Dynamic Output Feedback Controller Synthesis Research Articles

Reduced order dynamic controller synthesis conditions for LPV periodic discrete-time systems subject to input saturation

A method for the synthesis of reduced-order dynamic output-feedback controllers for periodic discrete-time LPV systems, subject to input saturations and external noises, is proposed in this paper. The controllers are designed to guarantee the robustness of the closed-loop system to exogenous noises, achieved through the minimization of a bound for the L2 gain. The proposed method is based on a two-stage procedure, where a state-feedback gain is computed in the first stage and then applied on the second step to generate the desired controller. A third stage is then developed to synthesize an anti-windup compensation to deal with the input saturation, but since the controller is not fixed in this step, the control system dynamics can be redesigned to better aggregate the desired robustness to the external noises and input saturation, decreasing the conservativeness of the technique. The validity of the proposed method is validate through a numerical example.

Solution to negative-imaginary control problem for uncertain LTI systems with multi-objective performance

This paper addresses the problem of dynamic output feedback controller synthesis in LMI framework for LTI generalized plants with negative-imaginary uncertainties. The proposed technique transforms the controller synthesized nominal closed-loop system into a strongly strict negative-imaginary system and exploits the DC loop gain condition pertaining to negative-imaginary theory to establish internal stability in presence of negative-imaginary uncertainties. Apart from making the closed-loop system robustly stable, the designed output feedback controller also facilitates multi-objective performance of the closed-loop system such as minimizing the H2 and H∞ norms, reducing the peak overshoot, increasing the decay rate, optimizing the settling time, etc. Illustrative examples have been studied to demonstrate the usefulness of the proposed control scheme. A thorough μ-analysis subjected to ‘mixed’ two-block perturbations is included in the examples to show that the designed controller can also facilitate a certain level of robust H∞ performance in presence of stable NI/SNI uncertainties.

H∞ Dynamic output feedback control of LPV time-delay systems via dilated linear matrix inequalities

This paper uses the linear matrix inequality dilation approach to deal with robust stability and H∞ dynamic output feedback controller synthesis for linear parameter varying delayed systems with variable delay. This approach can express the original non-convex problem in terms of convex linear matrix inequalities and consequently reduces the conservatism of linear matrix inequality synthesis without dilation. Both delay-dependent stability and H∞ performance are studied in a quadratic context. Furthermore, a Lyapunov–Krasovskii functional is used to derive a delay-dependent criterion formulated in terms of a linear matrix inequality that will be used to search for an H∞ linear parameter varying delayed dynamic output feedback controller. To achieve this aim we use an integral inequality which plays a key role in the derivation of this criterion and enables the reduction of the H∞ cost in comparison to other results.

A framework for optimal actuator/sensor selection in a control system

ABSTRACTWhen dealing with large-scale systems, manual selection of a subset of components (sensors/actuators), or equivalently identification of a favourable structure for the controller, that guarantees a certain closed-loop performance, is not very feasible. This paper is dedicated to the problem of concurrent optimal selection of actuators/sensors which can equivalently be considered as the structure identification for the controller. In the context of a multi-channel dynamic output feedback controller synthesis, we formulate and analyse a framework in which we incorporate two extra terms for penalising the number of actuators and sensors into the variational formulations of controller synthesis problems in order to induce a favourable controller structure. We then develop an explicit scheme as well as an iterative process for the purpose of dealing with the multi-objective problem of controller structure and control law co-design. It is also stressed that the immediate application of the proposed approach lies within the fault accommodation stage of a fault tolerant control scheme. By two numerical examples, we demonstrate the remarkable performance of the proposed approach.

