Simultaneous state and output disturbance estimations for a class of switched linear systems with unknown inputs

The paper considers the issues of state estimation and output disturbance reconstruction for a class of switched linear systems with unknown inputs. A singular switched system is derived from the original switched system by taking the output disturbance as a part of a new extended state vector. For the constructed singular switched system, a robust sliding-mode switched observer which can not only estimate the states of original switched system but also reconstruct output disturbances is proposed, where the switching of the observer is synchronous with that of the switched system. A sufficient condition is provided to guarantee the existence of the switched observer by the feasibility of an optimisation problem with linear matrix inequality constraint, and the corresponding switching signal with average dwell time is designed such that the convergence of the estimation error system is proven to be exponential. Based on the state estimation of singular switched system, the methods of state estimation and output disturbance reconstruction of original switched system are proposed. Finally, the simulation results confirm the predicted performance of the proposed methods.     

Adaptive disturbance observer‐based control for stochastic systems with multiple heterogeneous disturbances

Antidisturbance control problem is discussed for stochastic systems with multiple heterogeneous disturbances, which include the white noise and the disturbance with unknown frequencies and amplitudes. An adaptive disturbance observer is designed to estimate the disturbance with unknown frequencies and amplitudes, based on which, an adaptive disturbance observer‐based control scheme is proposed by combining adaptive technique and linear matrix inequality method. It is proved that the closed‐loop system is asymptotically bounded in mean square when multiple heterogeneous disturbances exist simultaneously and that the equilibrium is globally asymptotically stable in probability as additive disturbance disappears. Finally, two simulation examples, including a wind turbine system, are given to show the effectiveness of the proposed scheme.     

基于参考模型的扰动观测器控制系统

为了补偿控制系统的未知动态和外部扰动,论文提出一种基于参考模型的扰动观测器控制系统.首先,分析了二阶理想参考模型控制系统的设计,并通过闭环传递函数证明了参考模型控制系统的稳定性.然后,设计了二阶系统扰动观测器和基于参考模型的扰动观测器控制律,分析了二阶闭环控制误差系统收敛性.并推广到n阶控制系统,证明了n阶闭环控制误差系统稳定性.最后,仿真实验结果表明,与线性自抗扰控制(LADRC)系统相比,基于参考模型的扰动观测器控制系统阶跃响应的跟踪精度和抗扰性能明显优于LADRC系统,扰动的估计精度高,控制输入量小于LADRC系统;基于参考模型的扰动观测器控制系统正弦跟踪精度和扰动的估计精度也高于LADRC系统.该新型控制系统结构简单,抗扰性能好,控制效率高,具有重要的工程应用价值.     

Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach

In this paper the disturbance attenuation and rejection problem is investigated for a class of MIMO nonlinear systems in the disturbance‐observer‐based control (DOBC) framework. The unknown external disturbances are supposed to be generated by an exogenous system, where some classic assumptions on disturbances can be removed. Two kinds of nonlinear dynamics in the plants are considered, respectively, which correspond to the known and unknown functions. Design schemes are presented for both the full‐order and reduced‐order disturbance observers via LMI‐based algorithms. For the plants with known nonlinearity, it is shown that the full‐order observer can be constructed by augmenting the estimation of disturbances into the full‐state estimation, and the reduced‐order ones can be designed by using of the separation principle. For the uncertain nonlinearity, the problem can be reduced to a robust observer design problem. By integrating the disturbance observers with conventional control laws, the disturbances can be rejected and the desired dynamic performances can be guaranteed. If the disturbance also has perturbations, it is shown that the proposed approaches are infeasible and further research is required in the future. Finally, simulations for a flight control system is given to demonstrate the effectiveness of the results. Copyright © 2005 John Wiley & Sons, Ltd.     

