基于时变增益扩张状态观测器的逆变器系统自适应 super-twisting电压鲁棒控制

针对电压源逆变器系统中负载扰动和参数摄动, 本文提出了一种基于时变增益扩张状态观测器的自适应 super-twisting鲁棒电压控制新方法. 首先考虑负载扰动, 建立单相逆变器系统的动态模型, 进而考虑系统参数摄动, 通过引入非测量辅助状态变量, 将上述动态模型转化为只包含匹配扰动的状态方程; 其次, 设计时变增益扩张状态 观测器, 以实现对非测量辅助状态变量与包含负载变化和参数摄动等因素在内的集总不确定项的估计; 最后, 基于 此扩张状态观测器, 设计采用自适应super-twisting算法的滑模控制律, 以实现逆变器系统输出电压对其参考电压的 快速准确跟踪并增强系统鲁棒性. 仿真实验结果表明: 所提出的时变增益扩张状态观测器可在保证观测误差收敛 的同时, 有效抑制“初始微分峰值”现象; 采用自适应super-twisting算法的滑模控制策略可使逆变器系统输出电压 具有较高跟踪精度和较小总谐波失真率, 增强系统的抗干扰能力, 并降低控制输入信号“抖振”.     

带宽化扰动观测复合滑模的闭链机构协调控制

针对闭链机构关节协调控制问题,在耦合空间中提出了一种带宽化扰动观测器复合等速趋近律的滑模控制方法.扰动观测器保留扩张状态观测器的计算结构,使用观测误差的比例、积分、微分(P, I, D)估计扰动;它与滑模控制复合,不但放宽了滑模切换增益的边界条件,而且消除了抖振.使用等速趋近律,切换增益可根据执行器饱和限制条件计算获得,其他控制参数结合带宽参数化法整定.仿真和实验表明,带宽化扰动观测器复合滑模控制,可以在系统限制允许的范围内有效解决闭链机构协调控制问题,且具有参数物理意义明确,易整定的优点.     

基于ESO的一类线性时变系统自学习滑模控制方法

针对一类线性时变系统的控制问题,提出了一种基于扩张状态观测器的自学习滑模控制方法。该方法首先设计了两种非线性光滑函数, 然后将两种光滑函数分别应用于扩张状态观测器和滑模趋近律的设计。为了进一步提高系统的自适应控制能力, 使用最速下降法对滑模控制器的增益参数进行自学习镇定。仿真结果表明了该控制方法不仅响应速度快、控制精度高, 而且有效解决了现有理论方法难以解决的问题, 因而是一种有效的不依赖于被控对象模型的LTV系统控制方法。     

具有参数不确定性的非线性系统的鲁棒输出跟踪

研究具有非线性参数化的非线性系统的输出跟踪问题.采用时变状态反馈控制律, 指数镇定输出跟踪误差,并保证非线性系统的所有状态是有界的.为了实现时变状态反馈控 制律,设计高增益鲁棒观测器观测构造该控制律所需要的状态,使得整个闭环系统的输出能 渐近跟踪期望输出,且该闭环系统中所有信号都是有界的.     

用扰动状态观测器镇定混沌系统

通过将符合特定条件的非线性系统分解为一个线性系统和一个附加扰动信号加和的形式,把扰动观测器应用于非线性系统的控制中,用以确立非线性系统中的扰动,并通过它来消除非线性扰动,以实现对非线性系统的镇定。使用扰动观测器来确定Duffing系统中的非线性,并且通过扰动观测器的加入来最终消除了Duffing系统中存在的非线性。在仿真实验中使系统的输出稳定在周期状态,实现了对Duffing系统的镇定,达到了较好的控制效果。     

未知扰动下双起升桥吊时变滑模同步控制

为实现双起升桥吊系统在未知扰动下的同步控制,提出了一种基于变增益扩张状态观测器的时变滑模控制方案。首先,基于耦合误差设计了一种新的时变滑模面,可有效消除趋近阶段,确保初始状态系统的全局鲁棒性;其次,改进的超螺旋算法有效抑制控制器中的抖振现象;然后,变增益扩张状态观测器的设计是为了估计补偿系统中存在的非匹配干扰,有效增强了控制器的鲁棒性;此外,李雅普诺夫理论用于证明受控系统的稳定性。最后,通过仿真验证了所设计的控制器可以有效实现双起升桥吊系统的同步控制。     

角速度约束下的刚体飞行器鲁棒有限时间姿态镇定

针对角速度状态受限条件下的刚体飞行器姿态镇定控制问题,提出一种基于扰动观测器的时变状态增益有限时间姿态控制方法.针对基于修正型罗德里格斯参数(MRPs)描述的刚体飞行器姿态控制模型,首先,利用齐次性理论并充分考虑到系统的模型结构特点,设计一种带有角速度约束项的有限时间姿态控制器,使得系统有限时间镇定;其次,在初始状态满足受限条件的情况下,角速度在任意时刻都可以被约束在期望的范围内;然后,针对存在外部干扰的姿态环动力学系统,提出一种带扰动估计补偿的复合有限时间姿态镇定控制器;最后,通过与其他两种控制方法的仿真比较,验证了所提出控制方案的有效性和优越性.     

