Robust adaptive fault‐tolerant control of uncertain linear systems via sliding‐mode output feedback

This paper is concerned with the robust adaptive fault‐tolerant compensation control problem via sliding‐mode output feedback for uncertain linear systems with actuator faults and exogenous disturbances. Mismatched disturbance attenuation is performed via H_∞ norm minimization. By incorporating the matrix full‐rank factorization technique with sliding surface design successfully, the total failure of certain actuators can be coped with, under the assumption that redundancy is available in the system. Without the need for a fault detection and isolation mechanism, an adaptive sliding mode controller, where the gain of the nonlinear unit vector term is updated automatically to compensate the effects of actuator faults, is designed to guarantee the asymptotic stability and adaptive H_∞ performance of closed‐loop systems. The effectiveness of the proposed design method is illustrated via a B747‐100/200 aircraft model. Copyright © 2014 John Wiley & Sons, Ltd.     

Characterization,Modeling and H∞ control of n‐DOF Piezoelectric Actuators: application to A 3‐DOF Precise Positioner

This paper deals with the characterization, the modeling and the closed‐loop control of multivariable piezoelectric actuators, with an application to a 3‐DOF piezoelectric tube scanner, widely used in precise positioning. These actuators are typified by hysteresis and creep nonlinearities, badly damped oscillation and strong couplings between their axis. First, during the modeling, we propose to decouple the system and to use a linear model where the couplings and the two nonlinearities are integrated through an external fictive disturbance. From the obtained monovariable systems, monovariable H_∞ controllers are calculated by using specifications based on model approximation. The experimental tests demonstrate the efficiency of the method to reject simultaneously the couplings, hysteresis, creep and badly damped oscillations. Furthermore, the bandwidth of the closed‐loop and the open‐loop systems are compared and the results show that the proposed control technique allows to achieve a convenient closed‐loop bandwidth and precision for all the axis of the precise positioner.     

SVD‐Based Accurate Identification and Compensation of the Coupling Hysteresis and Creep Dynamics in Piezoelectric Actuators

In this paper, the coupling hysteresis and creep in piezoelectric actuators are identified and compensated for accurate tracking. First, we present the coupling hysteresis and creep model in smart actuators. Next, a complete identification strategy is designed according to the properties of the Preisach model. Then, an approach for parameter updating of the coupling model is provided. With the identified hysteresis and creep, the model‐based inversion compensation is designed. Finally, we apply the model identification and compensation to a piezoelectric stage to demonstrate the effectiveness of the proposed approaches. Significant reduction of the tracking error is achieved with the model‐based inversion feedforward compensator in which the relative errors at 10 Hz and 50 Hz are reduced to 1.85% and 4.53%, respectively. In addition, the model‐based feedforward is augmented with an integral feedback controller. With the composite controller, the relative errors at 10 Hz and 50 Hz are reduced to 0.42% and 3.04%, respectively.     

Discretization Of A Non‐Linear,Continuous‐Time Control Law With Small Control Delays

This paper considers time‐discretized, non‐linear, continuous‐time control laws with small computational time‐delays. The discretized control is not initiated immediately after the sampling instant t_i. Small variable computational delays ∞ are assumed to be present. Provided the sampling time ∞ is small and the maximum ratio ∞ is known, then the main theorem provides a stability result. In contrast to a former result, the theoretical framework considers robust control problems allowing a class of uncertainty and disturbances to be investigated. The different techniques are compared numerically for a discretized continuous‐time sliding‐mode based state‐feedback control.     

On‐off iterative adaptive controller for low‐power micro‐robotic step regulation

A novel model‐free iterative adaptive controller is presented for low‐power control of piezoelectric actuators. The controller uses simple adaptation rules based on known general behavior of piezoelectric actuators to adjust on‐off switching times to drive piezoelectric actuators through a desired transient step motion. Adaptation rules are based on small numbers of measurements taken during each iteration of the actuator movement. Combined with the use of only on‐off control inputs, controller implementation can be possible at much lower overall power levels than would be needed to implement a conventional control strategy such as through pulse‐width‐modulation (PWM) with real‐time feedback. Such power savings are particularly important for the intended controller application to piezoelectric microactuators driving autonomous terrestrial micro‐robots. A method for predicting convergence of systems with nominally linear dynamics and unknown, bounded nonlinearities is described, and applied to a sample target piezoelectric actuator. The controller is tested in simulation and experimentally on a piezoelectric cantilever actuator, and shows predicted convergence to the desired response. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Integrated fault estimation and fault‐tolerant control for uncertain Lipschitz nonlinear systems

