Adaptive notch filters are local adaptive observers

Several continuous‐time frequency estimators for a measured sinusoidal signal, which have been proposed in the literature, are reviewed, reinterpreted and compared both theoretically and by simulations. It is argued that adaptive notch filters are feedback algorithms that contain a local adaptive observer in the feedback loop. It is shown that the adaptive notch filter (ANF), which was originally conceived as a discrete‐time ANF, is basically equivalent to the recently proposed adapted frequency locked loop called orthogonal signal generator. They both require a sufficiently slow frequency estimation and can be interpreted as third‐order adaptive observers. They exhibit local convergence properties for the estimation errors, that is, the convergence to zero is guaranteed provided that their initial error is sufficiently small. Three adaptive observers, which were independently proposed in 2002, are third‐order frequency estimators whose estimation errors are exponentially convergent to zero from any initial condition and for any value of frequency, amplitude and phase in the measured sinusoidal signal. They have the additional advantage of not requiring the frequency estimation dynamics to be sufficiently slow. Conversely, they may be interpreted as adaptive notch filters. Second‐order frequency estimators have been proposed as well: they may be interpreted as adaptive reduced‐order observers. Copyright © 2015 John Wiley & Sons, Ltd.     

一类具有高增益观测器的非线性系统的输出调节

针对具有由非线性外部系统产生的未知不确定性函数和未建模动态的非线性不确定系统,研究了其跟踪和干扰抑制问题。首先运用状态变换将输出调节问题转化为非线性系统的镇定问题,接着引入动态信号解决了动态扰动,并设计出高增益的状态观测器去估计不可测的状态。然后根据外系统信息设计自适应的非线性内模,结合自适应控制理论、Backstepping设计方法、模糊控制方法和Lyapunov法给出了输出反馈的自适应模糊控制器和自适应控制律,所提出的输出反馈控制器和自适应律能够实现整个闭环系统的跟踪和干扰抑制,并使得跟踪误差能渐近收敛到给定的任意小的领域内。最后仿真结果验证了所提出的控制器的有效性。     

A globally stable practically implementable PI passivity-based controller for switched power converters

In this article, we propose a PI passivity-based controller, applicable to a large class of switched power converters, that ensures global state regulation to a desired equilibrium point. A solution to this problem requires full state-feedback, which makes it practically unfeasible. To overcome this limitation we construct a state observer that is implementable with measurements that are available in practical applications. The observer reconstructs the state in finite-time, ensuring global convergence of the PI. An adaptive version of the observer, where some parameters of the converter are estimated, is also proposed. The excitation requirement for the observer is very weak and is satisfied in normal operation of the converters. Realistic simulation results illustrate the excellent performance and robustness vis-à-vis noise and parameter uncertainty of the proposed output-feedback PI.     

An adaptive observer for joint estimation of states and parameters in both state and output equations

An adaptive observer is a recursive algorithm for joint state–parameter estimation of parameterized state‐space systems. Previous works on globally convergent adaptive observers consider unknown parameters either in state equations or in output equations, but not in both of them. In this paper, a new adaptive observer is designed for linear time‐varying systems with unknown parameters in both state and output equations. Its global convergence for simultaneous estimation of states and parameters is formally established under appropriate assumptions. A numerical example is presented to illustrate the performance of this adaptive observer. Copyright © 2011 John Wiley & Sons, Ltd.     

Modeling and distributed adaptive fault-tolerant vibration control for bridge beam with single-parameter adaptive neural network

Modeling and vibration control of a bridge beam system are considered in this article. The beam bridge with both ends fixed can be regarded as an Euler-Bernoulli beam, which is a typical distributed parameter system. First, the partial differential equations (PDE) model of the bridge was established according to the Hamilton principle. Then, a reasonable distributed control law was designed on the PDE model to eliminate the elastic deformation and suppress the vibration of the bridge. At the same time, uncertainties related to system status were considered during the design of the closed-loop system. In addition, the possible actuator and sensor faults in the control system were analyzed. Single-parameter adaptive neural networks were used to estimate the effects of coupling terms for uncertainties and faults. The parameter estimation adaptive law was designed to replace the adjustment of neural network weights, which simplifies the algorithm and facilitates practical engineering applications. Finally, the feasibility of the control system was verified by simulation.     

基于自适应迭代学习的机械手轨迹跟踪控制研究

针对具有初始误差的机械手轨迹跟踪控制问题,设计了一种带初态学习的模糊自适应迭代学习控制策略。控制策略中引入了初态学习控制律,放宽了系统初始状态严格重复的限制,利用Lyapunov函数对系统进行收敛性分析,克服了系统全局Lipschitz连续条件的约束,同时设计了模糊控制器对增益以及自适应律参数进行整定,最后将算法应用到机械手控制中,通过与传统自适应迭代学习控制对比,前者收敛速度和精度明显提高,验证了控制策略的有效性。     

Sampled-data adaptive observer for state and parameter affine systems with distributed and discrete output delays

