Robust MRAC to disturbance using VS‐type adaptive identifier

It is well known that variable structure (VS)‐type model reference adaptive controls (MRAC) are robust to disturbances. However, almost all conventional design schemes of VS‐MRAC may cause chattering because of the switching function used in the control synthesis input. In this paper, we propose a new design scheme of MRAC which uses a VS‐type adaptive identifier. This design scheme can avoid occurrence of chattering. Furthermore, this design scheme is robust to disturbances. © 1999 Scripta Technica, Electr Eng Jpn, 130(2): 80–87, 2000     

Fractional‐order multivariable composite model reference adaptive control

A novel multivariable composite model reference adaptive control scheme is developed for multivariable fractional‐order systems with arbitrary relative degree. Firstly, by introducing right gain matrix to substitute left gain matrix, the stringent symmetry assumption is no longer required. The design procedures of controller with certain and uncertain high‐frequency gain matrix are then provided, respectively. The (robust) stability of the resulting closed‐loop control system is investigated by indirect Lyapunov method. It is shown that the composite model reference adaptive control can achieve better performance on output tracking than that of model reference adaptive control. Finally, the effectiveness and applicability of the proposed control scheme are demonstrated in 3 numerical examples.     

Experimental evaluation of combined model reference adaptive controller in a pH regulation process

An experimental evaluation of the combined model reference adaptive control (CMRAC) is presented in this paper. This adaptive control scheme was used to control a relatively complex process like the pH of a solution in a tank reactor at laboratory level. For comparison purposes, some very well‐known control strategies were also implemented, which include PID control and standard model reference adaptive control (MRAC). Tracking and regulation capabilities of the control strategies studied were analysed and compared. Experimental results indicate that CMRAC behaves as well as the standard MRAC and a very well‐tuned PID for a specific and known operating point. Advantages of the adaptive controllers are shown when the operating point changes. Copyright © 2002 John Wiley & Sons, Ltd.     

Simple and robust speed sensorless vector control of induction motor using stator current based MRAC

A novel rotor speed estimation method using model reference adaptive control (MRAC) is proposed to improve the performance of a sensorless vector controller. In MRAC methods, state variables, such as rotor flux and back EMF are estimated in a reference model and then compared with state variables estimated by using an adjustable model. The difference of these state variables is then used in an estimation of rotor speed. We propose a new MRAC method that uses the stator current as the state variable for estimating the speed. In conventional MRAC methods, the difference between state variables has the unclear relationship with the speed estimation error. But, in the proposed method, the stator current error is represented as a function of the first degree for the error value in the speed estimation. Therefore, the proposed method can produce a fast speed estimation and is robust to variations in the parameter error. In addition, the proposed method offers a considerable improvement in the performance of a sensorless vector controller at a low speed. The superiority of the proposed method is verified by simulation and experiments in a low speed region and at zero-speed.     

Accommodation of unknown actuator faults using output feedback‐based adaptive robust control

In this paper, we solve the problem of output tracking for linear uncertain systems in the presence of unknown actuator failures using discontinuous projection‐based output feedback adaptive robust control (ARC). The faulty actuators are characterized as unknown inputs stuck at unknown values experiencing bounded disturbance and actuators losing effectiveness at unknown instants of time. Many existing techniques to solve this problem use model reference adaptive control (MRAC), which may not be well suited for handling various disturbances and modeling errors inherent to any realistic system model. Robust control‐based fault‐tolerant schemes have guaranteed transient performance and are capable of dealing with modeling errors to certain degrees. But, the steady‐state tracking accuracy of robust controllers, e.g. sliding mode controller, is limited. In comparison, the backstepping‐based output feedback adaptive robust fault‐tolerant control (ARFTC) strategy presented here can effectively deal with such uncertainties and overcome the drawbacks of individual adaptive and robust controls. Comparative simulation studies are performed on a linearized Boeing 747 model, which shows the effectiveness of the proposed scheme. Copyright © 2011 John Wiley & Sons, Ltd.     