Robust output regulation of a triaxial MEMS gyroscope via nonlinear active disturbance rejection

This paper presents a nonlinear disturbance rejection–based controller for the robust output regulation of a triaxial microelectromechanical system (MEMS) vibratory gyroscope. In a MEMS gyroscope, parameter variations, mechanical couplings, suspension system nonlinearities, thermal noise, and centripetal/Coriolis forces are the main uncertainty sources. In the dynamical equations of the gyroscope, these uncertainties appear as a matched total disturbance, which does not coincide with the required structure of a standard output regulation problem. More specifically, the total disturbance is not guaranteed to belong to the solution space of a fixed dynamical system. Therefore, we propose a control system that comprises a nominal output regulator equipped with a disturbance rejection loop. On the basis of a suitable reference dynamics of the gyroscope, the control system is developed as the stabilization of a zero‐error invariant manifold in the tracking error space. In the disturbance rejection loop, a nonlinear extended state observer (ESO) is designed to estimate the total disturbance. The convergence of the ESO is analyzed in a Lyapunov‐Lurie framework by linear matrix inequalities (LMIs). In the nominal output regulation loop, the stabilization problem of the desired manifold is tackled by introducing a suitable distance coordinate. Next, to achieve guaranteed attenuation of the ESO estimation errors, an energy‐to‐peak design is pursued. On the basis of the center manifold theory, the stability of the overall closed‐loop system is guaranteed. The efficacy of the proposed control method is assessed through software simulations.     

Adaptive disturbance estimation and cancelation for ships under thruster saturation

This work addresses the problem of disturbance estimation and cancelation for ships with ocean disturbances and modeling uncertainties under thruster saturation effects. The ocean disturbances are expressed as the multiple sinusoidal disturbances with unknown frequencies, amplitudes, and phases. By means of a parametric exogenous system and a canonical model with unknown disturbances being inputs, the ocean disturbances are represented as the multivariate regression model with unavailable regressors and regression parameters. An observer is employed to provide the regressor estimation, such that the disturbance estimation and cancelation are converted to the adaptive control problem. The robust control term with the adaptive technique attenuates the modeling uncertainties. The thruster saturation effects are reduced using the state vectors from the auxiliary dynamic filter to online correct the control errors. The ship disturbance cancelation controller is derived via the adaptive backstepping. The closed‐loop tracking system is guaranteed to be uniformly ultimately stable and the ship's position and heading navigate along with desired trajectories. The proposed adaptive control scheme is validated by simulations with comparisons on a 1:70 scaled model ship CyberShip II in different cases.     

含不匹配扰动非严格反馈系统的输出反馈补偿控制

针对一类非严格反馈非线性系统,系统中包含不确定函数和未知外部扰动,提出一种带不匹配扰动补偿的输出反馈模糊控制器.采用模糊逻辑系统逼近未知的非线性函数,同时构造模糊状态观测器观测系统未知状态.考虑观测器和控制器会受到外部扰动和模糊逼近误差构成的不匹配总扰动信号影响,采用改进的扰动观测器对不匹配扰动进行估计和补偿,使扰动观测误差能够在有限时间内平缓地收敛到任意小的范围,消除不匹配扰动信号对模糊观测器设计的影响.同时在控制器设计中进行扰动的精确补偿,提高系统的抗扰动性.通过Lyapunov函数证明了闭环系统所有信号都是有界的.最后,通过数值仿真进一步验证了所提出方法的有效性.     

Feedback passification of switched stochastic time‐delay systems with multiple disturbances via DOBC

This paper is concerned with the problem of feedback passification for switched stochastic time‐delay systems with multiple disturbances subject to mode‐dependent average dwell‐time switching. The multiple disturbances are composed of two parts: one is given through an exogenous system and the other is described in the form of norm‐bounded vector. A disturbance observer is constructed to estimate an exogenous disturbance. Then, a state feedback controller that includes the estimation value is designed to guarantee the passivity of the closed‐loop system. The observer and controller gains are developed via linear matrix inequalities. The effectiveness of the proposed method is verified through a numerical example and an application example to PWM‐driven boost converter.     

Composite hierarchical anti‐disturbance control for nonlinear systems with DOBC and fuzzy control

Anti‐disturbance control and estimation problem is introduced for a class of nonlinear system subject to disturbances. The adaptive disturbance observers are constructed separately from the controller design to estimate the disturbance with partial known information. By integrating disturbance‐observer‐based control with fuzzy control, a novel type of composite hierarchical anti‐disturbance control scheme is presented for a class of nonlinear system with unknown nonlinear dynamics. Simulations for a flight control system are given to demonstrate the effectiveness of the results compared with the previous schemes.Copyright © 2012 John Wiley & Sons, Ltd.     

