Robust Control Synthesis Research Articles

Genetic Algorithm-Based Model Order Reduction of Aeroservoelastic Systems with Consistent States

This paper presents a model order reduction framework to construct linear parameter-varying reduced-order models of flexible aircraft for aeroservoelasticity analysis and control synthesis in broad two-dimensional flight parameter space. Genetic algorithms are used to automatically determine physical states for reduction and to generate reduced-order models at grid points within parameter space while minimizing the trial-and-error process. In addition, balanced truncation for unstable systems is used in conjunction with the congruence transformation technique to achieve locally optimal realization and “weak” fulfillment of state consistency across the entire parameter space. Therefore, aeroservoelasticity reduced-order models at any flight condition can be obtained simply through model interpolation. The methodology is applied to the pitch-plant model of the X-56A Multi-Use Technology Testbed currently being tested at NASA Armstrong Flight Research Center for flutter suppression and gust load alleviation. The present studies indicate that the reduced-order model with more than reduction in the number of states relative to the original model is able to accurately predict system response among all input–output channels. The genetic-algorithm-guided approach exceeds manual and empirical state selection in terms of efficiency and accuracy. The interpolated aeroservoelasticity reduced-order models exhibit smooth pole transition and continuously varying gains along a set of prescribed flight conditions, which verifies consistent state representation obtained by congruence transformation. The present model order reduction framework can be used by control engineers for robust aeroservoelasticity controller synthesis and novel vehicle design.

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.

Synthesis of Robust Constrained Inventory Control in Supply Networks on the Base of Descriptor System Approach

Synthesis of Robust Constrained Inventory Control in Supply Networks on the Base of Descriptor System Approach

Synthesis of Adaptive Robust Controllers for a Class of Nonlinear Systems with Input Saturations

This paper deals with a design problem of an adaptive robust controller for a class of nonlinear systems with specified input saturations. For the nonlinear system under consideration, the nonlinearity means unknown perturbations and satisfies the matching condition. In this paper, we show that sufficient conditions for the existence of the proposed adaptive robust controller giving consideration to input saturations are given in terms of linear matrix inequalities (LMIs). Finally, simple illustrative examples are shown.

Notice of Violation of IEEE Publication Principles: Reliable Output Feedback Control of Discrete-Time Fuzzy Affine Systems With Actuator Faults

Notice of Violation of IEEE Publication Principles <br><br>After careful consideration by a duly constituted committee, an author of this article, Hamid Reza Karimi, was found to have acted in violation of the IEEE Principles of Ethical Publishing by artificially inflating the number of citations to this article. <br/> This article studies the robust and reliable H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> static output feedback (SOF) control for nonlinear systems with actuator faults in a descriptor system framework. The nonlinear plant is characterized by a discrete-time Takagi-Sugeno (T-S) fuzzy affine model with parameter uncertainties, and the Markov chain is utilized to describe the actuator-fault behaviors. Specifically, by adopting a state-output augmentation approach, the original system is firstly reformulated into the descriptor fuzzy affine system. Based upon a novel piecewise Markovian Lyapunov function (LF), the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance analysis condition for the underlying system is then presented, and furthermore the robust and reliable SOF controller synthesis is carried out. It is shown that by invoking the redundancy properties induced by the descriptor formulation, combined with some convexifying techniques, the existence of the desired reliable controller can be explicitly determined by the solution of a convex optimization problem. Finally, simulation studies are applied to confirm the effectiveness of the developed method.

Convex Synthesis of Robust Controllers for Linear Systems With Polytopic Time-Varying Uncertainty

The design of robust controllers for linear systems with structured time-varying uncertainty is a fundamental problem in control systems. This problem is still open because the available methods for robust analysis lead to nonconvex optimization whenever design variables are present. This paper proposes a novel approach that overcomes this difficulty. Specifically, continuous-time linear systems with polytopic time-varying uncertainty are considered. The basic problem consists of designing a robust static output feedback controller ensuring robust asymptotical stability. A novel approach is proposed through the introduction of robust stabilizability functions (RSFs), i.e., functions able to establish whether a controller is robustly asymptotically stabilizing. In particular, RSFs based on homogeneous polynomial Lyapunov functions (HPLFs) are searched for. The proposed approach requires the solution of two convex optimization problems with constraints expressed as linear matrix inequalities (LMIs). For any size of the LMIs, the proposed approach provides a sufficient condition for the existence of a sought controller. Moreover, this condition is also necessary when the size of the LMIs is large enough. Several extensions of the proposed methodology are presented, which deal with the synthesis of controllers ensuring desired decay rate, fixed-order dynamic output controllers, and controllers with the minimum norm.