参数在线跟踪的直流传动双神经网络模型参考自适应控制

针对在“基于Hopfield神经网络的直流传动系统模型参考自适应控制“^[8]一文中指出的所提神经网络控制器在负载转矩未知和变化情况下的缺陷,将作者先前所提出的交流传动系统参数自动跟踪神经网络^[2]引入直流传动系统,构成具有参数在线跟踪功能的直流传动双神经网络模型参考自适应控制模式,进一步提高了系统的控制性能。     

无刷直流电动机模型参考自适应控制研究

研究了梯形波无刷直流电动机控制系统稳定性问题.在负载转矩、转动惯量、阻尼系数和绕组电流等发生波动引起转速变化时,根据模型参考自适应控制原理构造参考模型,设计转速自适应控制律,使控制系统具有较强的鲁棒性和稳定性.通过仿真和实验证明,该模型参考自适应控制器能够准确跟踪给定的参考速度.     

Transient performance improvement in indirect model reference adaptive control using perturbation‐based extremum seeking identifier

One of the main drawbacks of model reference adaptive control (MRAC) is the weakness of its transient performance. The key reason of this imperfection is parameter's estimation error convergence. For many cases in the closed‐loop control, the plant input signal cannot satisfy the persistence of excitation (PE) condition which yields poor parameters estimation error convergence. In this paper, we use a fast perturbation‐based extremum seeking (PES) scheme without steady‐state oscillation as the parameter identifier in indirect MRAC. The estimated parameters through the PES identifier contain the additive sinusoidal signals with distinct frequencies in the transient, which satisfy the PE condition of the plant input. Therefore, convergence of the parameters estimation error to zero will be guaranteed that results in improvement of transient performance for indirect MRAC. Also, the contrary effects on the steady‐state behaviour is eliminated since the sinusoidal excitation signals amplitude exponentially converge to zero and reinitiate with every change in the unknown parameters. Simulation results for a second order example have been presented to illustrate the effectiveness of the proposed scheme.     

Discrete‐time multivariable robust model reference adaptive control based on Kp = LDS factorization: an input–output approach

A direct scheme of robust model reference adaptive control is reinvestigated, in an input–output approach, for a large class of discrete‐time multivariable systems with unmodeled dynamics and bounded disturbances. Compared with the existing results, in virtue of a high‐frequency gain matrix factorization, the assumptions required in the scheme are further relaxed without overmuch complicating the controller structure, and a permissible range of the gain parameter in a modified adaptive algorithm is clearly specified. Moreover, paralleling the continuous‐time theoretic framework, robust stability and robust tracking performance are analyzed by using the multivariable versions of some important technical lemmas, such as an exponentially weighted norm‐relation lemma and two swapping lemmas. Copyright © 2012 John Wiley & Sons, Ltd.     

异步电机基于MRAC的转子时间常数在线辨识算法的统一描述

应用于异步电机转子时间常数在线辨识的模型参考自适应控制器(MRAC),依据其参考模型设计的不同,有着不同的算法形式。在深入分析转子时间常数T_r偏差对电机间接磁场定向、输出电磁转矩、无功功率影响的基础上,运用李雅普诺夫稳定理论提出了T_r在线辨识的统一MRAC自适应律,通过自适应律中参数的不同配置,可以得到多种基于MRAC的T_r在线辨识算法。借助于统一自适应律理论,为多种辨识模型间的演化和对比提供了理论依据。同时,该文所提自适应律的统一描述也有助于基于MRAC的T_r辨识理论体系的完善,使得辨识模型的选择有章可循。仿真和实验结果验证了该文分析的有效性。     

