Rejection of nonharmonic disturbances in a class of nonlinear systems with nonlinear exosystems

This paper proposes an asymptotic rejection algorithm for rejecting exotic disturbances in nonlinear systems. The disturbances, which are produced by nonlinear exosystems, are nonharmonic and periodic. A new internal model is proposed to deal with the disturbances. Further, an adaptive output feedback controller is designed to ensure that the system's state variables can asymptotically converge to zero, and the disturbances can be completely rejected. The proposed algorithm can be used in many applications, e.g. active vibration control, and the avoidance of nonharmonic distortion in nonlinear circuits. An example is performed to demonstrate that the proposed algorithm can completely reject the nonharmonic periodic disturbances produced by nonlinear exosystems. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Asymptotic rejection of unmatched general periodic disturbances with nonlinear Lipschitz internal models

This article deals with asymptotic rejection of general periodic disturbances in a class of nonlinear systems by exploiting observer design with Lipschitz output nonlinearities for the internal model design. It is shown that a class of general periodic distances can be modelled as outputs of linear systems with nonlinear output functions. Based on this observation, a nonlinear observer design with output Lipschitz nonlinearities is investigated and integrated for the internal model design to estimate the phase and amplitude of the desired feedforward input for asymptotic disturbance rejection in a class of nonlinear systems with input-to-state stable zero dynamics. A number of problems on disturbance rejection can be formulated in the disturbance rejection form shown in this article to which the proposed nonlinear Lipschitz internal model can be applied. Two examples are included to demonstrate the proposed design strategies.     

Global adaptive output regulation of a class of nonlinear systems with nonlinear exosystems

This paper deals with global output regulation with nonlinear exosystems for a class of uncertain nonlinear output feedback systems. The circle criterion is exploited for the internal model design to accommodate the nonlinearities in the exosystems, and the explicit conditions are given for the exosystems such that the proposed internal model design can be applied. The uncertainties of the output feedback systems are in the form of unknown constant parameters, and adaptive control techniques are used to ensure the global stability of the proposed control design for output regulation.     

An adaptive disturbance rejection control scheme for multivariable nonlinear systems

An adaptive disturbance rejection control scheme is developed for uncertain multi-input multi-output nonlinear systems in the presence of unmatched input disturbances. The nominal output rejection scheme is first developed, for which the relative degree characterisation of the control and disturbance system models from multivariable nonlinear systems is specified as a key design condition for this disturbance output rejection design. The adaptive disturbance rejection control design is then completed by deriving an error model in terms of parameter errors and tracking error, and constructing adaptive parameter-updated laws and adaptive parameter projection algorithms. All closed-loop signals are guaranteed to be bounded and the plant output tracks a given reference output asymptotically despite the uncertainties of system and disturbance parameters. The developed adaptive disturbance rejection scheme is applied to turbulence compensation for aircraft fight control. Simulation results from a benchmark aircraft model verify the desired system performance.     

Adaptive rejection of non-linear disturbances in extended non-linear output feedback systems

This paper deals with asymptotic rejection of disturbances generated from non-linear exosystems for uncertain nonlinear systems in an extended output feedback form, which allows the vector field coupled with the system input to have different nonlinear functions of the system output as its elements. A new internal model design is proposed to deal with nonlinear functions of the system output that are coupled with the input and the unknown disturbance. Adaptive control techniques are then used to deal with the uncertainty in the system. The proposed adaptive disturbance rejection algorithm with the new internal model design ensures the asymptotic rejection of the unknown nonlinear disturbance and the boundedness of all the variables.     

Output tracking control of MIMO fuzzy nonlinear systems using variable structure control approach

The output tracking control problem for nonlinear systems in the presence of both parameter perturbations and external disturbances is studied. Our approach is based on the Takagi-Sugeno (T-S) fuzzy modeling method and a variable structure control (VSC) technique. Therefore, the systems considered are not and need not be in the triangular and parametric strict-feedback form, which are prevalent among adaptive model following control for nonlinear systems, or in the normal form, which pervades almost all existing results in neuro-fuzzy model following control approach. We first study the problem of stabilization of T-S fuzzy systems by using a VSC technique. A method for the design of a switching surface based on linear matrix inequalities is developed and a stabilizing controller based on a reaching law concept in the presence of both parameter perturbations and external disturbances is proposed. Then, the method is extended to design controllers for output tracking of T-S fuzzy nonlinear systems in two cases, i.e. systems which possess the so-called strong passive subsystems and strong stable zero dynamics, respectively. Finally, illustrative examples are presented to demonstrate the whole design procedure from the original nonlinear systems to their fuzzification and finally to the realization of the desired controllers. Simulation results show that the goal of output tracking can be achieved by the proposed controllers.     