We are considering the problem of sampled-data observer design for nonlinear time-varying systems that are state-affine. The novelty lies in that both distributed and discrete delays are considered in the output equation. The latter is also subject to a parameter uncertainty of nonaffine nature due to output sampling. Interestingly, all system delays are modeled using a single distributed representation, involving a distribution function, allowing thus for a unified treatment of delays. A Kalman-like observer is developed to cope with both state and parameter uncertainty. Its main components are (i) a time-varying-gain state-estimator involving both output and parameter rate injections; (ii) a distributed-nature adaptive output-predictor that compensate for all delay effects, including that of output sampling; (iii) an parameter-estimator that is optimized in the sense that it makes use of all available information. The resulting observer is shown to be exponentially convergent, for small delays and sampling intervals, provided the input signal is sufficiently exciting. The analysis is performed using a Lyapunov–Krasovskii functional, Halanay's lemma, Wirtinger's inequality, and other tools.     

永磁同步电动机的自适应非线性轨迹跟踪控制

系统地发展了一种基于观测器的永磁同步电动机自适应非线性轨迹跟踪控制系统. 系统中包括负载转矩、负载转动惯量以及电机参数在内的所有参数是不确定的,并且加速度是不可测的.设计的非线性观测器用以估计那些不易测得的状态量.基于Lyapunov稳定理论的设计方法保证了控制系统的稳定性和跟踪误差的收敛性.实验结果证明了该控制系统的稳定性和有效性.     

Adaptive prescribed performance control for hydraulic system with disturbance compensation

In this article, an adaptive prescribed performance controller is developed for hydraulic system with uncertainties. An extraordinary feature is that better prescribed performance control can be achieved by compensating the uncertainties including parameter uncertainties and disturbances. For this reason, the transformation of system output error is realized by a prescribed performance function, which is employed to constrain the boundary of tracking error and convergence rate, then the tracking error of the original system with a priori prescribed performance can be realized by stabilizing the transformed system. Adaptive control is employed to solve the system parametric uncertainties; extended state observers are built to estimate the multiple disturbances. Based on the backstepping method, they are integrated into the design of the novel controller to guarantee prescribed tracking error performance. The stability analysis of the proposed controller is carried out via the Lyapunov theory. Finally, experimental results indicate good performance of the proposed algorithm.     

Regulation-triggered adaptive control of a hyperbolic PDE-ODE model with boundary interconnections

We present a certainty equivalence-based adaptive boundary control scheme with a regulation-triggered batch least-squares identifier, for a heterodirectional transport partial differential equation-ordinary differential equation (PDE-ODE) system where the transport speeds of both transport PDEs are unknown. We use a nominal controller which is fed piecewise-constant parameter estimates from an event-triggered parameter update law that applies a least-squares estimator to data “batches” collected over time intervals between the triggers. A parameter update is triggered by an observed growth in the norm of the PDE state. The proposed triggering-based adaptive control guarantees: (1) the absence of a Zeno phenomenon; (2) parameter estimates are convergent to the true values in finite time (from most initial conditions); (3) exponential regulation of the plant states to zero. The effectiveness of the proposed design is verified by a numerical example.     

考虑线路运行状态的智能电网调度自适应控制研究

当前智能电网调度均忽略线路运行状态的影响,其自适应控制过程存在缺陷.该文充分考虑影响输电线路运行状态的内在、外在因素,从自然老化、健康状态、天气条件以及负载电流四个方面分析线路运行状态;利用所确定的线路运行状态,从并网时与孤岛时线路潮流优化控制两方面,建立智能电网调度模型,并利用模型预测控制方法中的域参数设置,求解智能...     

压力传感器幅频特性不确定度评定方法研究

本文提出一种压力传感器幅频特性不确定度评定方法。 首先,基于核密度估计法计算压力传感器模型参数的概率密度 分布,采用舍选抽样法生成符合概率密度分布的伪随机数;然后,提出一种自适应蒙特卡洛迭代收敛阈值优化方法,实现最优迭 代次数的准确估计;最后,基于最优迭代次数,采用自适应蒙特卡洛法对压力传感器幅频特性的不确定度进行评定,得到其最优 估计值、标准不确定度和给定置信概率下的不确定度区间。 通过压力传感器幅频特性不确定度评定实验验证本文方法的性能。 实验结果表明,本文方法得到的压力传感器幅频特性不确定度绝对误差的均值和最大值分别为 8. 837×10-5 和 5. 103×10-3,与 蒙特卡洛法(实验次数为 100 000)相比分别降低了大约 55%和 76%,与自适应蒙特卡洛法相比分别降低了大约 67%和 79%,说 明本文方法可以有效地评定压力传感器幅频特性的不确定度。     

Adaptive observer for a class of nonlinear systems with time‐varying delays

The adaptive observer design problems have been extensively studied in literature for both linear and nonlinear systems. Some researches have also been carried out on adaptive observer design for linear time‐delay systems, but there is no significant work on adaptive observer design for nonlinear time‐delay systems. In this work, the adaptive observer design problem for a class of nonlinear time‐delay systems is considered. The observer is designed for the nonlinear systems whose nonlinear functions satisfy Lipschitz condition. Like conventional adaptive observers for the systems without time delays, this observer also estimates both states and unknown parameters simultaneously. For this property, it will be very much useful for many real‐time systems where time delays cannot be avoided. The sufficient conditions for existence of the observer are derived using the linear matrix inequality approach. With the help of a numerical example, effectiveness of the proposed observer is demonstrated. Copyright © 2012 John Wiley & Sons, Ltd.     

