Adaptive robust control of nonlinear systems with dynamic uncertainties

In this paper, the discontinuous projection‐based adaptive robust control (ARC) approach is extended to a class of nonlinear systems subjected to parametric uncertainties as well as all three types of nonlinear uncertainties—uncertainties could be state‐dependent, time‐dependent, and/or dynamic. Departing from the existing robust adaptive control approach, the proposed approach differentiates between dynamic uncertainties with and without known structural information. Specifically, adaptive robust observers are constructed to eliminate the effect of dynamic uncertainties with known structural information for an improved steady‐state output tracking performance—asymptotic output tracking is achieved when the system is subjected to parametric uncertainties and dynamic uncertainties with known structural information only. In addition, dynamic normalization signals are introduced to construct ARC laws to deal with other uncertainties including dynamic uncertainties without known structural information not only for global stability but also for a guaranteed robust performance in general. Copyright © 2008 John Wiley & Sons, Ltd.     

Adaptive robust boundary control of shaft vibrations under perturbations with unknown upper bounds

This paper presents robust and adaptive boundary control designs to stabilize the two‐dimensional vibration of hybrid shaft model. The hybrid shaft is mathematically represented by a set of partial differential equations, governing the shaft vibrations, coupled to ordinary differential equations, describing rigid body spinning and dynamic boundary conditions. The control objective is to stabilize the transverse vibrations of the perturbed shaft while regulating the spinning rate. To achieve this, the paper first establishes robust boundary control laws that fulfil the control objective in the presence of modeling uncertainties and external disturbances operating over the shaft domain and boundary. Lyapunov‐based analyses show that the proposed robust control exponentially stabilizes the shaft with vanishing distributive perturbations, while assuring ultimately bounded vibrations in the case of nonvanishing perturbations. Then, adaptive control philosophy is utilized to achieve redesigned robust controllers that only use online adaptation of control gains without acquiring the knowledge of bounds on perturbations, as well as dynamic parameters. An advantage of this design is avoiding an overconservative robust control law, which may induce poor stability and chattering in tackling system perturbations with unknown upper bounds. Simulations through finite element method illustrate the results. Copyright © 2014 John Wiley & Sons, Ltd.     

Multiple‐model adaptive robust dynamic surface control with estimator resetting

A multiple‐model adaptive robust dynamic surface control with estimator resetting is investigated for a class of semi‐strict feedback nonlinear systems in this paper. The transient performance is mainly considered. The multiple models are composed of fixed models, one adaptive model, and one identification model that can be obtained when the persistent exciting condition is satisfied. The transient performance of the final tracking system can be improved significantly by designing proper switching mechanism during the parameter tuning procedure. The semi‐globally uniformly ultimately bounded stability of the closed‐loop system can be easily achieved because of the framework of adaptive robust dynamic surface control. Numerical examples are provided to demonstrate the effectiveness of the proposed multiple‐model controller. Copyright © 2014 John Wiley & Sons, Ltd.     

数控机床多轴联动伺服电机的零相位自适应鲁棒交叉耦合控制

针对驱动多轴联动数控机床的高精度永磁同步电动机交流伺服系统,在分析系统轮廓误差的基础上,提出了将零相位误差跟踪控制器(zero phase error tracking controller,ZPETC)、自适应鲁棒控制器(adaptive robust controller,ARC)和交叉耦合控制器(cross coupling controller,CCC)相结合的控制策略。ZPETC提高了系统动态响应的快速性,消除系统的滞后现象,实现准确跟踪;ARC克服系统参数变化、负载扰动等不确定性因素的影响,增强系统的品质鲁棒性和稳定性;CCC用以消除各轴之间的增益参数和动态参数不匹配的影响。仿真分析表明所提出的控制方案有效,可提高零件的轮廓加工精度。     

Adaptive robust output feedback control for attitude tracking of quadrotor unmanned aerial vehicles

This work proposes a new adaptive robust output feedback control method for attitude reference tracking of a quadrotor unmanned aerial vehicle without using the angular velocity measurements. By using the K-filters well known in the adaptive control community, the necessity of velocity measurements or estimating is avoided. The attitude system model is transformed into a second-order model where the angular velocity measurements are not involved. However, the model includes mismatched uncertainties which should be estimated and compensated by the disturbance observers (DOBs). The controller is designed in a backstepping manner, and the dynamic surface technique is adopted to avoid the explosion of the controller complexity. For each Euler angle axis, the prescribed performance control technique is adopted to ensure a prescribed performance, the lumped disturbance is compensated by a DOB, and furthermore an adaptive law is introduced to adaptively update the corresponding uncertain inertia parameter which affects the control performance significantly. The control performance of the overall control system is analyzed rigorously from the viewpoint of input-to-state practical stability. In addition, it is shown how the adaptive laws contribute to improving the control performance. And simulation examples are provided to demonstrate the performance of the proposed method.     