Robust distributed model predictive control of linear systems with structured time-varying uncertainties

ABSTRACTIn this work, synthesis of robust distributed model predictive control (MPC) is presented for a class of linear systems subject to structured time-varying uncertainties. By decomposing a global system into smaller dimensional subsystems, a set of distributed MPC controllers, instead of a centralised controller, are designed. To ensure the robust stability of the closed-loop system with respect to model uncertainties, distributed state feedback laws are obtained by solving a min–max optimisation problem. The design of robust distributed MPC is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints. An iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance. The simulation results show the effectiveness of the proposed robust distributed MPC algorithm.

Non-fragile control of fuzzy affine dynamic systems via piecewise Lyapunov functions

This paper addresses the robust H∞ static output feedback (SOF) controller design problem for a class of uncertain fuzzy affine systems that are robust against both the plant parameter perturbations and controller gain variations. More specifically, the purpose is to synthesize a non-fragile piecewise affine SOF controller guaranteeing the stability of the resulting closed-loop fuzzy affine dynamic system with certainH∞ performance index. Based on piecewise quadratic Lyapunov functions and applying some convexification procedures, two different approaches are proposed to solve the robust and non-fragile piecewise affine SOF controller synthesis problem. It is shown that the piecewise affine controller gains can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, simulation examples are given to illustrate the effectiveness of the proposed methods.

Robust model predictive control synthesis for state-delayed systems with randomly occurring input saturation nonlinearities

In this paper, a model predictive control algorithm is presented for linear parameter varying systems with both state delays and randomly occurring input saturation. The input saturation is assumed to be occurred randomly with Bernoulli-distributed white sequences. A constant sate feedback law is designed at each time instant to ensure the robust stability of the closed-loop system with respect to polytopic uncertainties. The optimization of model predictive controller is cast into solving a linear matrix inequalities optimization problem. Then, the results are extended to gain-scheduled approach in which a set of state feedback laws are designed for each vertex of the system model. The state feedback law is scheduled by the time varying model parameters to achieve less conservatism in controller design. Finally, two examples are employed to show the effectiveness of the proposed algorithms.

Synthesis of Distributed Robust H-Infinity Controllers for Interconnected Discrete Time Systems

This paper presents an algorithm for the synthesis of robust distributed controllers for interconnected linear discrete-time systems. For a network of interconnected uncertain linear time-invariant systems, the distributed controller achieves robust stability and a guaranteed level of robust performance in a well-defined H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> sense. The setting of this paper is in discrete time. Based on the theory of dissipative dynamical systems, conditions for the analysis of robust stability and robust performance of networks are derived in terms of feasibility tests of linear matrix inequalities. From these conditions, computationally tractable synthesis conditions are derived. An iterative D-K type of synthesis algorithm is proposed that yields a robust distributed controller. Convergence properties of the algorithm are inferred.

Robust control synthesis for dynamic vessel positioning

This article considers key theoretical and practical issues that arise in the robust control synthesis for dynamic positioning. A dynamically positioned vessel maintains its position (fixed location or predetermined track) by means of active thrusters and propellers. The concise kinematics and vessel dynamics are presented using three degrees of freedom model for describing the horizontal motions. Then, the mixed H∞ and µ-synthesis framework has been employed to deal with perturbed model under external disturbances as well as measurement noises. To avoid excessive control energy for dynamic positioning system, the high frequency waves have been filtered using simple weighting functions. Using optimal Hankel-norm model approximation, the resulting full-order controller has been significantly reduced to make it easy to implement the practical works. Next, the simulation results in both frequency and time domains are presented to demonstrate the effectiveness of the robust control algorithms using the appropriate weighting functions. Finally, it is found that the proposed dynamic positioning system provides good maneuverability and robustness over a wide range of operating conditions, even under parametric variations and sea disturbances with sensor noises.

