Dynamic Output Feedback Compensator Research Articles

Global state regulation of time-delay minimum-phase systems by delay-free dynamic compensation

This paper studies the global control problem, in the sense of “almost stabilization” or state regulation, for a class of time-delay minimum-phase nonlinear systems via delay-free dynamic compensation. Both dynamic state and output feedback control schemes are developed. By taking advantage of dynamic rather than static feedback, we design delay-independent dynamic state and output feedback compensators, respectively, to achieve asymptotic state regulation with global stability. In the case of dynamic state feedback, a structural condition is imposed on the inverse dynamics that are nonlinear yet imply linear zero dynamics. In the case of dynamic output feedback, more strict conditions on the nonlinearity are characterized to guarantee the existence of a dynamic output controller. In both cases, it is proved by the Lyapunov–Krasovskii functional method, combined with the Barbalat’s lemma, that all the states of the time-delay minimum-phase systems are regulated to zero and boundedness of the closed-loop system is ensured. Two examples are given to validate the proposed delay-free dynamic compensators.

Output Feedback Constrained Regulation of Linear Systems via Controlled-Invariant Sets

Design of output feedback controllers applied to the regulation problem for constrained linear discrete-time systems via set-invariance techniques is studied. Output feedback controlled-invariant (OFCI) polyhedra are used to ensure that state and input constraints are satisfied even in the presence of additive disturbances and measurement noise. Necessary and sufficient conditions for a polyhedral set to be OFCI are presented. A dynamic output feedback compensator is proposed through the construction of an OFCI set for an augmented system. Based on the measured output and on the compensator state, which constitutes an estimate of the system state, a suitable control sequence is computed via linear programming to enforce the constraints. The uncertainty on the state is progressively reduced using the contraction of an invariant set associated to the estimator. With our approach, as illustrated through numerical examples, by embedding the estimator in the compensator structure and using the OFCI concept, it is possible to obtain solutions with larger sets of admissible initial states and admissible initial estimation errors, compared to approaches available in the literature.

One Step Anti-Windup Design for Nonlinear Systems: An Indirect LMI-Based Approach

This paper proposes an indirect linear matrix inequality (LMI) approach to design one step anti-windup dynamic output feedback compensator for a class of nonlinear systems subject to actuator saturation. When the system state satisfies certain conditions, the nonlinear system can be reconstructed accurately by T-S fuzzy model, based on Lyapunov stability analysis and a result about matrix inequality, we show that the feasibility of an LMI guarantees the solvability of the corresponding one step anti-windup compensator. Once the solvability issue is determined, then we give an algorithm of one step anti-windup nonlinear dynamic output feedback compensator. The effectiveness of the proposed method is illustrated with numerical example.

Transition between grid-connected mode and islanded mode in VSI-fed microgrids

This paper investigates the behaviour of a microgrid system during transition between grid-connected mode and islanded mode of operation. During the grid-connected mode the microgrid sources will be controlled to provide constant real and reactive power injection. During the islanded mode the sources will be controlled to provide constant voltage and frequency operation. Special control schemes are needed to ensure proper transition from constant P–Q mode to constant f–V mode and vice versa. Transition from one mode to other will introduce severe transients in the system. Two kinds of transition schemes based on the status of the off-line controller are discussed and a comparative study is presented for various step changes in the load. An additional-pole-placement-based output feedback controller augmentation during transition between the modes is proposed to reduce the transients. A static output feedback compensator design is proposed for the grid connected to island mode transition and a dynamic output feedback compensator design is proposed for resynchronisation. The performance of the output feedback controllers is tested under various operating conditions and found to be satisfactory for the tested conditions.

