Filtering adaptive neural network controller for multivariable nonlinear systems with mismatched uncertainties

This paper synthesizes a filtering adaptive neural network controller for multivariable nonlinear systems with mismatched uncertainties. The multivariable nonlinear systems under consideration have both matched and mismatched uncertainties, which satisfy the semiglobal Lipschitz condition. The nonlinear uncertainties are approximated by a Gaussian radial basis function (GRBF)‐based neural network incorporated with a piecewise constant adaptive law, where the adaptive law will generate adaptive parameters by solving the error dynamics between the real system and the state predictor with the neglection of unknowns. The combination of GRBF‐based neural network and piecewise constant adaptive law relaxes hardware limitations (CPU). A filtering control law is designed to handle the nonlinear uncertainties and deliver a good tracking performance with guaranteed robustness. The matched uncertainties are cancelled directly by adopting their opposite in the control signal, whereas a dynamic inversion of the system is required to eliminate the effect of the mismatched uncertainties on the output. Since the virtual reference system defines the best performance that can be achieved by the closed‐loop system, the uniform performance bounds are derived for the states and control signals via comparison. To validate the theoretical findings, comparisons between the model reference adaptive control method and the proposed filtering adaptive neural network control architecture with the implementation of different sampling time are carried out.     

Decentralized filtering adaptive constrained tracking control for interconnected nonlinear systems

This paper presents a novel decentralized filtering adaptive constrained tracking control framework for uncertain interconnected nonlinear systems. Each subsystem has its own decentralized controller based on the established decentralized state predictor. For each subsystem, a piecewise constant adaptive law will generate total uncertainty estimates by solving the error dynamics between the host system and decentralized state predictor with the neglection of unknowns, whereas a decentralized filtering control law is designed to compensate both local and mismatched uncertainties from other subsystems, as well as achieve the local objective tracking of the host system. The achievement of global objective depends on the achievement of local objective for each subsystem. In the control scheme, the nonlinear uncertainties are compensated for within the bandwidth of low‐pass filters, while the trade‐off between tracking and constraints violation avoidance is formulated as a numerical constrained optimization problem which is solved periodically. Priority is given to constraints violation avoidance at the cost of deteriorated tracking performance. The uniform performance bounds are derived for the system states and control inputs as compared to the corresponding signals of a bounded closed‐loop reference system, which assumes partial cancelation of uncertainties within the bandwidth of the control signal. Compared with model predictive control (MPC) and unconstrained controller, the proposed control architecture is capable of solving the tracking control problems for interconnected nonlinear systems subject to constraints and uncertainties.     

On Finite‐Time Stabilization of Active Disturbance Rejection Control for Uncertain Nonlinear Systems

This paper designs the active disturbance rejection control (ADRC) to achieve finite‐time stabilization for a class of uncertain nonlinear systems. The proposed control incorporates both an extended state observer (ESO) as well as an adaptive sliding mode controller. The ESO is utilized to estimate the full system states and the total uncertainties, and the adaptive strategy is incorporated to deal with the estimation errors. It is proved that, with the application of the proposed control law, semi‐global finite‐time stabilization can be achieved. Effectiveness of the proposed method is illustrated with a numerical example.     

航天器姿态机动及稳定的自抗扰控制

针对航天器动力学参数不确定性以及系统存在外部持续干扰的问题, 提出了一种自抗扰姿态控制器的设计方法. 在为期望姿态安排过渡过程的基础上, 设计了扩张状态观测器, 对参数不确定性和外部干扰进行估计, 并实时补偿. 为抑制跟踪误差, 设计了非线性状态误差反馈律. 仿真结果表明, 该控制器不仅能很好地估计并补偿系统受到的持续干扰, 而且对航天器动力学参数的不确定性具有较强的鲁棒性, 满足航天器姿态快速机动和高稳定度的控制要求, 性能指标明显优于PD控制.     