This paper proposes an integrated fault estimation and fault‐tolerant control (FTC) design for Lipschitz non‐linear systems subject to uncertainty, disturbance, and actuator/sensor faults. A non‐linear unknown input observer without rank requirement is developed to estimate the system state and fault simultaneously, and based on these estimates an adaptive sliding mode FTC system is constructed. The observer and controller gains are obtained together via H_∞ optimization with a single‐step linear matrix inequality (LMI) formulation so as to achieve overall optimal FTC system design. A single‐link manipulator example is given to illustrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust output‐feedback control of state‐multiplicative noisy discrete‐time systems

Linear discrete‐time systems with stochastic and deterministic polytopic type uncertainties in their state‐space model are considered. A dynamic output‐feedback controller is obtained via a new approach that allows a derivation of a controller in spite of parameter uncertainty. In the proposed approach, the system is described via a difference equation and an augmented system is then used to obtain the output‐feedback controller parameters. The controller is obtained without assuming a specific structure to the quadratic Lyapunov function, and it is the first time that an output‐feedback controller is obtained for robust state‐multiplicative systems. The controller minimizes the stochastic L₂‐gain of the closed‐loop where a cost function is defined to be the expected value of the standard performance index with respect to the stochastic uncertainty. Two examples are given where the second of which demonstrates the applicability of our theory to a robot manipulator system. Copyright © 2016 John Wiley & Sons, Ltd.     

A test for stability robustness of linear time‐varying systems utilizing the linear time‐invariant ν‐gap metric

A stability robustness test is developed for internally stable, nominal, linear time‐invariant (LTI) feedback systems subject to structured, linear time‐varying uncertainty. There exists (in the literature) a necessary and sufficient structured small gain condition that determines robust stability in such cases. In this paper, the structured small gain theorem is utilized to formulate a (sufficient) stability robustness condition in a scaled LTI ν‐gap metric framework. The scaled LTI ν‐gap metric stability condition is shown to be computable via linear matrix inequality techniques, similar to the structured small gain condition. Apart from a comparison with a generalized robust stability margin as the final part of the stability test, however, the solution algorithm implemented to test the scaled LTI ν‐gap metric stability robustness condition is shown to be independent of knowledge about the controller transfer function (as opposed to the LMI feasibility problem associated with the scaled small gain condition which is dependent on knowledge about the controller). Thus, given a nominal plant and a structured uncertainty set, the stability robustness condition presented in this paper provides a single constraint on a controller (in terms of a large enough generalized robust stability margin) that (sufficiently) guarantees to stabilize all plants in the uncertainty set. Copyright © 2008 John Wiley & Sons, Ltd.     

Gain‐scheduled dynamic output feedback control for discrete‐time LPV systems

This paper presents synthesis conditions for the design of gain‐scheduled dynamic output feedback controllers for discrete‐time linear parameter‐varying systems. The state‐space matrix representation of the plant and of the controller can have a homogeneous polynomial dependency of arbitrary degree on the scheduling parameter. As an immediate extension, conditions for the synthesis of a multiobjective ??_∞ and ??₂ gain‐scheduled dynamic feedback controller are also provided. The scheduling parameters vary inside a polytope and are assumed to be a priori unknown, but measured in real‐time. If bounds on the rate of parameter variation are known, they can be taken into account, providing less conservative results. The geometric properties of the uncertainty domain are exploited to derive finite sets of linear matrix inequalities based on the existence of a homogeneous polynomially parameter‐dependent Lyapunov function. An application of the control design to a realistic engineering problem illustrates the benefits of the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust fault diagnosis and fault‐tolerant control for non‐Gaussian uncertain stochastic distribution control systems

The purpose of fault diagnosis of stochastic distribution control systems is to use the measured input and the system output probability density function to obtain the fault estimation information. A fault diagnosis and sliding mode fault‐tolerant control algorithms are proposed for non‐Gaussian uncertain stochastic distribution control systems with probability density function approximation error. The unknown input caused by model uncertainty can be considered as an exogenous disturbance, and the augmented observation error dynamic system is constructed using the thought of unknown input observer. Stability analysis is performed for the observation error dynamic system, and the H_∞ performance is guaranteed. Based on the information of fault estimation and the desired output probability density function, the sliding mode fault‐tolerant controller is designed to make the post‐fault output probability density function still track the desired distribution. This method avoids the difficulties of design of fault diagnosis observer caused by the uncertain input, and fault diagnosis and fault‐tolerant control are integrated. Two different illustrated examples are given to demonstrate the effectiveness of the proposed algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Output‐Feedback Control for Continuous‐time Interval Positive Systems under L1 Performance

