Output‐feedback co‐ordinated decentralized adaptive tracking: The case of MIMO subsystems with delayed interconnections

Exact decentralized output‐feedback Lyapunov‐based designs of direct model reference adaptive control (MRAC) for linear interconnected delay systems with MIMO subsystems are introduced. The design process uses a co‐ordinated decentralized structure of adaptive control with reference model co‐ordination which requires an exchange of signals between the different reference models. It is shown that in the framework of the reference model co‐ordination zero residual tracking error is possible, exactly as in the case with SISO subsystems. We develop decentralized MRAC on the base of a priori information about only the local subsystems gain frequency matrices without additional a priori knowledge about the full system gain frequency matrix. To achieve a better adaptation performance we propose proportional, integral time‐delayed adaptation laws. The appropriate Lyapunov–Krasovskii type functional is suggested to design the update mechanism for the controller parameters, and in order to prove stability. Two different adaptive DMRAC schemes are proposed, being the first asymptotic exact zero tracking results for linear interconnected delay systems with MIMO subsystems. Copyright © 2005 John Wiley & Sons, Ltd.     

Model reference adaptive iterative learning control for linear systems

In this paper, we propose a model reference adaptive control (MRAC) strategy for continuous‐time single‐input single‐output (SISO) linear time‐invariant (LTI) systems with unknown parameters, performing repetitive tasks. This is achieved through the introduction of a discrete‐type parametric adaptation law in the ‘iteration domain’, which is directly obtained from the continuous‐time parametric adaptation law used in standard MRAC schemes. In fact, at the first iteration, we apply a standard MRAC to the system under consideration, while for the subsequent iterations, the parameters are appropriately updated along the iteration‐axis, in order to enhance the tracking performance from iteration to iteration. This approach is referred to as the model reference adaptive iterative learning control (MRAILC). In the case of systems with relative degree one, we obtain a pointwise convergence of the tracking error to zero, over the whole finite time interval, when the number of iterations tends to infinity. In the general case, i.e. systems with arbitrary relative degree, we show that the tracking error converges to a prescribed small domain around zero, over the whole finite time interval, when the number of iterations tends to infinity. It is worth noting that this approach allows: (1) to extend existing MRAC schemes, in a straightforward manner, to repetitive systems; (2) to avoid the use of the output time derivatives, which are generally required in traditional iterative learning control (ILC) strategies dealing with systems with high relative degree; (3) to handle systems with multiple tracking objectives (i.e. the desired trajectory can be iteration‐varying). Finally, simulation results are carried out to support the theoretical development. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

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.     

Microprocessor-Based Adjustable-Speed DC Motor Drives Using Model Reference Adaptive Control

Model reference adaptive control (MRAC) is applied to microprocessor-based adjustable-speed dc motor drives. The algorithm of the MRAC is based on the linear model following control (LMFC) and is the combination of the adaptive controller with the LMFC. The MRAC-based speed controller allows the indistinctness and/or inaccuracy in the motor and load parameters in the system design stage. It also maintains the prescribed control performance in the presence of the motor parameter perturbations and the load disturbances. The experimental setup is constructed using a microprocessor. The experimental results confirm the useful effects of the MRAC-based speed controller.     

Adaptive multi-dimensional Taylor network funnel control of a class of nonlinear systems with asymmetric input saturation

In view of the result and performance of control are affected by the existence of input constraints and requirements, adaptive multi-dimensional Taylor network (MTN) funnel control problem is studied for a class of nonlinear systems with asymmetric input saturation in this paper. Firstly, the effect of asymmetric input saturation can overcome by introducing the Gaussian error function, namely, the asymmetric saturation model is represented as a simple linear model with a bounded disturbance. Secondly, MTNs are employed to approximate the unknown functions in the controller design. Then, an adaptive MTN tracking controller is developed by blends the idea of funnel control into backstepping, which can guarantee that the tracking error always meets the given prescribed performance regarding the transient and steady state responses as well as the output of system tracks the give continuous reference signal. Finally, the effectiveness of the proposed control is demonstrated using two examples.     

Decentralized robust adaptive-output feedback controller for power system load frequency control

In this paper, a new model reference-decentralized robust adaptive-output feedback controller is proposed for the load frequency control (LFC) of large-scale power systems with unknown parameters. This control strategy requires only local input–output data and can follow random changes in the operating conditions. The controller is designed such that the trajectory errors and the control gains of each area remain uniformly bounded. In the proposed method, firstly an adaptive observer is designed to estimate the state variables and system parameters using local data only. Then a locally linear combination of the estimated states and the model reference states are used to design a robust adaptive-output feedback controller for each area. Simulation results for a three-area power system show that the proposed controller achieves good performance even in the presence of plant parameter changes and system non-linearities. Received: 18 October 2001/Accepted: 24 October 2001     

基于模型参考模糊自适应控制的永磁同步电机控制器设计

基于模型参考模糊自适应控制(MRFAC)方法设计永磁同步电机(PMSM)速度控制器.该控制器具有传统模型参考自适应控制构架.传统模型参考自适应控制系统中的反馈控制器和常规自适应机构分别由主模糊控制器、模糊自适应机构替代,模糊逆模型结合自适应调整算法构成的模糊自适应机构对主控制器参数进行实时调整,以达到快速适应对象参数和状态变化的目的.利用模块化建模工具Matlab/SimuIink建立PMSM控制系统模型.仿真结果表明了所设计控制器运行平稳,具有良好的动、静态特性.     

