An adaptive robust observer for velocity estimation in an electro‐hydraulic system

This paper proposes the design of an observer to estimate the velocity of an electro‐hydraulic system by using pressure measurements only. The difficulties involved in the design of an observer for such a system include the highly nonlinear system dynamics, severe parametric uncertainties such as large variation of inertial load and unmatched model uncertainties. In order to address these issues, a nonlinear model‐based adaptive robust observer is designed to estimate the velocity. The contributions of the proposed work is twofold. First, it introduces a novel coordinate transformation to reconstruct the velocity estimate. And second, from a structural viewpoint, the design has two important features: (i) an underlying robust filter structure, which can attenuate the effect of uncertain nonlinearities such as friction and disturbances on the velocity estimation, and (ii) an adaptation mechanism to reduce the extent of parametric uncertainties. Experimental results on the swing motion control of an electro‐hydraulic robot arm demonstrate the effectiveness of the proposed observer. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust fault estimation and fault-tolerant tracking control for uncertain Takagi–Sugeno fuzzy systems: Application to single link manipulator

This article concerns the estimation and tracking control problems for Takagi–Sugeno systems with disturbances and norm bounded uncertainties in presence of sensor and actuator faults (SAF). First, we propose a robust fuzzy observer (RFO) design method to estimate both state and SAF for the considered class of the nonlinear systems. Then, this RFO-based fault tolerant tracking control is developed not only to compensate the SAF effects but also to ensure the state convergence to desired trajectories in spite of their presence. To reduce the conservatism of design conditions, observer and controller gains are calculated in a single step by solving a set of linear matrix inequality constraints. H_∞ criterion is used to attenuate disturbance effects and to reduce the tracking error. Finally, simulation results by considering two types of actuator fault and comparative study on a single link flexible joint manipulator are provided to underline the performances of the mentioned process.     

An integrated fault estimation and fault tolerant control method using H∞-based adaptive observers

An integrated fault estimation/fault-tolerant control (FTC) scheme is developed in this article for nonlinear Lipschitz systems in the presence of external disturbances and actuator failures. To address this problem, coupled uncertainties between the observer error dynamics and the control system are considered, which is conveniently ignored in control approaches based on the separation principle. An H_∞ -based adaptive observer is proposed to simultaneously estimate the system states and actuator faults without the restrictive strictly positive realness or persistent excitation conditions. The FTC is constructed by sliding mode control using the estimated states generated by the developed observer. A novel sufficient condition is derived in terms of linear matrix inequality (LMI) including both the system control dynamics and the estimation errors; then, the control parameters and observer gains are simultaneously obtained via solving the mentioned LMI based on the H_∞ optimization. Finally, a flexible joint robot is considered to illustrate the effectiveness of the developed method.     

基于改进内模控制的永磁同步电机电流环设计

永磁同步电机(PMSM)作为一种高阶非线性系统,由于参数摄动和外部干扰的原因,传统内模控制器不能保证其精确的控制要求。在传统内模控制的基础上,设计了一种基于指数收敛的误差干扰观测器。在解耦和反电动势补偿情况下,建立内模控制器,然后由内模控制器的输出和反馈电流,构造误差干扰观测器的状态方程,输出误差补偿信号,补偿电机运行过程中参数变动和干扰因素,实现PMSM的高精度控制。建立MATLAB/Simulink仿真模型,仿真中人为增加不确定量和扰动。仿真结果表明,在存在不确定信号和负载扰动时,采用改进的内模控制可以实现电流补偿,降低电流纹波,减小电流稳态误差,同时提高转速响应速度,降低扰动误差。     

Fault detection for a class of nonlinear networked control systems

In this paper, an observer‐based fault detection (FD) method is presented for a class of nonlinear networked control systems (NCSs) with Markov transfer delays. Firstly, based on Euler approximate method, a nonlinear NCS model with uncertainty is proposed using the Takagi‐Sugeno (T‐S) fuzzy model. Some geometric conditions are given to transfer the NCS model into an output‐feedback form. Then, the H_∞ FD observer is designed such that the estimation error (residual) converges to zero, if there exist no fault and uncertainty in the system, or the residual is minimized in the sense of H_∞ norm, when system contains fault and uncertainties. Furthermore, to simplify the model, the approximate model without uncertainty is considered. Then, sufficient conditions for the existence of FD observer gain and the sampling time of NCSs are given to achieve the semiglobal practical property. An inverted pendulum example is used to illustrate the efficiency of the developed techniques. Copyright © 2009 John Wiley & Sons, Ltd.     