水轮机调速系统全系数自适应控制方案研究

本文对水轮机调速系统的特性和控制性能的要求作了分析,基于全系数自适应控制方法给出一种自适应控制方案。文中分别从广义被控对象模型的建立,采样周期的选取,自适应控制规律的设计等方面讨论了控制方案设计的问题。仿真结果表明,本文给出的控制方案可以在较大的参数变化范围内保持系统稳定性,对于过渡过程的动态性能表现出较强的鲁棒性和良好的适应性。     

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.     

Adaptive robust nonlinear control of a magnetic levitation system via DSC technique

This paper considers the position tracking problem of a popular magnetic levitation system in the presence of modeling errors due to uncertainties of physical parameters. The recently developed dynamic surface control (DSC) technique is modified and applied to the system under study, to overcome the problem of “explosion of terms” associated with the backstepping design procedure. The input‐to‐state stability (ISS) property is ensured by the robust nonlinear damping terms, and the ultimate control error bounds are made sufficiently small by the adaptive laws. Experimental results are included to show the excellent position tracking performance of the designed control system. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 149(4): 42–51, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20092     

Neural network adaptive robust control with application to precision motion control of linear motors

In this paper, neural networks (NNs) and adaptive robust control (ARC) design philosophy are integrated to design performance‐oriented control laws for a class of single‐input–single‐output (SISO) nth‐order non‐ linear systems. Both repeatable (or state dependent) unknown non‐linearities and non‐repeatable unknown non‐linearities such as external disturbances are considered. In addition, unknown non‐linearities can exist in the control input channel as well. All unknown but repeatable non‐linear functions are approximated by outputs of multi‐layer neural networks to achieve a better model compensation for an improved performance. All NN weights are tuned on‐line with no prior training needed. In order to avoid the possible divergence of the on‐line tuning of neural network, discontinuous projection method with fictitious bounds is used in the NN weight adjusting laws to make sure that all NN weights are tuned within a prescribed range. By doing so, even in the presence of approximation error and non‐repeatable non‐linearities such as disturbances, a controlled learning is achieved and the possible destabilizing effect of on‐line tuning of NN weights is avoided. Certain robust control terms are constructed to attenuate various model uncertainties effectively for a guaranteed output tracking transient performance and a guaranteed final tracking accuracy in general. In addition, if the unknown repeatable model uncertainties are in the functional range of the neural networks and the ideal weights fall within the prescribed range, asymptotic output tracking is also achieved to retain the perfect learning capability of neural networks in the ideal situation. The proposed neural network adaptive control (NNARC) strategy is then applied to the precision motion control of a linear motor drive system to help to realize the high‐performance potential of such a drive technology. NN is employed to compensate for the effects of the lumped unknown non‐linearities due to the position dependent friction and electro‐magnetic ripple forces. Comparative experiments verify the high‐performance nature of the proposed NNARC. With an encoder resolution of 1 µm, for a low‐speed back‐and‐forth movement, the position tracking error is kept within ±2 µm during the most execution time while the maximum tracking error during the entire run is kept within ±5.6 µm. Copyright © 2001 John Wiley & Sons, Ltd.     

Adaptive neural network output feedback stabilization of nonlinear non‐minimum phase systems

This paper presents an adaptive output feedback stabilization method based on neural networks (NNs) for nonlinear non‐minimum phase systems. The proposed controller comprises a linear, a neuro‐adaptive, and an adaptive robustifying parts. The NN is designed to approximate the matched uncertainties of the system. The inputs of the NN are the tapped delays of the system input–output signals. In addition, an appropriate reference signal is proposed to compensate the unmatched uncertainties inherent in the internal system dynamics. The adaptation laws for the NN weights and adaptive gains are obtained using Lyapunov's direct method. These adaptation laws employ a linear observer of system dynamics that is realizable. The ultimate boundedness of the error signals are analytically shown using Lyapunov's method. The effectiveness of the proposed scheme is shown by applying to a translation oscillator rotational actuator model. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust adaptive steering control for unmanned surface vehicle with unknown control direction and input saturation