无刷直流电机的模型参考模糊自适应方法及实验研究

将模糊控制器植入模型参考自适应控制系统构架中,主模糊控制器用于取代传统模型参考自适应控制中的反馈控制器,模糊逆模型结合自适应调整算法取代复杂的常规自适应规则,形成了模型参考模糊自适应控制方法.将此方法应用于无刷直流电机(BLDCM)调速系统,设计模型参考模糊自适应速度控制器,仿真及基于dSPACE的实验结果表明:控制系统运行平稳,速度跟踪快速准确,具有良好的动、静态特性.     

Decentralized robust adaptive load frequency control using interactions estimation

In this paper, a new model reference decentralized adaptive output feedback controller is proposed for load-frequency control (LFC) of large-scale power systems with unknown parameters. The main problem with a decentralized robust LFC is that the interactions are treated as disturbances. This results in a conservative control action to maintain stability in the worst-case scenario. Furthermore, to improve the performance of the decentralized LFC, the proposed method estimates the interactions from other subsystems to modify the adaptive controller so that the interactions are effectively neutralized. The other important features of the proposed controller are: (1) no prior information about the system parameters is required, (2) random changes in the operating conditions are traced, (3) only the local input–output data are needed, (4) the robustness of the overall system against the system parameter uncertainties is guaranteed. To show the effectiveness of the proposed controller, a three-area power system is studied. The simulation results are promising and highlight the remarkable performance of the controller even in the presence of both plant parameter changes and high interactions.     

Transients in output feedback adaptive systems with observer‐like reference models

This note presents analysis and quantification of transient dynamics in Model Reference Adaptive Control (MRAC) with output feedback and observer‐like reference models. A practical design methodology for this class of systems was first introduced in 1 , 2 , where an output error feedback was added to the reference model dynamics. Here, this design is complemented with an analysis of the corresponding transients. Specifically, it is shown that employing observer‐like reference models in MRAC leads to a trade‐off between achieving fast transient dynamics and using large error feedback gains in the modified reference model. For clarity sake, only systems with matched uncertainties are analyzed, yet the reported results can be extended to a broader class of uncertainties by utilizing MRAC modifications for robustness 3 , 4 . The note ends with a summary of the derived results and a discussion on practical design guidelines for adaptive output feedback controllers with observer‐like reference models. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

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。     

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.     

A new robust model reference control with improved performance for a class of multivariable unknown plants

Motivated by recent works on parametrization of multivariable plants for model reference adaptive control (MRAC), a new robust model reference control (MRC) scheme for a class of multivariable unknown plants is presented. The salient feature of this control scheme is the improved performance of the output-tracking property, which is hardly attainable by the traditional MRAC schemes. The controller here is devised using the concept of variable structure design which prevails in the robust control context. It is shown by a Lyapunov approach that without any persistent excitation the global stability of the overall system is achieved and the tracking errors will converge to a residual set. The size of that set can be directly related to the size of unmodelled dynamics and output disturbances explicitly as long as a set of control parameters is chosen properly (large).     

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.     

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.     

A gain‐scheduled control algorithm for input constrained systems to track time‐varying references using controller state resets

In this paper, we propose a control law for a discrete‐time linear system with actuator saturation to track time‐varying reference signals. The proposed control law consists of a feedback controller and a target recalculation mechanism. The feedback controller includes an integrator to achieve zero steady‐state error in the case where the reference signal is constant. The feedback gains of the controller are parameterized by a single scheduling parameter. In the proposed control algorithm, when the tracking error is large, a modified reference signal is computed by the target recalculation mechanism so that feasibility of the algorithm and stability of the control system are guaranteed at all times. At this stage, the controller state is modified online so that the tracking control performance is improved. Further, when the tracking error becomes small, the scheduling parameter and the controller state are updated simultaneously so that the tracking control performance is improved. The problems of determining the scheduling parameter, the controller state, and the modified reference signal are reduced to convex optimization problems with linear matrix inequality constraints. The effectiveness of the proposed control method is shown through an experiment. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Reduced‐order robust adaptive control design of uncertain SISO linear systems

In this paper, a stability and robustness preserving adaptive controller order‐reduction method is developed for a class of uncertain linear systems affected by system and measurement noises. In this method, we immediately start the integrator backstepping procedure of the controller design without first stabilizing a filtered dynamics of the output. This relieves us from generating the reference trajectory for the filtered dynamics of the output and thus reducing the controller order by n, n being the dimension of the system state. The stability of the filtered dynamics is indirectly proved via an existing state signal. The trade‐off for this order reduction is that the worst‐case estimate for the expanded state vector has to be chosen as a suboptimal choice rather than the optimal choice. It is shown that the resulting reduced‐order adaptive controller preserves the stability and robustness properties of the full‐order adaptive controller in disturbance attenuation, boundedness of closed‐loop signals, and output tracking. The proposed order‐reduction scheme is also applied to a class of single‐input single‐output linear systems with partly measured disturbances. Two examples are presented to illustrate the performance of the reduced‐order controller in this paper. Copyright © 2007 John Wiley & Sons, Ltd.     

Non‐certainty equivalent adaptive control for lower triangular systems based on dynamic scaling and filter

A new adaptive controller is designed on the basis of dynamic scaling and filter for lower triangular systems. Compared with the available adaptive results in the literature, the proposed adaptive approach does not necessarily need to satisfy the certainty equivalence principle and allows for prescribed dynamics to be assigned to the parameter estimation error. The proposed adaptive state feedback controller that ensures all signals of closed‐loop systems are globally bounded while keeping the output tracking error to the origin simultaneously. It is interesting to note that, viewed from a Lyapunov perspective, the proposed method provides a procedure to add cross terms between the parameter estimates and the system states in every design step. Finally, two comparatively simulation examples are given, highlighting the advantages of the proposed methodology. Copyright © 2013 John Wiley & Sons, Ltd.