基于扩展反电势估算的内插式永磁同步电动机无传感器控制

提出一种基于扩展反电势估算的内插式永磁同步电动机(IPMSM)无传感器控制策略，拟用于永磁无轴承电机地无位置/速度传感器运行。定义了包含传统反电势及定子电感位置信息的扩展反电势(Extended EMF, EEMF)，以此建立静止坐标系中的IPMSM新型数学模型。通过滑模观测器对两相静止坐标系中分量EEMF的估算检测出转子的空间位置；基于Lyapunov函数分析观测参数的收敛性；采用模型参考自适应算法得到了转子的估算速度。实验运行验证了该无传感器控制策略的有效性。     

A clarifying analysis of feedback error learning in an LTI framework

Feedback error learning (FEL) is a proposed technique for reference‐feedforward adaptive control. FEL in a linear and time‐invariant (LTI) framework has been studied recently; the studies can be seen as proposed solutions to a ‘feedforward MRAC’ problem. This paper reanalyzes two suggested schemes with new interpretations and conclusions. It motivates the suggestion of an alternative scheme for reference‐feedforward adaptive control, based on a certainty‐equivalence approach. The suggested scheme differs from the analyzed ones by a slight change in both the estimator and the control law. Boundedness and error convergence are then guaranteed when the estimator uses normalization combined with parameter projection onto a convex set where stability of the estimated closed‐loop system holds. Copyright © 2008 John Wiley & Sons, Ltd.     

Adaptive‐optimal control under time‐varying stochastic uncertainty using past learning

An adaptive‐optimal control architecture is presented for adaptive control of constrained aerospace systems with matched uncertainties that are subject to dynamic stochastic change. The architecture brings together three key elements, ie, model predictive control–based reference command shaping, Gaussian process (GP)–based Bayesian nonparametric model reference adaptive control (MRAC), and online GP clustering over nonstationary GPs. Model predictive control optimizes reference model and its shaped output is passed into GP–based MRAC, which is used to learn the model in presence of significant time‐varying stochastic uncertainty while maintaining stability. Based on a likelihood ratio test, the changepoints are detected and learned. Lastly, the models are created and clustered by non‐Bayesian clustering algorithm. The key salient feature of our architecture is that not only can it detect changes but also it uses online GP clustering to enable the controller to utilize past learning of similar models to significantly reduce learning transients. Furthermore, persistence of excitation conditions are significantly relaxed due to the use of GP‐MRAC. Stability of the architecture is argued theoretically and performance is validated empirically on different scenarios for wing rock dynamics.     

Model reference adaptive control system design for linear time‐varying systems with unstructured and bounded varying functions

In recent years, many methods of model reference adaptive control system (MRACS) for a linear time‐varying (LTV) plant have been proposed. These methods assumed that the structure of plant parameters is known in advance. However, it is difficult to get a priori information of plant parameters. In this paper, an MRACS design for an LTV system based on high‐order estimator (HOE) is proposed. By applying dynamic certainty equivalence (DyCE) to LTV plants, a new MRAC law of LTV system is derived without knowing the structure of the plant parameters. The MRACS law is generated by using high‐order derivatives of an estimated parameter, so that robust HOE with a normalization signal and σ modification for the system introduced. Our proposed method can attain better performance than conventional methods, such as estimation with variable forgetting factor (VF) and the gradient projection method (GPM). The robust HOE establishes the boundedness of all of the estimated parameters under the condition that the estimated parameter and the first derivative of the parameter are bounded. It is shown that all signals in the adaptive loop are bounded and the output error converges to a closed set. The proposed method is compared to the familiar schemes, the gradient projection method and the estimation based on forgetting factor through numerical simulations, and the effectiveness of our proposed method is shown. © 2000 Scripta Technica, Electr Eng Jpn, 130(4): 87–98, 2000     

