Output‐feedback control of a class of stochastic nonlinear systems with linearly bounded unmeasurable states

In this paper, the problems of stochastic disturbance attenuation and asymptotic stabilization via output feedback are investigated for a class of stochastic nonlinear systems with linearly bounded unmeasurable states. For the first problem, under the condition that the stochastic inverse dynamics are generalized stochastic input‐to‐state stable, a linear output‐feedback controller is explicitly constructed to make the closed‐loop system noise‐to‐state stable. For the second problem, under the conditions that the stochastic inverse dynamics are stochastic input‐to‐state stable and the intensity of noise is known to be a unit matrix, a linear output‐feedback controller is explicitly constructed to make the closed‐loop system globally asymptotically stable in probability. Using a feedback domination design method, we construct these two controllers in a unified way. Copyright © 2007 John Wiley & Sons, Ltd.     

Revisiting the IISS Small‐Gain Theorem through Transient Plus ISS Small‐Gain Regulation

Recently, the small‐gain theorem for input‐to‐state stable (ISS) systems has been extended to the class of integral input‐to‐state stable (iISS) systems. Feedback connections of two iISS systems are robustly stable with respect to disturbance if an extended small‐gain condition is satisfied. It has been proved that at least one of the two iISS subsystems needs to be ISS for guaranteeing globally asymptotic stability and iISS of the overall system. Making use of this necessary condition for the stability, this paper gives a new interpretation to the iISS small gain theorem as transient plus ISS small‐gain regulation. The observation provides useful information for designing and analyzing nonlinear control systems based on the iISS small‐gain theorem.     

Robust Wind Speed Estimation and Control of Variable Speed Wind Turbines

In this work, a robust control scheme for variable speed wind turbine system that incorporates a doubly feed induction generator is described. The sliding mode controller is designed in order to track the optimum wind turbine speed value that produces the maximum power extraction for different wind speed values. A robust sliding mode observer for the aerodynamic torque is also proposed in order to avoid the wind speed sensors in the control scheme. The controller uses the estimated aerodynamic torque in order to calculate the reference value for the wind turbine speed. Another sliding mode control is also proposed in order to maintain the dc‐link voltage constant regardless of the direction of the rotor power flow. The stability analysis of the proposed controller under disturbances and parameter uncertainties is provided using the Lyapunov stability theory. Finally, the simulation results show that the proposed control scheme provides a high‐performance turbine speed control, in order to obtain the maximum wind power generation, and a high‐performance dc‐link regulation in the presence of system uncertainties.     

一种基于最优未知输入观测器的故障诊断方法

针对含有未知输入干扰和噪音的不确定动态系统,使用全阶未知输入观测器(Unknown input observer, UIO)来消除干扰项,实现状态估计, 结合Kalman滤波器算法来求解状态反馈矩阵,以使得输出残差信号的协方差最小,从而增强系统对噪声的鲁棒性,实现了 一种基于最优未知输入观测器的残差产生器.采用极大似然比(Generalized likelihood ratio, GLR)的方法对残差信号进行评估,通过设定的阈值来提高诊断率. 最后以风力发电机组传动系统出现加性传感器故障和乘性传感器故障为例, 进行了残差信号的仿真,仿真结果说明了该方法的有效性.     

Integrated fault estimation and fault‐tolerant control for stochastic systems with Brownian motions

This paper presents an integrated robust fault estimation and fault‐tolerant control technique for stochastic systems subjected to Brownian parameter perturbations. The augmented system approach, unknown input observer method, and optimization technique are integrated to achieve robust simultaneous estimates of the system states and the means of faults concerned. Meanwhile, a robust fault‐tolerant control strategy is developed by using actuator and sensor signal compensation techniques. Stochastic linear time‐invariant systems, stochastic systems with Lipschitz nonlinear constraint, and stochastic systems with quadratic inner‐bounded nonlinear constraint are respectively investigated, and the corresponding fault‐tolerant control algorithms are addressed. Finally, the effectiveness of the proposed fault‐tolerant control techniques is demonstrated via the drivetrain system of a 4.8 MW benchmark wind turbine, a 3‐tank system, and a numerical nonlinear model.     