This paper is concerned with the design of an L₁‐induced output‐feedback controller for continuous‐time positive systems with interval uncertainties. A necessary and sufficient condition for stability and an L₁‐induced performance of interval positive linear systems is proposed in terms of linear inequalities. Based on this, conditions for the existence of robust static output‐feedback controllers are established and an iterative convex optimization approach is developed to solve the conditions. For special single‐input‐multiple‐output (SIMO) positive systems, the problem of controller synthesis is completely solved with the help of an analytical formula for the L₁‐induced norm. An illustrative example is provided to show the effectiveness and applicability of the theoretical results.     

H∞Fuzzy State‐Feedback Control Plus State‐Derivative‐Feedback Control Synthesis for Photovoltaic Systems

This paper addresses the problem of designing an H_∞fuzzy state‐ feedback (SF) plus state‐derivative‐feedback (SDF) control system for photovoltaic (PV) systems based on a linear matrix inequality (LMI) approach. The TS fuzzy controller is designed on the basis of the Takagi‐Sugeno (TS) fuzzy model. The sufficient condition is found such that the system with the fuzzy controller is asymptotically stable and an H_∞performance is satisfied. First, a dc/dc buck converter is considered to regulate the power output by controlling state and state‐derivative variables of PV systems. The dynamic model of PV systems is approximated by the TS fuzzy model in the form of nonlinear systems. Then, based on a well‐known Lyapunov functional approach, the synthetic is formulated of an H_∞fuzzy SF plus SDF control law, which guarantees the L₂‐gain from an exogenous input to the regulated output to be less than or equal to some prescribed value. Finally, to show effectiveness, the simulation of the PV systems with the proposed control is assessed by the computer programme. The proposed control method shows good performance for power output and high stability for the PV system.     

Robust Reliable H∞ Control for Discrete‐Time Systems with Actuator Delays

This article focuses on the robust state feedback reliable H_∞ control problem for discrete‐time systems. Discrete‐time systems with time‐varying delayed control input are formulated. Based on the Lyapunov–Krasovskii method and linear matrix inequality (LMI) approach, delay‐dependent sufficient conditions are developed for synthesizing the state feedback controller for an uncertain discrete‐time system. The parameter uncertainty is assumed to be norm bounded. A design scheme for the state feedback reliable H_∞ controller is proposed in terms of LMIs, which can guarantee the global asymptotic stability and the minimum disturbance attenuation level. Finally, numerical examples are provided to illustrate the effectiveness and reduced conservatism of the proposed methods.     

Robust Nonlinear Observer And Observer‐Backstepping Control Design For Surface Ships

A robust passive non‐linear observer, utilizing the sliding mode concept and acceleration feedback (AFB) technique, is developed for ships. The main advantage of the proposed observer is that it is robust and that it takes the Coriolis‐centripetal matrix (C‐matrix) into account. The observer reconstructs velocities of ships and bias from slowly varying environmental disturbances. It also filters out the noise and wave frequency data from measurements to protect the actuators from wear and excessive fuel consumption. The sliding mode technique is introduced to improve robust performance against neglected disturbances, uncertainties, and unmodeled dynamics. The acceleration feedback technique and coordinate transformation are used for reshaping the inertia matrix and removing the C‐matrix from the mathematical model. Then, the observer design and stability analysis become simpler. An output feedback controller using observer backstepping and the Lyapunov redesign technique is derived, and the global stability of the observer and observer‐controller system is shown by Lyapunov stability theory. A set of simulations was carried out to verify the performance of the proposed observer and controller.     

