs with guaranteed gain margins.

Unified optimal projection equations for simultaneous reduced-order, robust modelling, estimation and control

An optimal design problem which unifies reduced-order modelling, estimation and control problems is stated. Necessary conditions for optimality are obtained in the form of a coupled system of modified Riccati and Lyapunov equations. The results permit treatment of several new problems, such as reduced-order dynamic compensation with partially known disturbances and unified reduced-order control and estimation. Upon appropriate specialization, results obtained previously for the individual problems of reduced-order modelling, estimation and control are recovered. An additional feature is the inclusion of parameter uncertainty bounds so that the necessary conditions for an auxiliary minimization problem serve as sufficient conditions for simultaneous robust, reduced-order modelling, estimation and control.

Optimal projection equations for discrete-time fixed-order dynamic compensation of linear systems with multiplicative white noise

The optimal projection equations for discrete-time reduced-order dynamic compensation are generalized to include the effects of state-, control- and measurement-dependent noise. In addition, the discrete-time static output feedback problem with multiplicative disturbances is considered. For both problems, the design equations are presented in a concise, unified manner to facilitate their accessibility for developing numerical algorithms for practical applications.

Integrated Control of Distributed Parameter Systems

This work develops a new method for designing low-order dynamic compensators. This design procedure integrates the LOG-based reduced-order dynamic compensator synthesis with the low-authority algebraic controller synthesis. A comparison with a well-known method which exploits similar concepts is also presented

Linear discrete stochastic control with a reduced-order dynamic compensator

In continuous-time linear stochastic control with a fixed structure, reduced-order, dynamic compensator one obtains a quasisingular problem whereby part of the structure is arbitrary. The dual of this problem in discrete time is considered with a more general formulation. Using a quadratic performance index, the Hamiltonian for obtaining the necessary conditions is obtained which may be used to define the optimal linear reduced-order dynamic compensator and the controller gain. It is shown that the discrete problem does not have the quasisingular property of the continuous-time case as is seen by consideration of the Hamiltonian.