Robust and non-fragile static output feedback control for continuous-time semi-Markovian jump systems

This paper investigates the problem of robust and non-fragile [Formula: see text] static output feedback (SOF) controller design for a class of continuous-time semi-Markovian jump linear systems (S-MJLSs) with norm-bounded uncertainties. The systems under consideration are subject to a semi-Markov stochastic process with time-varying transition rates (TRs), which relax the traditional assumption on Markovian jump linear systems (MJLSs) that all of the TRs are constant. Based on a semi-Markovian Lyapunov function together with the property of cumulative distribution function, a sufficient condition for robust [Formula: see text] performance analysis is first derived. Then via some matrix inequality linearization procedures combined with sojourn-time decomposition idea, two approaches, namely, the convex linearization approach and iterative approach, are developed to solve the robust and non-fragile SOF controller synthesis problem. It is shown that the controller gains can be obtained by solving a set of strict linear matrix inequalities (LMIs) or a sequential minimization problem subject to LMI constraints. Finally, illustrative examples are provided to illustrate the effectiveness of the proposed approaches.

Robust Control of Three-Dimensional Compliant Mechanisms

Position control and vibration damping of flexible-link mechanisms are still challenging open issues in robotics. Finding solutions for these problems can lead to improvement in the operation and accuracy of the manipulators. In this paper, the synthesis of robust controllers based on H∞ loop shaping and μ-synthesis for both position control and vibration damping in a spatial flexible L-shape mechanism with gravity is presented. The design of the controllers is based on the evaluation of an uncertainty model which takes into account a ±20% uncertainty in the elasticity and mass density of the links. The response of each controller is tested also in the presence of external disturbances with the aid of highly accurate numerical simulations; furthermore, a comparison between the robust performances of synthesized controllers is presented in order to show the effectiveness of synthesized control systems.

Analytical synthesis of robust controllers of the given accuracy under external perturbations

An approach that allows finding a set of robust statistic feedback controllers that ensure the given control accuracy for the controlled parameters in a multiconnected control system under bounded parametric and external perturbations of various classes is proposed. To describe the set of controllers of the given accuracy, the results of analytically solving the matrix equations based on matrix canonization and parametrization of the Lyapunov equation are used. The solvability conditions of the synthesis problem ensure the robustness and optimal suppression of the perturbations. They are homogeneously represented as linear matrix inequalities obtained based on the Lyapunov functions. A methodological example is given.

Robust Stability Analysis and Synthesis for Uncertain Discrete-Time Networked Control Systems Over Fading Channels

This technical note investigates uncertain discrete-time networked control systems over fading channels. It is assumed that the plant is affected by polytopic uncertainty and is connected to the controller in closed-loop via fading channels which are modeled by multiplicative noise processes. Three contributions are proposed as follows. First, it is shown that robust stability in the mean square sense of the uncertain closed-loop networked control system is equivalent to the existence of a Lyapunov function in a certain class. Second, it is shown that the existence of a Lyapunov function in such a class is equivalent to the feasibility of a set of linear matrix inequalities (LMIs). Third, it is shown that the proposed condition can be exploited for the synthesis of robust controllers ensuring robust stability in the mean square sense of the uncertain closed-loop networked control system.

Dynamic Adaptive Robust Backstepping Control Design for an Uncertain Linear System

This paper builds on the existing adaptive robust control (ARC) synthesis method introduced by Yao et al. and presents a new method to synthesize ARCs. Based on dynamic backstepping, the approach explicitly addresses the uncertain dynamics which enters into the system via the higher-order channels of the state-space model. As such, the proposed dynamic ARC (D-ARC) method addresses the inherent weakness of the original approach where uncertainty in the higher-order channels is ignored. The proposed approach is illustrated in simulations for controlling a voice coil motor (VCM) actuator that serves as a read/write head for a single-stage hard disk drive (HDD). The effectiveness of the resulting D-ARC controller is validated by considering the transient performance, tracking errors, and disturbance rejection of the VCM operating in both the track-seeking and track-following modes.