On designing overlapping group mode‐dependent H∞ controllers of discrete‐time Markovian jump linear systems with incomplete mode transition probabilities

This paper is concerned with overlapping group mode‐dependent H_∞ control for a discrete‐time Markovian jump linear system, where global modes of the system are not completely available for controller design. Firstly, a randomly overlapping decomposition method is developed to reformulate the system by a set of locally overlapping switched groups with accessible group modes. The reformulated system switches among different group modes in an overlapping manner. Secondly, an overlapping group mode‐dependent state feedback controller is delicately constructed. Compared with some existing mode‐dependent controllers in the literature, the proposed controller has three features: (i) it does not require all exact knowledge of global modes; (ii) it takes full advantage of group mode information of the reformulated system; and (iii) it allows overlapping local modes to exist in the formed groups. Thirdly, sufficient conditions on the existence of a desired overlapping group mode‐dependent state feedback controller are derived such that the resultant closed‐loop system is stochastically stable with prescribed H_∞ performance. Furthermore, the proposed method is extended to design overlapping group mode‐dependent state feedback controllers subject to incomplete mode transition probabilities. The proposed overlapping group mode‐dependent framework is shown to be more general and includes traditional Markovian jump linear systems with completely accessible global modes as its special case. In the case of only one group in the reformulated system, it is shown that some existing result in existing literature can be retrieved. Finally, two illustrative examples are given to show the effectiveness of the obtained theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Mixed Event/Time‐Triggered Static Output Feedback L2‐Gain Control for Networked Control Systems

This paper considers the design of mixed event/time‐triggered controllers for networked control systems (NCSs) under transmission delay and possible packet dropout. Assuming that a conventional delayed static output feedback L₂‐gain controller exists, we propose an output‐based mixed event/time‐triggered communication scheme for reducing the network traffic in a NCS. Moreover, we show that a conventional delayed static output feedback L₂‐gain controller can be obtained by solving a linear matrix inequality with a matrix equality constraint. A numerical example is proposed for demonstrating the theoretical results.     

Delay‐ and Packet‐Disordering‐Dependent H∞ Output Tracking Control for Networked Control Systems

This paper is concerned with the problem of H_∞ output tracking control for networked control systems (NCSs) with network‐induced delay and packet disordering. Different from the results in existing literature, the controller design in this paper is both delay‐ and packet‐disordering‐dependent. Based on the different cases of consecutive predictions, the networked output tracking system is modeled into a switched system. Moreover, by the corresponding switching‐based Lyapunov functional approach, a linear matrix inequality (LMI)‐based procedure is proposed for designing state‐feedback controllers, which guarantees that the output of the closed‐loop NCSs tracks the output of a given reference model well in the H_∞ sense. In addition, the proposed method can be applied variously due to all kinds of prediction numbers of the consecutive disordering packet have been considered, and the designed controller is based on the prediction case in the last transmission interval, which brings about less conservatism. Finally numerical examples and simulations are used to illustrate the effectiveness and validity of the proposed switching‐based method and the delay‐ and packet‐disordering‐dependent H_∞ output tracking controller design.     

High-speed and precision control of a piezoelectric positioner with hysteresis,resonance and disturbance compensation

A novel composite control strategy is developed in this paper to compensate hysteresis, resonance and disturbances in a piezo-actuated nanopositioner. The control objective of the piezoelectric positioner is to achieve high tracking performance in terms of accuracy and speed. For this purpose, a Bouc–Wen model based hysteresis compensator is first applied to mitigate the hysteresis nonlinearity without the complex inverse hysteresis calculation. And then, the linear dynamic of the hysteresis compensated system is identified and inverted to account for the resonance. A model-based inversion feed-forward controller is designed to achieve high speed tracking. Afterwards, a high-gain feedback controller is designed based on a notch filter to handle the modeling inaccuracy and all kinds of disturbances. So, the feed-forward controller can be augmented to the feedback controller to realize high speed and precision tracking. The enhancement of tracking performance is demonstrated through several comparative experiments. The performance of 70 Hz bandwidth and 0.281 μm precision can be achieved, which validated the effectiveness of the proposed composite control scheme.     

An H∞non‐fragile observer‐based adaptive sliding mode controller design for uncertain fractional‐order nonlinear systems with time delay and input nonlinearity

In this paper the problem of non‐fragile adaptive sliding mode observer design is addressed for a class of nonlinear fractional‐order time‐delay systems with uncertainties, external disturbance, exogenous noise, and input nonlinearity. An H_∞ observer‐based adaptive sliding mode control considering the non‐fragility of the observer is proposed for this system. The sufficient asymptotic stability conditions are derived in the form of linear matrix inequalities. It is proven that the sliding surface is reachable in finite time. An illustrative example is provided which corroborates the effectiveness of the theoretical results.