Recursive filtering adaptive fault‐tolerant tracking control for uncertain switched multivariable nonlinear systems

This article synthesizes a recursive filtering adaptive fault‐tolerant tracking control method for uncertain switched multivariable nonlinear systems. The multivariable nonlinear systems under consideration have both matched and mismatched uncertainties, which satisfy the semiglobal Lipschitz condition. A piecewise constant adaptive law generates adaptive parameters by solving the error dynamics with the neglection of unknowns, and the recursive least squares is employed to minimize the residual error by categorizing the total uncertainty estimates into matched and mismatched components. A filtering control law is designed to compensate the actuator faults and nonlinear uncertainties such that a good tracking performance is delivered with guaranteed robustness. The matched component is canceled directly by adopting their opposite in the control signal, whereas a dynamic inversion of the system is performed to eliminate the effect of the mismatched component on the output. By exploiting the average dwell time principle, the error bounds are derived for the states and control inputs compared with the virtual reference system which defines the best performance that can be achieved by the closed‐loop system. Both numerical and practical examples are provided to illustrate the effectiveness of the proposed switching recursive filtering adaptive fault‐tolerant tracking control architecture, comparisons with model reference adaptive control are also carried out.     

未知死区输入非线性系统的双观测器动态面控制

针对一类含死区输入的严格反馈非线性系统,提出基于双观测器的自适应鲁棒控制算法.动态面的每一步设计中,第1观测器即跟踪信号观测器对指令信号进行观测,并得到指令信号的差分信号,消除传统动态面控制中计算复杂问题.第二观测器即扰动观测器在线估计高阶动态面控制系统中每一步的不确定模型,与跟踪信号观测器实现双反馈控制,提高控制效果...     

基于非线性L1自适应动态逆的飞行器姿态角控制

钊对常规动态逆控制器不能有效抵消系统中的不确定性这一缺点,提出了一种非线性L_1自适应动态逆控制方法.该方法能够克服常规动态逆的不足,在保证系统鲁棒性的前提下,提升飞行器姿态角控制效果.首先,采用时标分离原理,将姿态角控制系统分为内外两个回路:外回路采用常规动态逆控制器,用于姿态角的跟踪控制;内回路采用非线性L_1自适应控制器,用于角速率的控制.其中,L_1自适应控制器由静态反馈控制器和自适应控制器组成:静态反馈控制器通过状态反馈实现,用于保证内回路的稳定和具有期望的闭环特性;自适应控制器由状态观测器、自适应律和控制律组成,用于抵消系统中的不确定性.其次,对所提控制方法的稳定性进行了分析,结果证明了该控制方法能够保证内回路的稳定和外回路的误差有界.最后,在综合考虑多种不确定性的情况下,将本文提出的非线性L_1自适应动态逆控制方法用于某无人飞行器姿态角控制,仿真结果验证了该控制方法的有效性和鲁棒性.     

L1 adaptive output‐feedback control of multivariable nonlinear systems subject to constraints using online optimization

In this paper, an L₁ adaptive output‐feedback controller is developed for multivariable nonlinear systems subject to constraints using online optimization. In the L₁ adaptive architecture, an adaptive law will update the adaptive parameters that represent the nonlinear uncertainties such that the estimation error between the predicted state and the real state is driven to zero at every integration time step. Of course, neglection of the unknowns for solving the error dynamic equations will introduce an estimation error in the adaptive parameters. The magnitude of this error can be lessened by choosing a proper sampling time step. A control law is designed to compensate the nonlinear uncertainties and deliver a good tracking performance with guaranteed robustness. Model predictive control is introduced to solve a receding horizon optimization problem with various constraints maintained. Numerical examples are given to illustrate the design procedures, and the simulation results demonstrate the availability and feasibility of the developed framework.     

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.     