A multiobjective robust controller synthesis approach aided by multicriteria decision analysis

This paper proposes a methodology for robust dynamic output-feedback control synthesis of uncertain linear systems represented by polytopic models. This control problem results in a semi-infinite optimization problem. The proposed synthesis procedure improves a previous two-step procedure, composed of synthesis and analysis, by employing both a multiobjective evolutionary algorithm (MOEA) and a multiple criteria decision making (MCDM) strategy in the synthesis step. The analysis stage is performed via a Branch and Bound (B&B) algorithm, enabling the validation of the former step. In the proposed multiobjective approach, the project aim is to meet the specifications of (i) reference signal tracking response, (ii) disturbance rejection and (iii) measurement noise attenuation. The project specifications are quantified in terms of H∞ and H2 norms of closed-loop transfer functions. Essentially, this technique combines the flexibility of a dedicated MOEA together with the minimax semi-infinite programming problem. Since a MOEA evolves a set of candidate solutions in parallel, the suggested strategy provides a diverse set of controller designs, which is very useful for an a posteriori decision-making process. A proposed multicriteria decision-aid strategy is employed, in addition, as a controller design tool, aiming to incorporate the decision-maker preferences throughout the process, which (i) enables a guided evolutionary search to a trade-off region (of solutions) of practical interest and (ii) assists the definition of an adequate final controller, characterized by a reasonable practical trade-off concerning the criteria. The application of the suggested framework is illustrated on three case studies in order to demonstrate the effectiveness of the method presented.

Exact-memory and memoryless control of linear systems with time-varying input delay using dynamic IQCs

Input delay is an important type of actuator nonlinearity in control systems. In this paper, we will address the output-feedback control synthesis problem for linear systems with time-varying input delay under the integral quadratic constraint (IQC) framework. A new exact-memory control scheme is first proposed, which consists of a standard linear output-feedback control law and an internal delay loop. The delay loop is embedded in the controller structure so as to reproduce the input delay behavior of the plant. By using quadratic Lyapunov functions incorporated with dynamic IQC multipliers, the resulting dynamic output-feedback delay control synthesis problem is fully characterized by a set of linear matrix inequalities (LMIs), which are convex on all design variables including the scaling factors associated with the IQC multipliers. Moreover, the corresponding result on memoryless control is also derived for the case when the plant input-delay information is not available for feedback control. An application to network systems has been used to illustrate the effectiveness and usefulness of the proposed approach.

Mixed‐Objective Robust Dynamic Output Feedback Controller Synthesis for Continuous‐Time Polytopic Lpv Systems

AbstractA robust dynamic output feedback controller synthesis algorithm considering H∞/H2 performance and regional pole placement is addressed for a nonlinear system with parameter uncertainties and external disturbance. First, the formulation of a gain‐scheduled mixed‐objective robust dynamic output feedback controller for continuous‐time polytopic linear parameter varying (LPV) systems is presented. To reduce conservativeness, some auxiliary slack variables and parameter‐dependent Lyapunov functions are employed in addition to well‐established performance conditions. Then, sufficient conditions for the desired gain‐scheduled mixed‐objective robust dynamic output feedback controllers are cast into an efficiently tractable finite‐dimensional convex optimization problem in terms of linear matrix inequalities (LMIs). Finally, numerical simulation shows the validity of the proposed controller, which has good stability, strong robustness, satisfied disturbance attenuation ability, and smooth dynamic properties.

Asynchronous switching output feedback control of discrete-time switched linear systems

In this paper, the problem of dynamic output-feedback control synthesis is addressed for discrete-time switched linear systems under asynchronous switching. The proposed hybrid controller consists of a standard dynamic output-feedback switching control law and an impulsive reset law induced by controller state jumps. Using the average dwell time technique incorporating with multiple quadratic Lyapunov functions, the switching control synthesis conditions for asymptotic stability with guaranteed weighted ℓ2-gain performance are derived as a set of linear matrix inequalities (LMIs). The proposed hybrid synthesis scheme advances existing design methods for output-feedback asynchronous switching control of switched linear systems in two important aspects: LMI formulation of the synthesis problem; and arbitrary order of the controller state. A numerical example is used to illustrate the effectiveness and advantages of the proposed design technique.