广义非线性扩张状态观测器设计及性能分析

针对时变外扰,提出广义非线性扩张状态观测器设计方法.在分析传统扩张状态观测器的设计策略的基础上,通过对总扰动进行重构、引入广义扩张状态,设计反映扰动中已知分量的广义扩张状态观测器(扩张r+1阶).理论分析了观测器的收敛性,并得出了观测误差上界与扩张阶数的定量关系式.通过仿真对广义扩张状态观测器抑制外界正弦扰动的有效性进行检验,数值模拟结果表明,本文设计的观测器能够有效利用扰动中已知分量的信息,降低系统的不确定性,提高观测精度.     

双质量弹簧基准问题自抗扰控制研究

本文研究了自抗扰控制(ADRC)方法在双质量弹簧基准问题的应用.传统的自抗扰控制方法倾向于使用高增益控制来抑制扰动和模型不确定性,但是对于双质量弹簧基准问题,高增益在评分中受到较大惩罚,而且对于模型参数变化没有足够的鲁棒性.为解决这一问题,本文对ADRC设计提出了两种改进方案.首先,为了减小控制信号的幅度,将扩张状态观测器(ESO)的一个极点配置在原点.其次,采用阻尼比来调整带宽.结果表明,所提出的ADRC设计可以很好地解决双质量弹簧基准系统的控制问题.     

基于ESO的Buck型变换器趋近律控制

针对Buck型变换器系统中存在的时变干扰,如输出负载波动,本文提出一种基于扩张状态观测器(ESO)的趋近律控制方法。首先,对系统中存在的时变干扰进行建模,把抑制时变干扰问题转换为抑制匹配和非匹配扰动问题。其次,设计一种扩张状态观测器,用于估计匹配和非匹配扰动。然后,根据提出的新型指数幂次趋近律设计滑模控制器,结合ESO,有效抑制时变干扰对系统的影响,并通过Lyapunov稳定性定理分析观测器的收敛性和闭环控制系统的稳定性。最后,仿真结果验证了所提方法的有效性。     

Active disturbance rejection control approach to stabilization of lower triangular systems with uncertainty

In this paper, we apply the active disturbance rejection control (ADRC) to stabilization for lower triangular nonlinear systems with large uncertainties. We first design an extended state observer (ESO) to estimate the state and the uncertainty, in real time, simultaneously. The constant gain and the time‐varying gain are used in ESO design separately. The uncertainty is then compensated in the feedback loop. The practical stability for the closed‐loop system with constant gain ESO and the asymptotic stability with time‐varying gain ESO are proven. The constant gain ESO can deal with larger class of nonlinear systems but causes the peaking value near the initial stage that can be reduced significantly by time‐varying gain ESO. The nature of estimation/cancelation makes the ADRC very different from high‐gain control where the high gain is used in both observer and feedback. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

The active disturbance rejection control approach to stabilisation of coupled heat and ODE system subject to boundary control matched disturbance

We consider stabilisation for a linear ordinary differential equation system with input dynamics governed by a heat equation, subject to boundary control matched disturbance. The active disturbance rejection control approach is applied to estimate, in real time, the disturbance with both constant high gain and time-varying high gain. The disturbance is cancelled in the feedback loop. The closed-loop systems with constant high gain and time-varying high gain are shown, respectively, to be practically stable and asymptotically stable.     

Active disturbance rejection control to MIMO nonlinear systems with stochastic uncertainties: approximate decoupling and output-feedback stabilisation

ABSTRACT

In this paper, we apply the active disturbance rejection control, an emerging control technology, to output-feedback stabilisation for a class of uncertain multi-input multi-output nonlinear systems with vast stochastic uncertainties. Two types of extended state observers (ESO) are designed to estimate both unmeasured states and stochastic total disturbance which includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance without requiring the statistical characteristics, uncertain nonlinear interactions between subsystems, and uncertainties caused by the deviation of control parameters from their nominal values. The estimations decouple approximately the system after cancelling stochastic total disturbance in the feedback loop. As a result, we are able to design an ESO-based stabilising output-feedback and prove the practical mean square stability for the closed-loop system with constant gain ESO and the asymptotic mean square stability with time-varying gain ESO, respectively. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output-feedback control scheme.     