A robust adaptive steering control method is proposed to solve the control problem of the unmanned surface vehicle (USV) with uncertainties, unknown control direction, and input saturation. In the controller design process, the adaptive fuzzy system is incorporated into dynamic surface control (DSC) to approximate the uncertainty term induced by external environmental disturbances and model parameters. Then, the Nussbaum function is used to eliminate the requirement for a priori knowledge of the control direction. Besides, to handle the input saturation, the adaptive fuzzy DSC is extended by a second‐order nonlinear filter and antisaturation auxiliary function to compensate for the magnitude and rate saturation of the rudder. All signals of the closed‐loop system are proven to be uniformly ultimately bounded (UUB) by Lyapunov theorem and the Lemma of Nussbaum gain, and the course error can converge to a small neighborhood of zero through choosing design parameters appropriately. Finally, simulation results and comprehensive comparisons are shown for the USV course system, which is demonstrative of the proposed controller's effectiveness and robustness.     

Reaching phase free adaptive fuzzy synergetic power system stabilizer

In this paper, an adaptive fuzzy power system stabilizer is developed based on robust synergetic control theory and terminal attractor techniques. The main contribution consists in making the dynamic system insensitive to parameters variation. This aim is achieved using a new synergetic controller design such that power system states start, evolve and remain on a designer chosen attractor toward the equilibrium point therefore avoiding transient mode. Rendering the design more robust, fuzzy logic systems are used to approximate the unknown power system dynamic functions without calling upon usual model linearization and simplifications. Based on an indirect adaptive scheme and Lyapunov theory, adaptation laws are developed to make the controller handle parameters variations due to the different operating conditions occurring on the power system and to guarantee stability. The performance of the proposed stabilizer is evaluated for a single machine infinite bus system and for a multi machine power system under different type of disturbances. Simulation results show the effectiveness and robustness of the proposed stabilizer in damping power system oscillations under various disturbances and better overall performance than classical PSS and some other types of power stabilizers.     

Robust adaptive regulation of dynamically positioned ships with unknown dynamics and unknown disturbances

We develop a robust adaptive regulating control law for dynamically positioned ships subject to unknown dynamics and bounded unknown disturbances incorporating the radial basis function (RBF) neural network (NN), the dead zone adaptive technique, and a robust control term into the vectorial backstepping approach. The RBF NNs with the dead zone adaptive laws approximate the ship unknown dynamics. The adaptive law‐based robust control term compensates for unknown disturbances, NN approximation errors, and undesirable errors arising from the design procedures. The developed dynamic positioning (DP) control law regulates the ship position and heading to the desired values with arbitrarily small errors, while guaranteeing the uniform ultimate boundedness of all signals in the DP closed‐loop control system of ships. High‐fidelity simulations on two supply ships and comparisons demonstrate the effectiveness and the superiority of the developed DP control law.     

电液伺服系统的非线性鲁棒自适应控制

摘要：针对电液伺服非线性系统的参数不确定性以及模型不确定项，基于Lyapunov稳定方法，提出了一种适用于电液伺服系统的非线性鲁棒自适应控制策略。首先以跟踪误差为基础给出系统目标控制函数的定义方法，然后基于Lyapunov稳定性分析方法，给出了不确定参数的自适应律， 以及自适应控制器的设计。同时引入一种简单的鲁棒设计方法补偿系统的模型不确定项。该方法具有结构简单，鲁棒性强的特点，并且系统控制量平稳，无振动现象出现。仿真结果显示，采用该控制方法可取得良好的控制效果，并进一步证实了理论分析的正确性。     

不确定混沌电力系统的鲁棒自适应跟踪控制

针对混沌电力系统的跟踪控制问题,在考虑系统含有常参数不确定性及未知干扰的前提下,采用动态面控制方法,设计了鲁棒自适应跟踪控制器,保证了闭环系统的半全局渐近稳定,进而使输出渐近跟踪参考轨迹.理论分析及仿真结果表明,所设计的自适应非线性控制器能够有效抑制简单电力系统的混沌振荡,且具有一定的适应性及鲁棒性.     