Robust active sound radiation control of a piezo-laminated composite circular plate of arbitrary thickness based on the exact 3D elasticity model

A multi-objective mixed [Formula: see text]2/[Formula: see text]∞ robust output feedback control synthesis with regional pole placement constraints in a linear matrix inequalities framework is adopted for active low-frequency sound radiation control of an arbitrarily thick, rigidly baffled, simply supported, multi-layered piezo-composite circular panel. The adopted control system concurrently captures the benefits of both [Formula: see text]2 transient control performance and [Formula: see text]∞ robust stability in the face of external disturbances and system uncertainties. Also, the implemented volumetric sensing/actuation configuration avoids the typical problems associated with conventional (spatially discrete) piezoelectric sensor/actuator patches, where the total volume velocity can be effectively cancelled with the main contribution being to the long wavelength acoustic power emission. The elasto-acoustic analysis is based on the spatial state-space method in the context of exact 3D elasticity theory along with the Rayleigh integral formula where Neumann’s addition theorem is incorporated in the associated Hankel transform representation to arrive at a computationally efficient expression for the nonaxisymmetric pressure field within the acoustic half-space, valid in both near and far fields. Subspace system identification of the fully coupled structure–fluid interaction problem is performed, and the truncated modes are considered as multiplicative uncertainties in synthesis of the mixed-norm controller. Numerical simulations establish the ability of the implemented volumetric sensing/actuation methodology in cooperation with the multi-objective robust active control scheme for restraining low-frequency sound radiation from a [Formula: see text]/steel/PZT4 circular piezo-laminated plate, without provoking instability of the closed-loop system. Also, superior bandwidth frequency and tracking performance in comparison to the [Formula: see text] and [Formula: see text] controllers are observed. This work is believed to be the first such attempt to exactly model (and actively control) the 3D nonaxisymmetric acousto-elastodynamic frequency response of an arbitrarily thick, smart piezo-laminated circular plate in heavy fluid loading condition (i.e. without using any kind of far-field, low-frequency, and/or light fluid coupling approximations), with straightforward extensibility for any arbitrary through-thickness variation of distributed material properties.

Stability Robustness of Closed‐Loop Systems in Angular Metrics

AbstractH∞‐norm is widely used in the analysis and synthesis of robust control, a field which continues to flourish and develop. However, H∞‐norm can only be used to measure the distance between two stable systems, not unstable systems. Sometimes, it is not appropriate to measure the gap between two systems. In this paper, a new metric, angular metric, defined in linear spaces of real rational matrices, is used to measure the distance of two systems with different dimensions. It is also used to measure the uncertainties and describe the performance specifications of the robust control system. In the framework of this metric, the robust stability margin is proposed to characterize the stability robustness of the closed‐loop system. When both the plant and the controller have uncertainties simultaneously, we introduce structural robust stability and prove the necessary and sufficient conditions of the robust stability of the feedback control system.

Switching Robust Control for Bilateral Teleoperation

The inherent transparency-stability tradeoff in bilateral teleoperation poses a challenge to design controllers that find a proper balance between both requirements. Furthermore, when the environment of the teleoperation system varies within a large range, a single controller might not be sufficient to achieve both stability and high performance. In this paper, we propose the synthesis of a switching robust controller that allows to design multiple robust controllers suitable for different ranges of environment stiffness, so that an overall better performance is achieved. The controllers are scheduled using an estimate of the environment stiffness. During the design, we account for smooth switching among controllers and for the fact that environment estimators will have limited accuracy and uncertainty. We present synthesis, simulation, and experimental results of the proposed approach, thus showing the effectiveness of the method to improve the robust performance of the teleoperated system.

Delay Dependent Robust Load Frequency Control Synthesis in AC-DC Interconnected Power System Using Genetically Optimized Fuzzy Logic Controller

The load-frequency control (LFC) is used to restore the balance between load and generation in each control area by means of speed control. The objective of LFC is to minimize the transient deviations and steady state error to zero in advance. Conventionally, the membership functions and control rules of fuzzy logic control are obtained by trial and error method are experience of designers. To overcome this problem this paper focuses on a new optimization technique of a fuzzy logic controller based load frequency controller (LFC) tuned by genetic algorithm (GA) in co-ordination with frequency controllable HVDC links. In this proposed system Area 1–2, Area 2–3 are connected by frequency controllable High Voltage Direct Current transmission links and Area 2–3 is connected by normal AC tie-line. By using the system interconnections as the HVDC link, the tie-line power modulation of HVDC link through interconnections is possible. The advantage of incorporating time delays is important for satisfactory dynamical responses. The HVDC transmission link is to transfer power over long distance without any frequency deviation.