基于扩张状态观测器的 连铸结晶器振动位移系统自适应滑模控制

针对伺服电机驱动的连铸结晶器振动位移系统中存在时变负载转矩、参数不确定性等问题,本文提出了一种基于扩张状态观测器(extended state observer, ESO)的自适应非奇异终端滑模(nonsingular terminal sliding mode,NTSM)控制方法.首先,设计ESO对系统存在的综合扰动和不可测状态进行估计.然后,采用分层设计的方法,分别对位移跟踪子系统和电流环子系统设计基于ESO的自适应NTSM控制器和滑模控制器.为削弱ESO估计误差对跟踪精度的影响,在NTSM控制器中引入了自适应增益.可以证明,所设计的控制器能够保证闭环系统所有信号有界,系统状态可渐近收敛到原点附近的小邻域内.最后,仿真结果验证了所提出控制方法的有效性.     

近空间飞行器纵向抗干扰轨迹控制研究

针对近空间飞行器( nearspace vehicle,NSV) 在高超音速飞行时,气动参数变化剧烈且容易受到外界干扰的特点,研究了NSV 纵向轨迹系统的干扰问题,提出了鲁棒自适应动态面的回馈递推控制方法。首先对高度非线性、高度复杂的NSV 的纵向运动的模型进行坐标变换,采用输入－输出反馈线性化方法,将其转化为仿射非线性模型; 然后通过一阶低通滤波器对控制器设计中的虚拟控制律进行估计,从而避免了对其求导带来的计算膨胀问题; 再结合神经网络逼近理论以及虚拟控制器中的鲁棒项,一起消除近空间飞行器的纵向系统中存在的参数摄动不确定和外界干扰。最后通过稳定性分析,表明了该方法在降低系统控制器复杂性的同时仍具有很好的鲁棒性。     

基于模型信息的电静液作动器降阶线性自抗扰控制

针对电静液作动器(electro-hydrostatic actuators, EHA)系统存在内外部扰动、参数不确定性和变控制增益等问题,提出一种基于模型信息的降阶线性自抗扰位置控制方法.首先,基于系统模型信息选取控制增益.其次,通过降阶线性扩张观测器对系统总扰动进行估计,并在控制器中加入扰动项进行补偿.利用奇异摄动理论证明所提控制器可使闭环系统是半全局最终一致有界的,并且当观测器带宽足够大时,所提出的控制器理论上可以使系统输出以所需精度跟踪期望轨迹.仿真结果表明,所提控制方法响应速度较快,控制精度较高,对外部扰动和参数不确定性具有较强的鲁棒性.     

A novel adaptive nonsingular terminal sliding mode controller design and its application to active front steering system

Note that the amplitude of chattering existing in the sliding mode control method is proportional to the magnitude of the control gain. Therefore, the key issue to diminish the chattering is to decrease the value of sliding mode controller's gain to an acceptable minimal level defined by the so‐called reaching condition for the sliding mode's existence. For this reason, the nonsingular terminal sliding mode (NTSM) control method and the adaptive technique have been considered in this paper to develop a novel adaptive NTSM control method, which can be used to search the minimal value of the control gain automatically in the presence of the external disturbances. Meanwhile, the average value of a high‐frequency switching signal in the adaptive law can be provided by Arie Levant's differentiator rather than a low‐pass filter. The rigorous mathematical proof verifies that the system states can converge to the origin within a finite time under the proposed adaptive NTSM controller. Both the academic example and the practical application to an active front steering system are illustrated to show that the presented adaptive NTSM controller has better control performance than the conventional sliding mode controller.     

On a new adaptive sliding mode control for MIMO nonlinear systems with uncertainties of unknown bounds

This paper proposes a new approach of adaptive sliding mode controller designs for multiple‐input multiple‐output nonlinear systems with uncertainties of unknown bounds and limited available inputs. The goal is to obtain robust, smooth, and fast transient performance for real sliding mode control so that the phenomena of the slow response and the gain overestimation in most adaptive sliding mode controller designs can be greatly improved. We introduce an Integral/Exponential adaptation law with boundary‐layer targeting the reduction of the chatter levels of the sliding mode by significantly reducing the gain overestimation while simultaneously speeding up the system response to the uncertainties. The gain is further reduced when the system state is in the boundary layer. The simulation and experimental results demonstrate the proposed design. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust current and speed control of a permanent magnet synchronous motor using SMC and ADRC