Robust adaptive tracking control for a class of mechanical systems with unknown disturbances under actuator saturation

A robust adaptive tracking control scheme is presented for a class of multiple‐input and multiple‐output mechanical systems with unknown disturbances under actuator saturation. The unknown disturbances are expressed as the outputs of a linear exogenous system with unknown coefficient matrices. An adaptive disturbance observer is constructed for the online disturbance estimation. An actuator saturation compensator is introduced to attenuate the adverse effects of actuator saturation. The adaptive backstepping method is then applied to design the robust adaptive tracking control law. It is proved that the designed control law makes the system outputs track the desired trajectories and guarantees the global uniform ultimate stability of the closed‐loop control system. Simulations on a two‐link robotic manipulator verify the effectiveness of the proposed control scheme.     

Model reference resilient control for the helicopter with time‐varying disturbance

In this paper, the problem of model reference resilient control is investigated for the helicopter system with the time‐varying disturbance and unmeasurable states. Firstly, a disturbance observer and a state observer are built to estimate the time‐varying disturbance and unmeasurable states. Then, combining the methods of model reference control and disturbance observer–based control, the state feedback robust resilient control scheme and the dynamic output feedback robust resilient control method are proposed, respectively. Under the two developed robust resilient control schemes, sufficient conditions are obtained to guarantee that the helicopter system asymptotically tracks the reference model with H_∞ performance. Finally, simulation results are presented to show the effectiveness of the model reference resilient control method.     

一种反向递推正弦干扰观测器的设计方法

在多源干扰环境下,考虑一种基于输出信号的正弦干扰估计方法.引入低通滤波器激励干扰特性,得到一组级联关系的不可测信号,并将其分解为标准正弦虚拟干扰、等价有界干扰以及衰减项;在频率已知条件下,设计辅助滤波器,建立干扰频率与虚拟干扰之间关系,从而将外部正弦扰动表示为关于虚拟干扰的参数形式,利用虚拟干扰的估计值逐次降阶反推输入干扰.该干扰观测器设计方法独立于控制器结构,不需要估计等效干扰状态,可很大程度上降低计算复杂度.当不存在等价有界干扰时,这种反向递推方式可以渐近跟踪正弦干扰.在多源干扰环境下,通过调节辅助滤波器参数可以保证干扰误差动态一致最终有界特性.仿真和实验验证了该干扰观测结构的有效性.     

Stability analysis of a control system with nonlinear input uncertainty based on disturbance observer

In disturbance observer (DO)‐based control, control input attenuates a disturbance using observer output. Thus, the input may not achieve the attenuation if the input term includes uncertainty. Therefore, in order to correctly suppress the disturbance, it is essential to consider the uncertainty existing in the input term, and thus this article focuses on a nonlinear uncertainty in the input term. This article analyzes the stability and robustness of a DO‐based nonlinear control system with both the disturbance and the input uncertainty. We address the case that the disturbance and the uncertainty depend on time and states of a controlled system. The disturbance and the uncertainty are gathered in an integrated disturbance, and the integrated disturbance depends on many variables: the states, the control input, and the time. Therefore, a norm estimations for the disturbance and a time variation of the disturbance is difficult without knowledge of the state trajectory. Hence, a slope‐restriction for the disturbance is used for the stability analysis. Based on the mathematical analysis, we show input‐to‐state stability conditions due to extend the application class of the DO‐based controller to a control system with the disturbance and the nonlinear input uncertainty. The analytical results are verified by numerical simulations.     

Finite time state and disturbance estimation for robust performance of motion control systems using sliding modes

In this paper, simultaneous state and disturbance estimation of a drive system composed of motor connected to a load is proposed. Such a system is represented by a two mass model realising in a fourth-order plant. Backlash is introduced as the nonlinear disturbance in gears which is proposed to be estimated and in turn compensated. For this motion control system, a two-stage higher order sliding-mode observer is proposed for state and backlash estimation. The novelty lies in the fact that for this fourth-order system, output is considered from the motor end only, i.e. its angular displacement. The unmeasured states consisting of output derivative, load-side angular displacement and its derivative along with backlash are estimated in finite time. This disturbance due to backlash is unmatched in nature. The estimated states and disturbance are used to devise a robust sliding-mode control. This proposed scheme is validated in simulation and experimentation.     