A distributed leader‐following tracking controller using delayed control input information from neighbors

In this paper, we propose a simple, continuous, and distributed controller for the second‐order multiagent system to achieve leader‐following trajectory tracking, by exploiting the control input information of neighbors (CIIN) and using proportional‐derivative (PD) control in terms of local neighborhood synchronization error. A constant time delay is introduced in the CIIN as a design parameter to avoid the algebraic loop issue arising from the control input coupling. We develop an easily testable condition on the PD gains to ensure that the resulting neutral‐type error system is input‐to‐state stable for an arbitrary bounded delay, and prove that when the leader's acceleration is a Lipschitz continuous function with respect to time, the ultimate bound of tracking errors is strictly increasing with respect to the introduced time delay. Moreover, we analyze the robustness of the controller with respect to model uncertainties and show its potential advantages over two existing controllers in balancing the steady‐state tracking precision, the communication cost, and the continuity of controller signal. Finally, extensive simulations are conducted to show the effect of the delay on system stability, to verify the condition on PD gains, to confirm the robustness of the controller, and to demonstrate the detailed advantages.     

Robustness analysis of nonlinear observers for the slow variables of singularly perturbed systems

Estimation of unmeasured variables is a crucial objective in a broad range of applications. However, the estimation process turns into a challenging problem when the underlying model is nonlinear and even more so when additionally it exhibits multiple time scales. The existing results on estimation for systems with two time scales apply to a limited class of nonlinear plants and observers. We focus on analyzing nonlinear observers designed for the slow state variables of nonlinear singularly perturbed systems. Moreover, we consider the presence of bounded measurement noise in the system. We generalize current results by considering broader classes of plants and estimators to cover reduced‐order, full‐order, and higher‐order observers. First, we show that the singularly perturbed system has bounded solutions under an appropriate set of assumptions on the corresponding boundary layer and reduced systems. We then exploit this property to prove that, under reasonable assumptions, the error dynamics of the observer designed for the reduced system are semiglobally input‐to‐state practically stable when the observer is implemented on the original plant. We also conclude stability results when the measurement noise belongs to . In the absence of measurement noise, we state results on semiglobal practical asymptotical stability for the error dynamics. We illustrate the generality of our main results through three classes of systems with corresponding observers and one numerical example.     

永磁直驱风电机组的建模与仿真

针对永磁直驱风力发电机组建立了包括风力机、传动系统、永磁同步发电机、变流器各部分的数学模型;根据最大风能跟踪原理,提出了发电机侧和电网侧变流器的控制策略;在Matlab/Simulink仿真环境下建立了永磁直驱风电机组的仿真模型,对风速阶跃变化时机组运行情况进行了仿真。仿真结果验证了所提出控制策略的正确性和模型的合理性。     

Energy-based approach to the output feedback control of wind energy systems

Wind energy systems can be classified into constant speed and variable speed ones. In constant speed schemes, the generator is directly connected to the electric grid. On the other hand, variable speed operation can be accomplished interposing a static converter in the energy flow between the generator and the grid, permitting a high control flexibility. The main control objectives are the maximization of the conversion efficiency and the elimination of torque oscillations propagated through the drive train. It is assumed in this paper that the most flexible part of the system lies on the turbine, constraining the control solutions to generator speed feedback. The control task is addressed from a passivity-based control viewpoint. The drive train dynamics is modelled as a port-controlled Hamiltonian system with dissipation. Then, stabilization of the desired operating point is achieved through energy shaping and damping injection. Depending on the damping matrix assignment, different control solutions are recovered. Finally, a dynamic feedback controller which preserves the system structure is proposed to improve the system performance without measuring the wind velocity.     

Robustness analysis of systems' safety through a new notion of input‐to‐state safety

In this paper, we propose a new robustness notion that is applicable for certifying systems' safety with respect to external disturbance signals. The proposed input‐to‐state safety notion allows us to certify systems' safety in the presence of the disturbances, which is analogous to the notion of input‐to‐state stability for analyzing systems' stability.     