A second-order ordinary differential equation model is originally constructed for the phase q current system of a permanent magnet synchronous motor (PMSM). The phase q current model contains the effect of a counter electromotive force (CEMF), which introduces nonlinearity to the system. In order to compensate the nonlinearity and system uncertainties, a traditional sliding mode controller (SMC) combined with a low-pass filter (also known as a modified SMC) is designed on the phase q current model. The low-pass filter overcomes chattering effects in control efforts, and hence improves the performance of the controller. The phase q current control system is proved to be stable using Lyapunov approach. In addition, an alternative active disturbance rejection controller (ADRC) with a reduced-order extended state observer (ESO) is applied to control the speed output of PMSM. Both SMC and ADRC are simulated on the PMSM system. The simulation results demonstrate the effectiveness of these two controllers in successfully driving the current and speed outputs to desired values despite load disturbances and system uncertainties.     

双电机同步驱动伺服系统故障诊断与容错控制

本文针对双电机同步驱动伺服系统中执行器失效会导致系统性能下降甚至失稳的情况,提出了一种基于自适应滑模的故障诊断和容错控制策略.该方法通过设计各电机转速的自适应滑模状态观测器,在线估计各执行器的失效因子:当单个执行器部分失效时,通过自适应的方法调整控制器增益;当单个执行器全部失效时,重构系统的控制律.对于系统中存在非匹配不确定项的情况,提出在期望虚拟信号中引入基于扩张状态观测器的补偿项抑制方案;利用Lyapunov理论证明了闭环系统在正常和故障状况下的稳定性以及观测器的收敛性;仿真结果表明,所设计的控制策略能保证系统稳定跟踪指令信号,在单个执行器失效的情况下系统跟踪性能基本不下降.     

基于自适应模糊控制器和非线性扰动观测器的永磁直线同步电机反馈线性化控制

由于永磁直线同步电机(PMLSM)伺服系统应用于一些高精密场合,因此克服系统存在的负载扰动、参数变化等不确定性影响是提高系统性能的关键.针对不确定性问题,采用一种基于自适应模糊控制器(AFC)和非线性扰动观测器(NDO)的反馈线性化控制方法.首先设计反馈线性化控制器(FLC)实现系统的线性化,便于位置跟踪;其次采用NDO估计并补偿系统的不确定性,提高跟踪精度.但在实际运行过程中观测器增益较难选取,极易产生较大的观测误差,为此,采用AFC方法逼近NDO的观测误差,通过自适应律动态调整模糊规则,改善模糊控制器的学习能力,增强系统的鲁棒性,并用李雅普诺夫定理保证系统闭环稳定性.实验结果表明,与基于DOB和NDO的反馈线性化位置控制相比,该方法能够明显提高系统的跟踪性和鲁棒性.     

含摩擦非线性系统的自适应滑模控制

针对摩擦非线性的扰动抑制和输出反馈控制问题,提出一种高阶滑模扩张状态观测器(ESO),实时获得系统的状态信号.在此基础上,设计神经网络自适应权值调节律,以得到控制信号设计参数与输出跟踪性能之间的关系;同时,给出保证系统动态性能的观测器状态初值与自适应调节律参数初值的充要条件.最后,通过稳定性证明和仿真算例验证了所提出控制算法的有效性.     

用于带有量测噪声系统的新型扩张状态观测器

提出了扩张状态观测器的一种新的形式,用于处理量测环节带有噪声干扰时的情况.ESO可以对不确定系统中的内外扰动进行观测,并以此为基础构成自抗扰控制器.但其性能会受量测噪声的影响.本文利用滤波器消除噪声的影响,并把已知的滤波器方程扩展到原有的ESO中,以补偿滤波器对实际输出信号的偏移作用.数字仿真表明,该方法可以有效的解决输出噪声对扩张状态观测器的影响.