Composite stratified anti‐disturbance control for a class of MIMO discrete‐time systems with nonlinearity

Anti‐disturbance control and estimation problem are investigated for nonlinear system subject to multi‐source disturbances. The disturbances classified model is proposed based on the error and noise analysis of priori knowledge. The disturbance observers are constructed separately from the controller design to estimate the disturbance with partial known information. By integrating disturbance‐observer‐based control with discrete‐time sliding‐mode control (DSMC), a novel type of composite stratified anti‐disturbance control scheme is presented for a class of multiple‐input–multiple‐output discrete‐time systems with known and unknown nonlinear dynamics, respectively. Simulations for a flight control system are given to demonstrate the effectiveness of the results compared with the previous schemes. Copyright © 2011 John Wiley & Sons, Ltd.     

A new nonlinear robust disturbance observer

This paper presents a new nonlinear robust disturbance observer by using only the input–output information for minimum phase dynamical systems with arbitrarily relative degrees. The model uncertainties, the nonlinear parts of the system are merged into the disturbance term, and are regarded as a part of the disturbance. The disturbance is assumed bounded. However, the upper and lower bounds are assumed unknown. The new disturbance observer is inspired by the VSS control theory, whereas the upper and lower bounds of the disturbance are adaptively updated. The estimation error of the disturbance can be made as small as necessary by choosing the design parameters. The attraction of the proposed method lies in its robustness to disturbance and easiness to be implemented. Example and simulation results show the effectiveness of the proposed algorithm.     

基于干扰观测器的一类奇异系统H∞控制

提出了一种基于干扰观测器的奇异系统鲁棒H_∞控制方法.外部干扰广泛存在于奇异系统中,为了降低其对系统的影响,设计了一种奇异系统干扰观测器以估计系统干扰.然后给出闭环系统相容的条件,设计一种基于干扰观测器的鲁棒控制器,并基于李雅普诺夫稳定性理论证明了闭环系统的渐近稳定性,通过设计指标函数得到闭环系统具有鲁棒性能的条件.相对于传统鲁棒控制方法,基于干扰观测器的方法降低了系统设计的保守性.最后,通过仿真实验验证了所提出方法的正确性和有效性.     

Robust semiglobal swarm tracking of coupled harmonic oscillators with input saturation and external disturbance

The robust semiglobal swarm tracking problem of N coupled harmonic oscillators and 1 actual leader with input saturation and external disturbance on a directed communication topology is considered, in which the N coupled harmonic oscillators are referred to followers. First, the low‐and‐high gain feedback technique is introduced to construct a relative state‐dependent control algorithm. Then, an observer‐based control algorithm is designed based on the low‐and‐high gain feedback technique and the high‐gain observer design methodology. Sufficient conditions are derived to guarantee robust semiglobal swarm tracking for state‐feedback control and output‐feedback control, respectively. Numerical simulations are finally provided to verify the theoretic results.     

Variable high-gain disturbance observer design with online adaption of observer gains embedded in numerical integration

In this paper, a variable gain design approach for the high-gain disturbance observer, called Proportional-Integral-Observer (PI-Observer), is proposed to solve the problem of choosing suitable observer gains. The high-gain PI-Observer is successfully applied to estimate unknown inputs of systems together with the system states. It is known that reasonable estimations of unknown inputs can only be derived using high observer gains. On the other hand, extremely large gains will cause serious problems with respect to measurements noise and unmodeled dynamics. According to the analysis of the estimation quality regarding to the factors which influence the estimation results, the optimal level of observer gains is changing during the estimation, an online adaption for the observer gains is therefore developed. The designed PI-Observer, called Advanced PI-Observer (API-Observer), will use changing observer gains from the adaption algorithm, which is proved to give stable estimation error dynamics. Simulation results from an elastic beam example are shown to illustrate the implementation of the API-Observer.     

Active disturbance rejection control approach to output‐feedback stabilization of lower triangular nonlinear systems with stochastic uncertainty

In this paper, we apply the active disturbance rejection control approach to output‐feedback stabilization for uncertain lower triangular nonlinear systems with stochastic inverse dynamics and stochastic disturbance. We first design an extended state observer (ESO) to estimate both unmeasured states and stochastic total disturbance that includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance, and uncertainty caused by the deviation of control parameter from its nominal value. The stochastic total disturbance is then compensated in the feedback loop. The constant gain and the time‐varying gain are used in ESO design separately. The mean square practical stability for the closed‐loop system with constant gain ESO and the mean square asymptotic stability with time‐varying gain ESO are developed, respectively. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output‐feedback control scheme. Copyright © 2016 John Wiley & Sons, Ltd.