Input/output‐to‐state stability of nonlinear impulsive delay systems based on a new impulsive inequality

In this paper, input/output‐to‐state stability (IOSS) and integral IOSS (iIOSS) are investigated for nonlinear impulsive systems with delay. Based on a new impulsive inequality, we propose some sufficient criteria for IOSS and iIOSS of impulsive delay systems. It is shown that the obtained results for IOSS and iIOSS are regardless of the length of the impulsive interval and the size of time delay if the impulsive gain satisfies a given condition. In addition, based on the average impulsive interval method, some more useful sufficient conditions are derived for IOSS and iIOSS of impulsive delay systems with persistent large‐scale destabilizing impulses. Furthermore, a relationship is established among the average impulsive interval, impulses, time delay, and the decay of the system without impulses such that the impulsive delay system is input/output‐to‐state stable and integral input/output‐to‐state stable, respectively. Two examples are given to show the validity of the obtained results.     

Robust precision attitude tracking of an uncertain rigid spacecraft based on regulation theory

This paper explores regulation theory for the design of robust precision attitude tracking of an uncertain rigid spacecraft with external disturbances. Focusing on the attitude system in terms of unit quaternions with an unknown inertia matrix and unmodeled input disturbances, we first introduce specific nonlinear logic such that the resultant error‐quaternion system has an input‐to‐state stability property. Then, we establish an attitude deviation system with an output feedback normal form that has a strict vector relative degree of unity. This enables us to achieve robust output regulation based on an internal model. In particular, we can construct a high‐gain stabilizer for the relevant augmented system. As a major consequence, our study achieves not only precision attitude tracking with exponential convergence but also the input‐to‐state stability disturbance attenuation for the closed‐loop system. Finally, we show extensive simulation and experimental results to illustrate the approach.     

An observer-based blade-pitch controller of wind turbines in high wind speeds

The paper focuses on variable-rotor-speed/variable-blade-pitch wind turbines operating in the region of high wind speeds, where blade pitch and generator torque controllers are aimed at limiting the turbine's energy capture to the rated power value. Coupled design is described of an observer-based blade-pitch control input and a generator torque controller, both of which not requiring the availability of wind speed measurements. Closed loop convergence of the overall control system is proved. The proposed control solution has been validated on a 5-MW three-blade wind turbine using the National Renewable Energy Laboratory (NREL) wind turbine simulator FAST (Fatigue, Aerodynamics, Structures, and Turbulence) code.     

A new unified input‐to‐state stability criterion for impulsive stochastic delay systems with Markovian switching

In this paper, the problems of the input‐to‐state stability (ISS), the integral input‐to‐state stability (iISS), the stochastic input‐to‐state stability (SISS) and the e^λt(λ>0)‐weighted input‐to‐state stability (e^λt‐ISS) are investigated for nonlinear time‐varying impulsive stochastic delay systems with Markovian switching. We propose one unified criterion for the stabilizing impulse and the destabilizing impulse to guarantee the ISS, iISS, SISS and e^λt‐ISS for such systems. We verify that when the upper bound of the average impulsive interval is given, the stabilizing impulsive effect can stabilize the systems without ISS. We also show that the destabilizing impulsive signal with a given lower bound of the average impulsive interval can preserve the ISS of the systems. In addition, one criterion for guaranteeing the ISS of nonlinear time‐varying stochastic hybrid systems under no impulsive effect is derived. Two examples including one coupled dynamic systems model subject to external random perturbation of the continuous input and impulsive input disturbances are provided to illustrate the effectiveness of the theoretic results developed.     

On the pth moment integral input‐to‐state stability and input‐to‐state stability criteria for impulsive stochastic functional differential equations

In this paper, several new Razumikhin‐type theorems for impulsive stochastic functional differential equations are studied by applying stochastic analysis techniques and Razumikhin stability approach. By developing a new comparison principle for stochastic version, some novel criteria of the pth moment integral input‐to‐state stability and input‐to‐state stability are derived for the related systems. The feature of the criteria shows that time‐derivatives of the Razumikhin functions are allowed to be indefinite, even unbounded, which can loosen the constraints of the existing results. Finally, some examples are given to illustrate the usefulness and significance of the theoretical results.     