Extremum seeking for unknown scalar maps in cascade with a class of parabolic partial differential equations

We present a generalization of the scalar gradient extremum seeking (ES) algorithm, which maximizes static maps in the presence of infinite-dimensional dynamics described by parabolic partial differential equations (PDEs). The PDE dynamics contains reaction-advection-diffusion (RAD) like terms. Basically, the effects of the PDE dynamics in the additive dither signals are canceled out using the trajectory generation paradigm. Moreover, the inclusion of a boundary control for the PDE process stabilizes the closed-loop feedback system. By properly demodulating the map output corresponding to the manner in which it is perturbed, the ES algorithm maximizes the output of the unknown map. In particular, our parabolic PDE compensator employs the same perturbation-based (averaging-based) estimate for the Hessian of the function to be maximized applied in the previous publications free of PDEs. We prove local stability of the algorithm, real-time maximization of the map and convergence to a small neighborhood of the desired (unknown) extremum by means of backstepping transformation, Lyapunov functional and the theory of averaging in infinite dimensions. Finally, we present the generalization to the scalar Newton-based ES algorithm, which maximizes the map's higher derivatives in the presence of RAD-like dynamics. By modifying the demodulating signals, the ES algorithm maximizes the nth derivative only through measurements of the own map. The Newton-based ES approach removes the dependence of the convergence rate on the unknown Hessian of the higher derivative, an effort to improve performance and remove limitations of standard gradient-based ES. Numerical examples support the theoretical results.     

Adaptive state feedback control by orthogonal approximation functions

For a class of feedback linearizable systems a state feedback adaptive control based on orthogonal approximation functions is designed, under the assumption of matching conditions for the uncertainties and of known bounds on a given compact set for the unknown non‐linear function. By virtue of Bessel inequality, the bound on the unknown non‐linear function gives a bound on the norm of the optimal weight vector for any choice of the number of approximating functions, which allows us to design a robust state feedback adaptive scheme with parameter projections. The resulting control algorithm has several advantages over available schemes: it does not require a priori bounds on the approximation error and on the optimal weight vector; it is repeatable, since the set of initial conditions for the state and the parameter estimates from which a class of reference signals is tracked is explicitly given; it characterizes the L_∞ and L₂ performance of the tracking error in terms of both the approximation and the parameter estimation error; it gives full flexibility in the choice of the number of approximating orthogonal functions. Copyright © 2002 John Wiley & Sons, Ltd.     

基于复合控制的圆筒形永磁直线同步电机位置控制

针对圆筒形永磁直线同步电机,设计了一种位置控制系统。考虑到直线电机的推力脉动、摩擦力和系统模型的不确定性,采用干扰观测器(DOB)对其进行在线估算并进行补偿,经过补偿,系统模型近似等价其标称模型;基于标称模型设计速度前馈控制器,基于速度控制系统的模型设计位置前馈控制器,使得永磁直线同步电机控制系统的输出能够无误差地跟踪期望的速度和位置响应曲线;采用综合校正方法设计反馈控制器,保证系统的稳定性。最后给出了仿真结果。     

An adaptive controller–observer scheme for temperature control of non‐chain reactions in batch reactors

In this paper an adaptive controller–observer temperature control scheme is developed for a class of irreversible non‐chain reactions taking place in batch reactors. The scheme is based on a nonlinear observer for the estimation of the heat released by the reaction, where the heat transfer coefficient is adaptively estimated. Tracking of the desired reactor temperature is achieved via a two‐loop control scheme, where an independent adaptive estimate of the heat transfer coefficient is used as well. Remarkably, the observer and the controller can be designed and tuned separately. The convergence of both the nonlinear observer and of the overall controller–observer scheme is analyzed by resorting to a Lyapunov‐like argument. A comparative simulation case study is developed to test the performance of the proposed scheme and compare it with other approaches already known in the literature. Copyright © 2007 John Wiley & Sons, Ltd.     