Mode-dependent nonrational output feedback control for continuous-time semi-Markovian jump systems with time-varying delay

This paper is concerned with the problem of delay and mode-dependent robust ℋ∞ nonrational dynamic output feedback controller (DOFC) synthesis for a class of continuous-time semi-Markovian jump linear systems (S-MJLSs) with time-varying delay. Due to the relaxed conditions on the stochastic process, the S-MJLSs are with time-varying transition rates and can describe a broader class of dynamical systems than the traditional Markovian jump linear systems. By introducing a two-term approximation for the time-varying delay, the original system is firstly reformulated into a feedback interconnection configuration, which is well-posed in the sense that the scaled small gain (SSG) technique can be applied to the reformulated system to derive robust performance analysis criteria. Then, based on a semi-Markovian Lyapunov–Krasovskii formulation of SSG condition combined with the sojourn-time fractionizing technique, the ℋ∞ performance analysis and mode-dependent nonrational DOFC synthesis conditions for the underlying S-MJLSs are developed, respectively. It is shown that the controller gains can be obtained in terms of linear matrix inequalities. Finally, simulation studies are provided to illustrate the effectiveness and superiority of the proposed design method.

Robust observer‐based control design for uncertain singular systems with time‐delay

SUMMARYThis paper is concerned with the stability analysis and robust dynamic output feedback controller synthesis for uncertain continuous singular systems with time‐delay. First, on the basis of the Lyapunov functional method and by resorting to the delay‐partition technique, improved delay‐dependent sufficient conditions are presented to ensure the nominal unforced system to be admissible (i.e., to be regular, impulse‐free, and stable). Second, with the help of the obtained admissibility criterion, an observer‐based controller is designed by solving a set of LMIs. Finally, the validity and applicability of the proposed approach is shown by examples. Copyright © 2013 John Wiley & Sons, Ltd.

Simultaneous fault detection and control for stochastic time-delay systems

This paper is concerned with the simultaneous fault detection and control problem for Itô-type stochastic time-delay systems. A full-order dynamic output feedback controller is designed to achieve the desired control and detection objectives. The main contributions of this paper are as follows: (1) for stochastic time-delay systems, the controller design with multiple objectives can be addressed by employing the multiple Lyapunov functions approach, (2) the dynamic output feedback controller synthesis conditions described by linear matrix inequalities (LMIs) are derived and (3) within the proposed fault detection and control framework, a better integrated control and detection performance can be obtained. Some numerical examples including the comparison results are presented to show the advantages of the proposed method.

Dynamic output feedback control synthesis for stochastic time-delay systems

This article deals with the dynamic output feedback control synthesis problem for Itô-type stochastic time-delay systems. Our aim is to design a full order dynamic output feedback controller to achieve the desired control objectives. We will formulate the controller design problem as an H ∞ optimisation problem in the mean-square sense. The main contributions of this article are as follows: (i) for stochastic systems, the design of a controller with multiple objectives can be addressed without employing a unique Lyapunov function; (ii) using an inequality technique and Finsler Lemma, we provide convex controller synthesis conditions described by linear matrix inequalities (LMIs). Some examples are presented to show the effectiveness of the developed theoretical results.

Reference output tracking control for a flexible air-breathing hypersonic vehicle via output feedback

SUMMARY This paper addresses the problem of reference output tracking control for the longitudinal model of a flexible air-breathing hypersonic vehicle (FAHV) by utilizing the output feedback control approach. The dynamic characteristics of the FAHV along with the aerodynamic effects of hypersonic flight make the flight control of such systems highly challenging. Moreover, there exist some intricate couplings between the engine and flight dynamics as well as complex interaction between rigid and flexible modes in the longitudinal model. These couplings bring difficulty to the flight control design for the intractable hypersonic vehicle systems. This paper deals with the problem of reference output tracking control for the longitudinal model of the FAHV. By utilizing the trim condition information including the state of altitude, velocity, angle of attack, pitch angle, pitch rate and so on, the linearized model is established for the control design objective. Then, the reference output velocity and altitude tracking control design problem is proposed for the linearized model. The flexible models of the FAHV system are hardly measured because of the complex dynamics and the strong couplings of the FAHV. Thus, by using only limited flexible model information, the reference output tracking performance analysis criteria are obtained via Lyapunov stability theory. Then, based on linear matrix inequality optimization algorithm, the static output feedback controller is designed to stabilize the closed-loop systems, guarantee a certain bound for the closed-loop value of the cost function, and can make the control output achieve the reference velocity and altitude tracking performance. Subsequently, the condition of dynamic output feedback controller synthesis is given in terms of linear matrix inequalities and a numerical algorithm is developed to search for a desired dynamic output feedback controller which minimizes the cost bound and obtains the excellent reference altitude and velocity tracking performance simultaneously. The effectiveness of the proposed reference output tracking control method is demonstrated in simulation part. Furthermore, the superior reference velocity and altitude performance commands could be achieved via using static and dynamic output feedback controllers under lacking some unmeasured flexible states information in the measurement output vector. Copyright © 2011 John Wiley & Sons, Ltd.