A decentralized multivariable controller for hydrostatic wind turbine drivetrain

A hydrostatic drivetrain transmits wind turbine energy to a generator. One hydrostatic transmission system (HTS) configuration utilizes a fixed displacement pump and a variable displacement motor. The system dynamics are captured in a nonlinear multi‐input multi‐output mathematical model. This paper introduces a decentralized control configuration based on this model to achieve two desired objectives: maximizing the harvested energy without direct measurement of wind and regulating the frequency of the generator without using power electronic converters. To accomplish these objectives, suitable pairing of control actuators and system responses are identified through nonlinear relative gain arrays (RGA) analysis. The pairing also provides a strong decoupling of control loops. So maximum power point tracking (MPPT) is achieved independently while the generator speed is regulated to maintain the frequency of generated power at 60 Hz. Simulation results demonstrate robust performance of MPPT and frequency regulation in the presence of uncertainties in the turbine and HTS model. We also demonstrate that the RGA paired input‐out control configuration offers superior performance over other possible input–output paired control configurations.     

Output feedback regulation control for a class of cascade nonlinear systems by time‐varying Kalman observer

The global output feedback regulation problem is studied for a class of cascade nonlinear systems. The considered system represents more general classes of nonlinear uncertain systems, including the integral input‐to‐state stable (iISS) unmodeled dynamics, the unknown control direction, the parameter uncertainty, and the external disturbance additively in the input channel. Technically, we explore the changing supply rate technique for the iISS system to deal the iISS unmodeled dynamics and apply the Nussbaum‐type gain into the control design to overcome the unknown control direction. Additionally, a dynamic extended state observer in the form of a time‐varying Kalman observer is novelly constructed to overcome the unmeasured state components in the nonlinear uncertainties. It is shown that the global regulation problem is well addressed by the proposed method, and its efficacy is demonstrated by a fan speed control system.     

Strong stabilisation of a wind turbine tower model in the plane of the turbine blades

We investigate the strong stabilisation of a wind turbine tower model in the plane of the turbine blades, which comprises a nonuniform NASA Spacecraft Control Laboratory Experiment (SCOLE) system and a two-mass drive-train model (with gearbox). The control input is the torque created by the electrical generator. Using a strong stabilisation theorem for a class of impedance passive linear systems with bounded control and observation operators, we show that the wind turbine tower model can be strongly stabilised. The control is by static output feedback from the angular velocities of the nacelle and the generator rotor.     

Nonlinear PI control for variable pitch wind turbine

Wind turbine uses a pitch angle controller to reduce the power captured above the rated wind speed and release the mechanical stress of the drive train. This paper investigates a nonlinear PI (N-PI) based pitch angle controller, by designing an extended-order state and perturbation observer to estimate and compensate unknown time-varying nonlinearities and disturbances. The proposed N-PI does not require the accurate model and uses only one set of PI parameters to provide a global optimal performance under wind speed changes. Simulation verification is based on a simplified two-mass wind turbine model and a detailed aero-elastic wind turbine simulator (FAST), respectively. Simulation results show that the N-PI controller can provide better dynamic performances of power regulation, load stress reduction and actuator usage, comparing with the conventional PI and gain-scheduled PI controller, and better robustness against of model uncertainties than feedback linearization control.     

State‐feedback stabilization for stochastic high‐order nonlinear systems with SISS inverse dynamics

This paper investigates the problem of state‐feedback control for a class of stochastic high‐order nonlinear systems with stochastic inverse dynamics. Under the assumption that the inverse dynamics of the subsystem are stochastic input‐to‐state stable (SISS), by extending through adding a power integrator technique, choosing an appropriate Lyapunov function and using the idea of changing supply function, a smooth state‐feedback controller is explicitly constructed to render the system globally asymptotically stable in probability and the states can be regulated to the origin. A simulation example is provided to show the effectiveness of the proposed scheme. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society