Fixed-order Dynamic Output Feedback Research Articles

Finite-frequency fixed-order dynamic output-feedback control via a homogeneous polynomially parameter-dependent technique

This paper investigates the problem of fixed-order dynamic output-feedback (DOF) control for linear polytopic systems over finite-frequency ranges. Firstly, based on the generalized Kalman–Yakubovich-Popov lemma, we formulate the necessary and sufficient conditions for the finite-frequency disturbance-attenuation performance as bilinear matrix inequalities (BMIs), which are known to be NP-hard. In light of the homogeneous polynomially parameter-dependent technique, we construct relaxed synthesis conditions by employing higher-order decision variables dependent on the uncertainty parameter. To address the BMI problem, we develop an iterative procedure, under which feasible solutions to the original non-convex programming are achieved by vicariously solving a sequence of tractable convex approximations. Finally, we verify the efficacy of the theoretical results by an active suspension system.

Resilient fixed-order distributed dynamic output feedback load frequency control design for interconnected multi-area power systems

The paper proposes a novel H-&#x221E load frequency control &#x0028 LFC &#x0029 design method for multi-area power systems based on an integral-based non-fragile distributed fixed-order dynamic output feedback &#x0028 DOF &#x0029 tracking-regulator control scheme. To this end, we consider a nonlinear interconnected model for multi-area power systems which also include uncertainties and time-varying communication delays. The design procedure is formulated using semi-definite programming and linear matrix inequality &#x0028 LMI &#x0029 method. The solution of the proposed LMIs returns necessary parameters for the tracking controllers such that the impact of model uncertainty and load disturbances are minimized. The proposed controllers are capable of receiving all or part of subsystems information, whereas the outputs of each controller are local. These controllers are designed such that the resilient stability of the overall closed-loop system is guaranteed. Simulation results are provided to verify the effectiveness of the proposed scheme. Simulation results quantify that the distributed &#x0028 and decentralized &#x0029 controlled system behaves well in presence of large parameter perturbations and random disturbances on the power system.

Robust fixed‐order dynamic output feedback controller design for fractional‐order systems

This study deals with designing a robust fixed-order dynamic output feedback controller for uncertain fractional-order linear time-invariant systems by means of linear matrix inequalities (LMIs). The authors’ purpose is to design a low-order controller that stabilises the fractional-order linear system in the presence of model uncertainties. No limiting constraint on the state space matrices of the uncertain system is assumed in the design procedure. Furthermore, adopting the most complete model of linear controller, with direct feedthrough parameter, does not disturb the LMI-based approach of developing robust stabilising control. Eventually, the authors illustrate the advantages of the proposed method by some examples and their numerical simulation.

Decentralized Fixed-Order Piecewise Affine Dynamic Output Feedback Controller Design for Discrete-Time Nonlinear Large-Scale Systems

This paper proposes a novel decentralized robust $\mathscr H_{\infty }$ fixed-order dynamic output feedback (DOF) controller design approach for discrete-time nonlinear large-scale systems via Takagi-Sugeno fuzzy-affine models. By a state-input augmentation method and piecewise quadratic Lyapunov functions, some sufficient conditions for decentralized fixed-order piecewise affine DOF controller synthesis are given. It is shown that by some convexification techniques, the controller gains can be obtained by solving a set of linear matrix inequalities. Two simulation examples are carried out to verify the effectiveness of the proposed design method.

Robust Structured Control Design via LMI Optimization

AbstractThis paper presents a new procedure for discrete-time robust structured control design. Parameter-dependent nonconvex conditions for stabilizable and induced L2-norm performance controllers are solved by an iterative linear matrix inequalities (LMI) optimization. A wide class of controller structures including decentralized of any order, fixed-order dynamic output feedback, static output feedback can be designed robust to polytopic uncertainties. Stability is proven by a parameter-dependent Lyapunov function. Numerical examples on robust stability margins shows that the proposed procedure can obtain less conservative results than traditional stability criteria.

Robust Static and Fixed-order Dynamic Output Feedback Control of Discrete-time Lur'e Systems

AbstractThis paper considers the design of static and fixed-order dynamic output feedback controllers for discrete-time Lur'e systems with sector-bounded nonlinearities and polytopic parametric uncertainty. Controller design equations are derived for systems with multiple states, outputs, and nonlinearities in terms of linear matrix inequalities (LMIs). The design methods are based on parameter-dependent Lyapunov functions (PDLFs) combined with the latest in theoretical and iterative numerical methods for solving certain classes of nonconvex inequalities. The design methods are illustrated in several numerical examples.

Robust controller synthesis for systems with input nonlinearities: a trade-off between gain variation and parametric uncertainty

A feedback control-system design problem involving input nonlinearities and structured plant parameter uncertainities is considered. Multivariable absolute stability theory is merged with the guaranteed cost control approach to robust stability and performance to obtain a theory of full- and reduced-order robust control design that accounts for input time-varying sector bounded nonlinearities. The principal result is a sufficient condition for characterizing dynamic controllers of a fixed dimension which are guaranteed to provide robust stability for plant parametric variations and absolute stabilization for input nonlinearities. The proposed framework provides a systematic design trade-off between classical robustness guarantees (i.e., gain and phase margins) versus parametric robustness. Furthermore, the framework is directly applicable to uncertain systems with saturating controls and provides fixed-order dynamic output feedback controllers with guaranteed domains of attraction. © 1998 John Wiley & Sons, Ltd.

Nonlinear fixed-order dynamic compensation for passive systems

A method for designing nonlinear fixed-order (i.e. full- and reduced-order) dynamic passive controllers for passive systems is developed using nonlinear dissipation theory. Specifically, by extending linear passive controller synthesis frameworks a family of globally asymptotically stabilizing nonlinear passive controllers is developed that can serve to enhance system performance and energy dissipation. The proposed approach is applied to the rotational/translational proof-mass actuator (RTAC) nonlinear benchmark problem to develop fixed-order dynamic output feedback nonlinear controllers. © 1998 John Wiley & Sons, Ltd.

Nonlinear fixed‐order dynamic compensation for passive systems

A method for designing nonlinear fixed-order (i.e. full- and reduced-order) dynamic passive controllers for passive systems is developed using nonlinear dissipation theory. Specifically, by extending linear passive controller synthesis frameworks a family of globally asymptotically stabilizing nonlinear passive controllers is developed that can serve to enhance system performance and energy dissipation. The proposed approach is applied to the rotational/translational proof-mass actuator (RTAC) nonlinear benchmark problem to develop fixed-order dynamic output feedback nonlinear controllers. © 1998 John Wiley & Sons, Ltd.