Indirect model reference adaptive control with dynamic adjustment of parameters

The paper discusses in detail a new method for indirect model reference adaptive control (MRAC) of linear time-invariant continuous-time plants with unknown parameters. The method involves not only dynamic adjustment of plant parameter estimates but also those of the controller parameters. Hence the overall system can be described by a set of non-linear differential equations as in the case of direct control. Many of the difficulties encountered in the conventional indirect approach, where an algebraic equation is solved to determine the control parameters, are consequently bypassed in this method. The proof of stability of the equilibrium state of the overall system is found to be different from that used in direct control. Using Lyapunov's theory, it is first shown that the parameter errors between the parameter estimates of the identifier and the true parameters of the plant, as well as those between the actual parameters of the controller and their desired values, are bounded. Following this, using growth rates of signals in the adaptive loop as well as order arguments, it is shown that the error equations are globally uniformly stable and that the tracking (control) error tends to zero asymptotically. This in turn establishes the fact that both direct and indirect model reference adaptive schemes require the same amount of prior information to achieve stable adaptive control.     

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.     

平面开关磁阻电机模型参考自适应位置控制

为了提高平面开关磁阻电机的位置精确度,研究一种基于模型参考自适应控制理论的平面开关磁阻电机控制方法。采用最小二乘法辨识了平面开关磁阻电机的线性化模型参数,根据李亚普若夫稳定性理论,以力指令为控制量并采用输入输出变量设计了平面开关磁阻电机模型参考自适应位置控制器,基于dSPACE半实物实时仿真系统,构建了实时在线控制实验平台,进行了平面开关磁阻电机的模型参考自适应位置控制实验。研究表明:基于模型参考自适应控制的平面开关磁阻电机系统能平稳、准确地跟随给定位置,提高了电机位置精确度,验证了提出的平面开关磁阻电机模型参考自适应控制方法的可行性和有效性。     

Robust adaptive control for unmatched systems with guaranteed parameter estimation convergence

This paper provides a modified model reference adaptive control (MRAC) scheme to achieve better transient control performance for systems with unknown unmatched dynamics, where an adaptive law with guaranteed convergence is introduced. We first revisit the standard MRAC system and analyze the tracking error bound by using L₂‐norm and Cauchy‐Schwartz inequality. Based on this analysis, we suggest a feasible way to compensate the undesired transient dynamics induced by the gradient descent–based adaptive laws subject to sluggish convergence or even parameter drift. Then, a modified adaptive law with an alternative leakage term containing the parameter estimation error is developed. With this adaptive law, the convergence of both the estimation error and tracking error can be proved simultaneously. This enhanced convergence property can contribute to deriving smoother control signal and improved control response. Moreover, this paper provides a simple and numerically feasible approach to online verify the well‐known persistent excitation condition by testing the positive definiteness of an introduced auxiliary matrix. Comparative simulations based on a benchmark 3‐DOF helicopter model are given to validate the effectiveness of the proposed MRAC approach and show the improved performance over several other MRAC schemes.     

Adaptive control of Wiener-type nonlinear systems using neural networks

This paper proposes new adaptive control schemes with neural networks for Weiner-type nonlinear systems which have output nonlinearity. First, by adopting a robust adaptive control law and a functional link network (FLN), we present an adaptive linearizing scheme as a primary step for a model reference control scheme, where the FLN compensates the output nonlinearity. Second, we analyze the stability of the adaptive linearizing scheme by using a robust adaptive control technique, and demonstrate that all of the parameters are bounded and that the boundedness of all of the signals in the closed loop is guaranteed under some reasonable conditions. Third, based on the linearizing scheme, we present a new direct model reference adaptive control scheme by choosing the reference output appropriately. The stability of the system is guaranteed under several conditions in a similar manner. Finally, we illustrate the effectiveness of the proposed scheme through some numerical examples. © 1998 Scripta Technica. Electr Eng Jpn, 122(1): 37–48, 1998     

带负载转矩补偿的 PMSM 交流伺服系统自适应控制

设计了一个基于ＤＳＰ和ＰＭＳＭ自适应速度控制器，使用了模型参考自适应方法，具有计算量小的特点，能实时辨识系统参数，采用自适应负载转矩观测器补偿负载转矩扰动，实验表明本控制器在系统参数变化和负载转矩扰动的情况下具有良好的自适应能力。