Sensorless H∞ speed-tracking synthesis for surface-mount permanent magnet synchronous motor

In this paper, a sensorless speed tracking control is proposed for a surface-mount permanent magnet synchronous motor by using a nonlinear H∞-controller via stator currents measurements for feedback. An output feedback nonlinear H∞-controller was designed such that the undisturbed system is uniformly asymptotically stable around the desired speed reference, while also the effects of external vanishing and non-vanishing disturbances, noise, and input backlash were attenuated locally. The rotor position was calculated from the causal dynamic output feedback compensator and from the desired speed reference. The existence of the proper solutions of the perturbed differential Riccati equations ensures stabilizability and detectability of the control system. The efficiency of the proposed sensorless controller was supported by numerical simulations.

Dynamic Output Feedback Compensation Control for Discrete Closed-Loop Nonlinear System with Multiple Time-Delays

This paper addresses the dynamic output feedback control problem for a class of discrete system with uncertainties and multiple time-delays. First, the system is decomposed into two subsystems based on the output matrix and input control matrix. Secondly, a dynamic compensator is employed for the first subsystem, and then, given the multiple uncertainties, the output feedback controller is designed based on the second subsystem and the dynamic compensator. Thirdly, by choosing the Lyapunov-Krasovskii function, it can be seen that the developed controller makes the closed-loop system convergent to an adjustable region, which can be rendered arbitrary small by adjusting design parameters. Compared with the previous researches, the proposed controller is not only smooth and memoryless, but also only dependent on the system output. Furthermore, with the given dynamic compensator, the controller design conditions are relaxed, while the approach is extended to the conventional nonlinear system. Finally, numerical example is given to illustrate the effectiveness of the theoretical results.

Output feedback control of a class of nonminimum-phase nonlinear systems

Summary The problem of global stabilization by output feedback is investigated in this paper for a class of nonminimum-phase nonlinear systems. The system under consideration has a cascade configuration that consists of a driven system known as the inverse dynamics and a driving system. It is proved that although the zero dynamics may be unstable, there is an output feedback controller, globally stabilizing the nonminimum-phase system if both driven and driving systems have a lower-triangular form and satisfy a Lipschitz-like condition, and the inverse dynamics satisfy a stronger version of input-to-state stabilizability condition. A design procedure is provided for the construction of an n-dimensional dynamic output feedback compensator. Examples and simulations are also given to validate the effectiveness of the proposed output feedback controller. Copyright © 2016 John Wiley & Sons, Ltd.

Global asymptotic stabilisation in probability of nonlinear stochastic systems via passivity

ABSTRACTThe purpose of this paper is to develop a systematic method for global asymptotic stabilisation in probability of nonlinear control stochastic systems with stable in probability unforced dynamics. The method is based on the theory of passivity for nonaffine stochastic differential systems combined with the technique of Lyapunov asymptotic stability in probability for stochastic differential equations. In particular, we prove that a nonlinear stochastic differential system whose unforced dynamics are Lyapunov stable in probability is globally asymptotically stabilisable in probability provided some rank conditions involving the affine part of the system coefficients are satisfied. In this framework, we show that a stabilising smooth state feedback law can be designed explicitly. A dynamic output feedback compensator for a class of nonaffine stochastic systems is constructed as an application of our analysis.

Fuzzy dynamic output feedback control through nonlinear Takagi–Sugeno models

We present a convex way to design a fuzzy dynamic output feedback compensator for locally stabilizing a class of nonlinear discrete-time systems. This class consists of the systems described by Takagi–Sugeno (T–S) models with a sector bounded nonlinear additive term and saturated control signals. The local stabilization takes into account the domain of validity of these T–S models, which is a key issue for practical applications. Two types of nonlinear fuzzy compensators are considered, one having all matrices of the controller depending on fuzzy-grade membership functions and the other with only a subset of the matrices with such a dependency. The controller design includes a fuzzy anti-windup gain that handles saturating actuators. Besides, a time-performance index based on the λ-contractivity of the level set of the fuzzy Lyapunov function is proposed regarding the closed-loop system. Examples are given to illustrate the effectiveness of this proposal.