Dynamic Output Feedback Control Synthesis for Continuous-Time T–S Fuzzy Systems via a Switched Fuzzy Control Scheme

This correspondence paper is concerned with the problem of designing switched dynamic output feedback H(infinity) controllers for continuous-time Takagi-Sugeno (T-S) fuzzy systems. A new type of dynamic output feedback controllers, namely, switched dynamic parallel distributed compensation (SDPDC) controllers, is proposed, which are switched by basing on the values of membership functions. A new method for designing SDPDC controllers for guaranteeing stabilities and H(infinity) performances of closed-loop nonlinear systems is presented, where the design conditions are given in terms of the solvability of a set of linear matrix inequalities. It is shown that the new method provides better or at least the same results of the existing design methods via a pure DPDC scheme. A numerical example is given to illustrate the effectiveness of the proposed method.

Dynamic Output Feedback Control Synthesis with Mixed Frequency Small Gain Specifications

This paper is concerned with the control synthesis problem via dynamic output feedback for linear continuous-time systems with mixed frequency small gain specifications. A new method for designing dynamic output feedback controllers is presented such that the resulting closed-loop systems are asymptotically stable and meet the requirements of small gain specifications in both finite frequency ranges and the entire frequency range. The design conditions are given in terms of solutions to a set of linear matrix inequalities (LMIs). Finally, a numerical example is given to illustrate the design procedure and the advantage of the proposed method in comparison with the existing one.

Robust pole placement in LMI regions

Discusses analysis and synthesis techniques for robust pole placement in linear matrix inequality (LMI) regions, a class of convex regions of the complex plane that embraces most practically useful stability regions. The focus is on linear systems with static uncertainty on the state matrix. For this class of uncertain systems, the notion of quadratic stability and the related robustness analysis tests are generalized to arbitrary LMI regions. The resulting tests for robust pole clustering are all numerically tractable because they involve solving linear matrix inequalities (LMIs) and cover both unstructured and parameter uncertainty. These analysis results are then applied to the synthesis of dynamic output-feedback controllers that robustly assign the closed-loop poles in a prescribed LMI region. With some conservatism, this problem is again tractable via LMI optimization. In addition, robust pole placement can be combined with other control objectives, such as H/sub 2/ or H/sub /spl infin// performance, to capture realistic sets of design specifications. Physically motivated examples demonstrate the effectiveness of this robust pole clustering technique.

Synthesis of output-feedback control laws for linear multivariable continuous-time systems

It is known (Porter and Bradshaw 1978 a) that, in the case of self-conjugate distinct eigenvalue spectra, the closed-loop eigenstructure assignable by output feedback is constrained by the requirement that the eigenvectors and reciprocal eigenvectors lie in well-defined subspaces. In this paper a technique is presented which can be used to select the eigenvectors and reciprocal eigenvectors from these subspaces in the case of appropriately augmented (Kimura 1975) controllable and observable continuous-time systems. Thin technique is ideally suited to digital-computer implementation and therefore greatly facilitates the synthesis of both static (Porter and Bradshaw 1978 a) and dynamic (Porter and Bradshaw 1978 b) output-feedback controllers.