Robust nonlinear adaptive backstepping excitation controller design for rejecting external disturbances in multimachine power systems

This paper proposes a new approach to design a robust adaptive backstepping excitation controller for multimachine power systems in order to reject external disturbances. The parameters which significantly affect the stability of power systems (also called stability sensitive parameters) are considered as unknown and the external disturbances are incorporated into the power system model. The proposed excitation controller is designed in such a way that it is adaptive to the unknown parameters and robust to external disturbances. The stability sensitive parameters are estimated through the adaptation laws and the convergences of these adaptation laws are obtained through the negative semi-definiteness of control Lyapunov functions (CLFs). The proposed controller not only provides robustness property against external disturbances but also overcomes the over-parameterization problem of stability sensitive parameters which usually appears in some conventional adaptive methods. Finally, the performance of the proposed controller is tested on a two-area four machine 11-bus power system by considering external disturbances under different scenarios and is compared to that of an existing nonlinear adaptive backstepping controller. Simulation results illustrate the robustness of the proposed controller over an existing one in terms of rejecting external disturbances.     

Neural network–based direct adaptive robust control of unknown MIMO nonlinear systems using state observer

This paper focuses on the problem of adaptive robust tracking control for a class of uncertain multiple-input and multiple-output (MIMO) nonlinear system. Unlike most previous research studies, model dynamics, disturbances, and state variables are unknown in this paper. A novel observer-based direct adaptive neuro-sliding mode control approach is proposed of which the only required knowledge is the system output. By incorporating the Adaptive Linear Neuron (ADALINE) neural network (NN) into the conventional sliding mode observer, the proposed observer has favorable performance. In the controller, a radial basis function (RBF) NN is constructed to approximate the unknown equivalent control laws and the estimation of the sliding surface is applied as the input. A gain-adaptation sliding mode term is designed to enhance the robustness of the control system. Besides, the free parameters of the ADALINE NN and the RBFNN are updated online by adaptive laws to obtain optimal approximation performance. Finally, the comparative simulations are given to show the effectiveness and merits of proposed scheme.     

Robust adaptive output‐feedback control for a class of nonlinear systems with hysteresis compensation controller

In this paper, a robust adaptive output‐feedback dynamic surface control scheme is proposed for a class of single‐input single‐output nonlinear systems preceded by unknown hysteresis with the following features: (1) a hysteresis compensator is designed in the control signal to compensate the hysteresis nonlinearities with only the availability of the output of the control system; (2) by estimating the norm of the unknown parameter vector and the maximum value of the hysteresis density function, the number of the estimated parameters is reduced, which implies that the computational burden is greatly reduced; (3) by introducing the initializing technique, the initial conditions of the state observer and adaptive laws of unknown parameters can be properly chosen, and the arbitrarily small norm of the tracking error is achieved. It is proved that all the signals in the closed‐loop system are ultimately uniformly bounded and can be arbitrarily small. Simulation results show the validity of the proposed scheme.     

基于LMI的永磁同步电机鲁棒H∞自补偿滑模控制

针对传统矢量控制方案由滑模增益选择保守造成抗负载扰动与参数摄动等不确定因素的鲁棒性差的问题,设计了基于线性矩阵不等式(LMI)的鲁棒H_∞滑模速度控制器和电流控制器。在速度控制器设计中,将求解H_∞状态反馈控制器增益问题转化为求解具有约束条件的LMI问题,从而求出H_∞状态反馈控制器增益,构成滑模面。在此基础上,设计出基于范数有界的滑模控制律,使系统状态可以实现有限时间内到达所需滑模面。在电流控制器设计中,同理设计出滑模面与滑模控制律,对于滑模控制律中的复合项采用自适应方式进行估计,消除了滑模开关增益选择的保守性。仿真与实验验证了所提控制策略的有效性。     

Dynamic modeling and adaptive robust boundary control of a flexible robotic arm with 2‐dimensional rigid body rotation

This paper investigates the control of a single‐link flexible robot manipulator with a tip payload appointed to rotate about 2 perpendicular axes in space. The control objective is to regulate the rigid body rotation of the manipulator with guaranteeing the stability of its vibration in the presence of exogenous disturbances. To achieve this, a Lyapunov‐based control design procedure is used and accomplished in some steps. First, the partial differential equation (PDE) dynamic model governing the rigid‐flexible hybrid motion of the arm is derived by applying Hamilton's principle. Next, based on the developed PDE model, an adaptive robust boundary control is established using the Lyapunov redesign approach. To this end, an adaptation mechanism is proposed so that the robust boundary control gains are dynamically updated online and there is no need for prior knowledge of disturbance upper bounds. The actuators and sensors are fully implemented at the arm boundary without using distributed actuators or sensors. Furthermore, in order to avoid control errors resulting from the spillover, control design is directly based on infinite‐dimensional PDE model without resorting to model truncation. Simulation results illustrate the efficacy of the considered method.