Consensus of descriptor multi‐agent systems via dynamic compensators

This study deals with the consensus problem via dynamic output feedback (dynamic compensator) for descriptor (singular) multi-agent systems with fixed topologies and agents described by general linear systems. Only output information of each agent can be delivered from its neighbour agents. Based on graph, algebra and descriptor linear system theory, the necessary and sufficient conditions are proposed for the existence of dynamic compensators solving the considered problem. The given conditions depend on both the topologies within descriptor multi-agent systems and the structure properties of each agent dynamics. According to non-zero eigenvalues of the Laplacian matrix of the weighted digraph are the same or different, two consensus algorithms via dynamic compensators are proposed, respectively. The provided examples demonstrate the effectiveness of the proposed consensus algorithms.

Dynamic output feedback control of constrained descriptor systems

This paper aims to present an approach for design of dynamic output feedback compensators for linear discrete-time descriptor systems subject to state and control constraints. To this end, output-feedback controlled-invariant polyhedra are constructed by taking a pair of polyhedral sets: a controlled-invariant set and a conditioned-invariant set. By defining an augmented system composed of the original system plus the dynamic compensator, a control action can be computed online, which optimizes the contraction rate of the augmented state trajectory and enforces the constraints. The results are illustrated through numerical examples, which show that the proposed dynamic compensators outperform static feedback controllers under the same conditions.

Full-Order Dynamic Output-Feedback Compensator for Time-Stamped Networked Control Systems

We present a method for the synthesis of a full-order dynamic output-feedback compensator for time-stamped Networked Control Systems (NCS). The methodology is obtained from the use of a polytopic approximation for the NCS representation, based on the exact discretization of the originally linear time-invariant system. The dynamics of the proposed compensator depends on the delays induced by the network, which are considered not to be greater than the sampling period and can be computed from information provided by time-stamped messages. A parameter-dependent Lyapunov function is associated to the closed-loop system to ensure stability and some time-performance. The synthesis of the compensator is described in terms of Linear Matrix Inequalities. Some numerical experiments are proposed to illustrate the applicability of the methodology.

Compensadores dinâmicos para sistemas discretos no tempo com parametros variantes e aplicação a um sistema fuzzy Takagi-Sugeno

Neste artigo, considera-se o problema de síntese de compensadores dinâmicos por realimentação de saídas para sistemas lineares, discretos no tempo, com parâmetros variantes. Sob a hipótese que os parâmetros variantes podem ser medidos ou estimados em tempo-real, são consideradas duas estruturas de compensadores dinâmicos, com ordem igual a da planta: uma parcialmente dependente e outra completamente dependente dos parâametros. A estabilidade e o desempenho do sistema em malha-fechada são garantidos via a utilização de uma funçao de Lyapunov dependente de parâmetros e condiçõs LMIs são estabelecidas e utilizadas para a síntese dos controladores. Um aspecto importante considerado, e que objetiva a aplicação prática dos resultados, particularmente no controle de sistemas não lineares, é a validade do modelo LPV utilizado para representar localmente o sistema a controlar. Os resultados propostos são aplicados sobre um sistema não linear representado localmente por um modelo fuzzy de Takagi-Sugeno.

Consensus of high-order linear systems using dynamic output feedback compensator: Low gain approach

In this paper, we study the consensus (and synchronization) problem for multi-agent linear dynamic systems. All the agents have identical MIMO linear dynamics which can be of any order, and only the output information of each agents is delivered throughout the communication network. It is shown that consensus is reached if there exists a stable compensator which simultaneously stabilizes N − 1 systems in a special form, where N is the number of agents. We show that there exists such a compensator under a very general condition. Finally, the consensus value is characterized as a function of initial conditions with stable compensators in place.