Boundary stabilization of a cascade of ODE‐wave systems subject to boundary control matched disturbance

In this paper, we are concerned with a cascade of ODE‐wave systems with the control actuator‐matched disturbance at the boundary of the wave equation. We use the sliding mode control (SMC) technique and the active disturbance rejection control method to overcome the disturbance, respectively. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of solution for the closed‐loop via SMC are proved, and the monotonicity of the ‘reaching condition’ is presented without the differentiation of the sliding mode function, for which it may not always exist for the weak solution of the closed‐loop system. Considering that the SMC usually requires the large control gain and may exhibit chattering behavior, we then develop an active disturbance rejection control to attenuate the disturbance. The disturbance is canceled in the feedback loop. The closed‐loop systems with constant high gain and time‐varying high gain are shown respectively to be practically stable and asymptotically stable. Then we continue to consider output feedback stabilization for this coupled ODE‐wave system, and we design a variable structure unknown input‐type state observer that is shown to be exponentially convergent. The disturbance is estimated through the extended state observer and then canceled in the feedback loop by its approximated value. These enable us to design an observer‐based output feedback stabilizing control to this uncertain coupled system. Copyright © 2016 John Wiley & Sons, Ltd.     

Stabilization of ODE with hyperbolic equation actuator subject to boundary control matched disturbance

ABSTRACT

In this paper, we consider stabilisation for a cascade of ODE and first-order hyperbolic equation with external disturbance flowing to the control end. The active disturbance rejection control (ADRC) and sliding mode control (SMC) approaches are adopted in investigation. By ADRC approach, the disturbance is estimated through a disturbance estimator with both time-varying high gain and constant high gain, and the disturbance is canceled online in the feedback loop. It is shown that the resulting closed-loop system with time-varying high gain is asymptotically stable and is practically stable with constant high gain. By SMC approach, the existence and uniqueness of the solution for the closed loop via SMC are proved, and the monotonicity of the ‘reaching condition’ is presented. The resulting closed-loop system is shown to be exponentially stable. The numerical experiments are carried out to illustrate effectiveness of the proposed control law.     

Extended state observer for uncertain lower triangular nonlinear systems

The extended state observer (ESO) is a key part of the active disturbance rejection control approach, a new control strategy in dealing with large uncertainty. In this paper, a nonlinear ESO is designed for a kind of lower triangular nonlinear systems with large uncertainty. The uncertainty may come from unmodeled system dynamics and external disturbance. We first investigate a nonlinear ESO with high constant gain and present a practical convergence. Two types of ESO are constructed with explicit error estimations. Secondly, a time varying gain ESO is proposed for reducing peaking value near the initial time caused by constant high gain approach. The numerical simulations are presented to show visually the peaking value reduction. The mechanism of peaking value reduction by time varying gain approach is analyzed.     

Output feedback stabilization of an unstable wave equation with general corrupted boundary observation

We consider boundary output feedback stabilization for an unstable wave equation with boundary observation subject to a general disturbance. We adopt for the first time the active disturbance rejection control approach to stabilization for a system described by the partial differential equation with corrupted output feedback. By the approach, the disturbance is first estimated by a relatively independent estimator; it is then canceled in the feedback loop. As a result, the control law can be designed almost as that for the system without disturbance. We show that with a time varying gain properly designed, the observer driven by the disturbance estimator is convergent, and that all subsystems in the closed-loop are asymptotically stable in the energy state space. We also provide numerical simulations which demonstrate the convergence results and underline the effect of the time varying gain estimator on peaking value reduction.     

Mittag‐Leffler stabilization for an unstable time‐fractional anomalous diffusion equation with boundary control matched disturbance

This paper addresses the Mittag‐Leffler stabilization for an unstable time‐fractional anomalous diffusion equation with boundary control subject to the control matched disturbance. The active disturbance rejection control (ADRC) approach is adopted for developing the control law. A state‐feedback scheme is designed to estimate the disturbance by constructing two auxiliary systems: One is to separate the disturbance from the original system to a Mittag‐Leffler stable system and the other is to estimate the disturbance finally. The proposed control law compensates the disturbance using its estimation and stabilizes system asymptotically. The closed‐loop system is shown to be Mittag‐Leffler stable and the constructed auxiliary systems in the closed loop are proved to be bounded. This is the first time for ADRC to be applied to a system described by the fractional partial differential system without using the high gain.     

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.