Learning‐based iterative modular adaptive control for nonlinear systems

In this paper, we study the problem of adaptive trajectory tracking control for a class of nonlinear systems with structured parametric uncertainties. We propose to use an iterative modular approach: we first design a robust nonlinear state feedback that renders the closed‐loop input‐to‐state stable (ISS). Here, the input is considered to be the estimation error of the uncertain parameters, and the state is considered to be the closed‐loop output tracking error. Next, we propose an iterative adaptive algorithm, where we augment this robust ISS controller with an iterative data‐driven learning algorithm to estimate online the parametric uncertainties of the model. We implement this method with two different learning approaches. The first one is a data‐driven multiparametric extremum seeking method, which guarantees local convergence results, and the second is a Bayesian optimization‐based method called Gaussian Process Upper Confidence Bound, which guarantees global results in a compact search set. The combination of the ISS feedback and the data‐driven learning algorithms gives a learning‐based modular indirect adaptive controller. We show the efficiency of this approach on a two‐link robot manipulator numerical example.     

基于微分同坯映射和扩张状态观测器的鲁棒励磁控制器设计

通过微分同坯映射将仿射非线性系统方程的非线性因素转换到含有控制输入的状态方程,转换后的系统中所有不确定项都归结到扩张状态变量中。利用扩张状态观测器观测该部分,并经状态反馈将其线性化。由于实际系统存在观测误差和模型误差,为了进一步考虑反馈线性之后系统的不确定性,将鲁棒控制引入励磁控制器的设计之中,使得设计的控制器具有更好的鲁棒性,最后在Matlab上进行仿真试验。仿真结果证明了该方法的有效性。     

Nonlinear Optimal Internal-Model Control for Multiple Time-Delay Systems with Application to Vehicle Suspensions

Abstract

The paper considers the nonlinear optimal vibration control problem for systems with multiple delays, i.e. control delay, state delay, and measurement delay, under reference input. The time-delay system is transformed into an equivalent delay-free one via functional transformations. The nonlinear optimal control law is designed by solving a Riccati equation, a Sylvester equation, and an adjoint differential equation. The effects generated by nonlinearity and time-delay are compensated by the nonlinear compensator and the memory terms in the designed controller. An internal model is constructed so that the disturbance will be rejected with zero steady-state error as well as the reference is tracked, through the dynamical compensator produced from the internal model. An observer is constructed to make the controller physically realizable. The result is extended to vehicle suspension systems. It is demonstrated that the road vibration that is encountered by the suspension will be canceled entirely by the proposed control. Numerical simulations illustrate the effectiveness of the presented controller.     

Neural observer-based small fault detection and isolation for uncertain nonlinear systems

Small faults (some weak faults with a tiny magnitude) are difficult to detect and may cause severe problems leading to degrading the system performance. This paper proposes an approach to estimate, detect, and isolate small faults in uncertain nonlinear systems subjected to model uncertainties, disturbances, and measurement noise. A robust observer is developed to alleviate the lack of full state measurement. Using the estimated state, a dynamical radial basis function neural networks observer is designed in form of LMI problem to accurately learn the function of the inseparable mixture between modeling uncertainty and the small fault. By exploiting the knowledge obtained by the learning phase, a bank of observers is constructed for both normal and fault modes. A set of residues is achieved by filtering the differences between the outputs of the bank of observers and the monitored system output. Due to the noise dampening characteristics of the filters and according to the smallest residual principle, the small faults can be detected and isolated successfully. Finally, rigorous analysis is performed to characterize the detection and isolation capabilities of the proposed scheme. Simulation results are used to prove the efficacy and merits of the proposed approach.     