Robust dynamic output feedback fuzzy Lyapunov stabilization of Takagi–Sugeno systems—A descriptor redundancy approach

This paper deals with Takagi–Sugeno (T–S) systems stabilization based on dynamic output feedback compensators (DOFC). In fact, only few results consider DOFC for T–S systems and most of them propose quadratic Lyapunov functions to provide stability conditions, which may lead to conservatism. In this work, to overcome this drawback and to enhance the closed-loop transient response, we provide for T–S uncertain closed-loop systems non-quadratic stability conditions. Based on a fuzzy Lyapunov candidate function and the descriptor redundancy property, these stability conditions are written in terms of linear matrix inequalities (LMI). Afterward, the DOFC is designed with H ∞ criterion in order to minimize the influence of external disturbances. Finally, a few academic examples illustrate the efficiency of the proposed approaches.

入力飽和を有するサーボ系に対する出力フィードバック補償器の設計方法

This paper considers linear time-invariant continuous-time servosystems with control input saturation nonlinearities, and proposes a design method of output feedback controllers satisfying a regional integral quadratic performance for the systems based on the generalized sector approach. The method assumes the output of the nonlinearities to be available for the control, and then it is an integrated design of dynamic output feedback and anti-windup compensators with a given servocompensator based on an error system regarding a steady state as a new origin. In this case, this paper clarifies that the design problem using the method can be recast as a convex optimization problem based on linear matrix inequalities (LMIs), and a problem setting initial states of the compensators can be recast as a problem solving linear matrix equations (LMEs), respectively. Finally, this paper points out that the proposed design method is helpful through a numerical example designing the servosystem with anti-windup structure via the derived LMIs and LMEs.

Robust quadratic stable dynamic output compensator

In this paper, a new robust quadratic stable dynamic output feedback compensator is introduced and applied to a car steering model subject to parameter uncertainties. Arbitrary-order dynamic output feedback controllers are used together with the robust quadratic stabilization algorithm (RQSA) to attain a family of robust dynamic output compensators. A treatment through solving Lyapunov-like matrix equations and a special state transformation are employed. The RQSA is based only on checking end points of an uncertainty bounding hyperpolyhedron. The combined algorithm is implemented, and the simulations reveal that the new compensator provides more robust, stable and reliable performance under a variety of uncertainties involved in the car steering system model.

Decentralized adaptive output feedback control via input/output inversion

A decentralized adaptive output feedback control design method is presented for control of large-scale interconnected systems. It is assumed that all the controllers share prior information about the subsystem reference models. Based on that information, a linear dynamic output feedback compensator and linearly parameterized neural network (NN) are introduced for each subsystem to partially cancel the effect of the interconnections on the tracking performance. Boundedness of error signals is shown through Lyapunov's direct method.

Intrinsic Observer-Based Stabilization for Simple Mechanical Systems on Lie Groups

This paper presents a dynamic observer for a class of simple mechanical systems on Lie groups. This observer provides velocity estimates based on configuration measurements. The observer is \textit{intrinsic}, so its performance does not depend on the choice of coordinates, and it is \textit{coordinate free}, in the sense that the equations may be written explicitly without specifying coordinates for the configuration space. Our main result is obtained by specializing a previous result of Aghannan and Rouchon concerning velocity estimation of simple mechanical systems on Riemannian manifolds to such systems on Lie groups. This specialization is nonobvious and extremely powerful. Further we extend the original result to include velocity-dependent external forces. This estimator, combined with a coordinate-free formulation of passivity-based state-feedback control, allows the construction of a coordinate-free, intrinsic dynamic output feedback compensator. This is, to our knowledge, the first time such a result has been reported. Explicit expressions are computed for the Lie groups $SO(3)$ and $SE(3)$, allowing easy specialization to practical problems of rigid body motion. The theory is illustrated via application to the axisymmetric top and to a six-degrees-of-freedom microelectromechanical system.

A parameterization of exponentially stabilizing controllers for linear mechanical systems subject to non-smooth impacts

The goal of this paper is to propose a family of dynamic output feedback compensators (whose state is subject to jumps at the impact times) that stabilize a given n degrees of freedom mechanical system, with linear continuous-time dynamics, subject to non-smooth impacts. An example is used in order to show how the available degrees of freedom can be used to satisfy additional important requirements, apart from asymptotic stability.