模糊自适应遗传算法在配电网络重构中的应用

以网损最小为目标函数,节点电压、网络辐射性和电源容量的限制为约束条件,建立了配电网络重构的优化数学模型。针对遗传算法的局限性,提出了一种新的模糊自适应遗传算法,缩短了染色体编码长度、设计了与进化代数、适应度、及个体排序相关的自适应交叉率与变异率,从而使得该算法能够有效地提高收敛速度,避免早熟收敛。重构算例说明该优化方法有效、实用。     

抑制新能源并网系统谐振的逆变器阻抗适配支路参数设计方法

随着高比例新能源并网成为发展趋势,新能源并网系统谐振成为影响新型电力系统安全稳定的潜在因素。由于风光资源在时间尺度上存在互补特性,可以通过调整逆变器并网特性实现系统阻尼的分时互济。针对逆变器阻抗适配支路的参数设计问题,提出阻尼系数的优化设计方法。首先,推导了阻尼互济控制逆变器的输出阻抗表达式,结合阻抗的幅值和相位分析阻尼系数对输出阻抗的影响,提出阻尼系数的初选设计方法。随后,从系统稳定性角度分析电网阻抗与阻尼系数之间的关系,为阻尼系数的优化提供了依据。为解决固定阻尼给控制带来的限制问题,提出了一种阻尼系数自适应的阻尼互济控制,使得控制更加灵活有效。最后,通过仿真和实验验证了阻抗适配支路参数设计方法的准确性以及阻尼系数自适应算法的有效性。     

Extremum seeking-based observer design for reduced order models of coupled thermal and fluid systems

We present an extremum seeking (ES)-based robust observer design for thermal-fluid systems, pursuing an application to efficient energy management in buildings. The model is originally described by Boussinesq equations which is given by a system of two coupled partial differential equations (PDEs) for the velocity field and temperature profile constrained to incompressible flow. Using proper orthogonal decomposition, the PDEs are reduced to a set of nonlinear ordinary differential equations. Given a set of temperature and velocity point measurements, a nonlinear state observer is designed to reconstruct the entire state under the error of initial states, and model parametric uncertainties. We prove that the closed loop system for the observer error state satisfies an estimate of L₂ norm in a sense of locally input-to-state stability with respect to parameter uncertainties. Moreover, the uncertain parameters estimate used in the designed observer are optimized through iterations of a data-driven ES algorithm. Numerical simulation of a two-dimensional Boussinesq PDE illustrates the performance of the proposed adaptive estimation method.     

一种具有时变观测器增益的摩擦补偿方法

为有效抑制摩擦扰动对光电平台性能的影响,针对环架轴系间的摩擦由LuGre模型描述的情况,设计自适应摩擦补偿控制器.提出一种采用具有时变增益摩擦状态观测器的摩擦补偿方法,通过类李雅普诺夫分析证明整个闭环系统跟踪误差的渐近收敛性.仿真结果表明,通过对时变增益函数中设计参数的适当选择,相比采用具有常数增益的观测器,系统的角速...     

Improved performance MRAC of linear and non-linear systems

The problem of improved performance adaptive control (IPAC) of a class of linear and non-linear systems is considered. A method for its solution is presented, the main feature of which lies in augmenting the ‘standard’ model reference adaptive controller by a signal properly designed to compensate for the effect of plant parameter uncertainty on the output error. One of the main performance improvement characteristics of the proposed IPAC is that the zero-state output error can be made arbitrarily small under standard model reference adaptive control (MRAC) assumptions in the case of linear systems, while a similar result holds true for a class of linearizable systems as well. the structure of the proposed controller is such that several existing MRAC results, such as exponential convergence of output and parameter errors in the presence of sufficiently rich reference inputs, remain valid. the proposed controller also achieves improved performance in the presence of a class of bounded disturbances and/or unmodelled dynamics as well as in the case of an adaptation switch-off.     

Disturbance observer-based adaptive boundary iterative learning control for a rigid-flexible manipulator with input backlash and endpoint constraint

In this article, an observer-based adaptive boundary iterative learning control law is developed for a class of two-link rigid-flexible manipulator with input backlash, the unknown external disturbance, and the endpoint constraint. To tackle the backlash nonlinearities and ensure the vibration suppression, the disturbance observers based upon the iterative learning conception are considered in the adaptive boundary control design. A barrier Lyapunov function is incorporated with boundary control law to restrict the endpoint state. Based on the defined barrier composite energy function, the tracking angle error convergence of the rigid part is guaranteed, and the vibrations of the flexible part are suppressed through the rigorous analysis. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed control.