双馈风电机组传动系统扭振抑制自抗扰控制

扭振是造成风电机组传动系统零部件疲劳损伤的主要原因之一。为了通过控制减小风电机组传动系统疲劳载荷,本文在分析风电机组传动系统中非线性不确定因素作用的基础上,设计了一种扭振抑制自抗扰控制器。该控制器将传动系统中的非线性不确定因素作用和外界扰动归结为系统总扰动,通过扩张状态观测器进行实时估计,并在发电机转矩控制中给予补偿,增强了控制器的适应性和鲁棒性。以3MW双馈风电机组为控制对象的试验结果表明,该控制器可以在不影响机组发电量的前提下抑制传动系统扭振,明显减小齿轮箱的转矩波动,从而减轻扭转载荷对主要零部件的疲劳损伤。     

Robust H∞ filtering for uncertain Markovian jump systems with mode‐dependent distributed delays

This paper deals with the problem of robust H_∞ filter design for Markovian jump systems with norm‐bounded time‐varying parameter uncertainties and mode‐dependent distributed delays. Both the state and the measurement equations are assumed to be with distributed delays. Sufficient conditions for the existence of robust H_∞ filters are obtained. Via solving a set of linear matrix inequalities, a desired filter can be constructed. The developed theory is illustrated by a simulation example. Copyright © 2009 John Wiley & Sons, Ltd.     

Nonlinear partial differential equation modeling and adaptive fault-tolerant vibration control of flexible rotatable manipulator in three-dimensional space

In this article, we investigate the problem of nonlinear modeling and adaptive boundary vibration control with actuator failure for a flexible rotatable manipulator in three-dimensional space, which is made up of a rotatable base and a flexible manipulator. In order to accurately reflect the characteristics of the distributed parameters, the Hamilton principle is introduced to derive the dynamic model expressed by partial differential equations (PDEs). Based on the model, an innovative boundary control scheme is proposed to eliminate the deflection and vibration simultaneously, and to guarantee that the rotatable base and the flexible manipulator can track the desired angle respectively. The adaptive law is developed to estimate the loss of the actuator. The effectiveness of the designed controller is verified from both theoretical analysis and numerical simulation.     

New approaches with sensorless drives

In this article, we investigate a means of extricating the position information involved in terminal voltages and currents to estimate the rotor position of a PM synchronous motor. One way to extract the position information is to construct the state observer based on the motor model including electrical and mechanical equations. Then, the stability of the observer is an important issue in providing accurate position information for the motor drive system. In order to stabilize the system, the gains of the observer have to be optimized. However, these schemes have some difficulties in determining the optimum gains of the observer under any operating condition because the electrical equations are nonlinear in such motor models. We present a new approach for constructing the observer to extract precise information from the rotor position, and its speed from the technical quantities. First, to overcome the aforementioned problem, we propose the control inputs that can eliminate the nonlinear term in the electrical equations and realize the linearization of the motor model. This permits use of linear control strategies to determine the characteristics of the system. Second, we perform the rotor-speed estimation by using the reduced-order observer based on the linearized model. Third, the rotor position is calculated by using the estimated rotor speed and then corrected by the d-axis current error. Thus, we realize the stable drive of the motor without position sensors by measuring only two line currents. Finally, the validity of the proposed control scheme is confirmed by experiments     

Distributed output estimation error observer-based adaptive fault-tolerant consensus tracking control of multi-agent systems

The purpose of this study is to discuss the fully distributed design of output estimation error observer and fault-tolerant consensus tracking control for a class of multi-agent systems with Lipschitz nonlinear dynamics and actuator faults. Firstly, based on the relative output measurements of neighboring agents, the distributed output estimation error observer is developed to adaptively estimate the state and fault information of each agent, and further overcome the difficulties of online updating the adaptive estimations of unknown hyper-parameters. Secondly, to achieve the state consensus tracking goal and compensate for the negative effects of actuator faults, the distributed fault-tolerant consensus tracking control scheme is proposed on the basis of the state estimation and adaptive fault estimation information, and has excellent robustness and consensus tracking control performance. Moreover, sufficient criteria can ensure that consensus tracking error of each agent converges to a small set near the origin. Finally, numerical simulations are provided to show the effectiveness of the proposed fully distributed algorithm.