Global stabilization and disturbance suppression of a class of nonlinear systems with uncertain internal model

This paper deals with global stabilization and disturbance suppression of a class of nonlinear systems using output feedback. The disturbances generated from a unknown linear exosystem are completely compensated. The order of the exosystem is assumed known and the eigenvalues are distinct. No other assumptions are needed in the control design. This means that the proposed control design is able to completely compensate the disturbances without knowing their amplitudes, frequencies and phases, as long as the number of different frequency components in the disturbances is known. A new formulation of state estimation is introduced to ensure the global stabilization and complete disturbance suppression. Adaptive control technique is used to design an adaptive internal model based on a recently introduced formulation of unknown exosystems and the parameters in the adaptive internal model converge to the actual values, from which the unknown disturbance frequencies can be calculated. In the proposed control design, a number of control coefficients are made adaptive so that the result is global with respect to unknown frequencies in the disturbances.     

可反馈线性化系统的鲁棒自适应容错控制设计

针对存在不确定执行器故障和未知不匹配干扰的可反馈线性化非线性系统, 提出一种鲁棒自适应容错控 制策略. 首先分别给出系统输入和扰动关于系统输出的相对阶, 针对两种相对阶之间的不同关系设计鲁棒控制器, 抑制干扰对系统输出的影响; 然后针对各故障情况分别设计容错控制器; 最后将各控制器进行融合得到一个综合 故障补偿控制器, 从而有效解决故障模式、类型、大小、时间和外界干扰等多重不确定性, 保证闭环系统稳定和渐近 输出跟踪性能. 仿真结果验证了所设计控制方案的可行性与有效性.     

Fuzzy model based adaptive control for a class of nonlinear systems

A fuzzy model based adaptive control algorithm for a class of continuous-time nonlinear dynamic systems is presented. The fuzzy model consisting of a set of linear fuzzy local models that are combined using a fuzzy inference mechanism is used to model a class of nonlinear systems. Each fuzzy local model represents a linearized model corresponding to the operating point of the controlled nonlinear system. The proposed control algorithm employs the fuzzy controller that is designed by considering the linear state feedback controller corresponding to the fuzzy local model with the maximum weight and the switching-σ modification adaptive controller to adaptively compensate for the plant nonlinearities. Stability robustness of the closed-loop system is analyzed in Lyapunov sense. It is shown, that the proposed control algorithm guarantees global stability of the system with the output of the system approaching the origin if there are no disturbances and uncertainties, converging to the neighborhood of the origin for all realizations of uncertainties and disturbances. The simulation examples for controlling inverted pendulum system are given to illustrate the effectiveness of the proposed method     

基于观测器的一类非线性系统的自适应模糊控制

针对一类有界的不确定非线性系统设计了模糊观测器和自适应控制器.该方法不需要系统状态完全可测的条件,而是通过模糊观测器估计系统的状态变量并且能保证观测误差是一致最终有界的.该自适应控制器取得了良好的控制效果并且保证了跟踪误差的一致最终有界性.仿真结果表明了本文所提出的方法有效性.     

一种无模型自适应积分终端滑模控制方法

针对一类包含扰动的非线性离散时间系统,提出一种新的无模型自适应离散积分终端滑模控制算法.该算法基于紧格式动态线性化数据模型,利用离散积分终端滑模控制算法设计无模型自适应控制器,并采用扰动估计技术估计系统的扰动项,其中动态线性化方法中“伪偏导数”的估计算法仅依赖于被控系统的I/O测量数据.理论分析证明了系统输入输出有界,并通过仿真实验验证了所提算法的有效性.     

Asymptotic rejection of unknown sinusoidal disturbances in nonlinear systems

This paper deals with global disturbance rejection of nonlinear systems. The disturbance is assumed to be sinusoidal with completely unknown phases, amplitude, and frequencies, but the number of distinct frequencies or the order of the corresponding unknown linear exosystem is known. Different from the common structural assumptions of nonlinear systems needed in literature for disturbance rejection of nonlinear systems, the proposed method only requires the information of control design with a known Lyapunov function when the system is disturbance-free, and a mild assumption needed for internal model design. The proposed disturbance rejection algorithm extends complete global rejection of unknown sinusoidal disturbances for nonlinear dynamic systems beyond the common nonlinear models such as the strict feedback forms and the output feedback forms.     

Robust adaptive tracking control for servo mechanisms with continuous friction compensation

In this paper, a robust adaptive tracking control scheme is developed for servo mechanisms with nonlinear friction dynamics. A continuously differentiable friction model is used to capture the friction behaviors (e.g. Stribeck effect, Coulombic friction and Viscous friction). The robust integral of the sign of the error (RISE) feedback term is employed to design an innovative adaptive controller to compensate nonlinear friction and bounded disturbances. To reduce the effect of noise pollution, the desired trajectory is employed to replace the output signal in controller design. The developed adaptive controller can guarantee the asymptotic tracking performance for nonlinear servo mechanisms in the presence of nonlinear friction and bounded disturbances. Comparative experimental results are used to validate the effectiveness of the developed control algorithm.     

Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

This paper addresses the output feedback tracking control of a class of multiple‐input and multiple‐output nonlinear systems subject to time‐varying input delay and additive bounded disturbances. Based on the backstepping design approach, an output feedback robust controller is proposed by integrating an extended state observer and a novel robust controller, which uses a desired trajectory‐based feedforward term to achieve an improved model compensation and a robust delay compensation feedback term based on the finite integral of the past control values to compensate for the time‐varying input delay. The extended state observer can simultaneously estimate the unmeasurable system states and the additive disturbances only with the output measurement and delayed control input. The proposed controller theoretically guarantees prescribed transient performance and steady‐state tracking accuracy in spite of the presence of time‐varying input delay and additive bounded disturbances based on Lyapunov stability analysis by using a Lyapunov‐Krasovskii functional. A specific study on a 2‐link robot manipulator is performed; based on the system model and the proposed design procedure, a suitable controller is developed, and comparative simulation results are obtained to demonstrate the effectiveness of the developed control scheme.     

Global robust tracking control of non-affine nonlinear systems with application to yaw control of UAV helicopter

In this paper, a novel robust nonlinear tracking control scheme is proposed for the yaw channel of an unmanned-aerial-vehicle helicopter that is non-affine in the control input. By a novel dynamic modeling technique, the non-affine nonlinear systems are approximated to facilitate the desired control design. In the controller design procedure, the terminal sliding model control method is introduced to deal with the unknown uncertainties/disturbances. Moreover, filter and disturbance estimator are combined to further reduce the chattering. A systematic procedure is developed and related theoretical and practical issues are discussed. The proposed nonlinear tracking control scheme can guarantee the asymptotic output tracking of the closed-loop control systems in spite of unknown uncertainties/disturbances. Finally, the simulation results on the dynamic model of a real helicopter-on-arm are provided to demonstrate the effectiveness of the proposed new control techniques.     

基于自组织小波小脑模型关节控制器的不确定非线性系统鲁棒自适应终端滑模控制

针对一类不确定非线性系统的跟踪控制问题,在考虑建模误差、参数不确定和外部干扰情况下,以良好的跟踪性能及强鲁棒性为目标,提出基于自组织小脑模型(self-organizing wavelet cerebellar model articulation controller,SOWCMAC)的鲁棒自适应积分末端(terminal)滑模控制策略.首先,将小脑模型、自组织神经网络和小波函数各自优势相结合,给出一种SOWCMAC,以保证干扰估计方法具有快速学习能力和更好的泛化能力.其次,设计两种改进的terminal滑模面构造方法,并分别给出各自的收敛时间.然后,基于SOWCMAC和改进的积分terminal滑模面,给出不确定非线性系统鲁棒自适应非奇异terminal控制器的设计过程,其中通过构造自适应鲁棒项抑制干扰估计误差对系统跟踪性能的影响,并利用Lyapunov理论证明闭环系统的稳定性.最后,将该方法应用于近空间飞行器姿态的控制仿真实验,结果表明所提出方法有效性.     

Iterative learning control design with high‐order internal model for discrete‐time nonlinear systems

In this paper, a high‐order internal model (HOIM)‐based iterative learning control (ILC) scheme is proposed for discrete‐time nonlinear systems to tackle the tracking problem under iteration‐varying desired trajectories. By incorporating the HOIM that is utilized to describe the variation of desired trajectories in the iteration domain into the ILC design, it is shown that the system output can converge to the desired trajectory along the iteration axis within arbitrarily small error. Furthermore, the learning property in the presence of state disturbances and output noise is discussed under HOIM‐based ILC with an integrator in the iteration axis. Two simulation examples are given to demonstrate the effectiveness of the proposed control method. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal higher order learning adaptive control approach for a class of SISO nonlinear systems

1IntroductionMany dynamic systems to be controlled have constant orslowly_varying uncertain parameters .Adaptive control is apopular approachtothe control ofsuchsystems [1] .Inthepast two decades ,significant progress has been made in theresearch and design of adaptive control systems [2,3] .Fairly complete and comprehensive guidelines are nowavailable for both design and implementation of adaptivecontrollers inthe cases where the systemunder control canbe adequately modeled as a linear dynami…     

Optimal higher order learning adaptive control approach for a class of SISO nonlinear systems

In this paper,an optimal higher order learning adaptive control approach is developed for a class of SISO nonlinear systems.This design is model-free and depends directly on pseudo-partial-derivatives derived on-line from the input and output information of the system.A novel weighted one-step-ahead control criterion function is proposed for the control law.The convergence analysis shows that the proposed control law can guarantee the convergence under the assumption that the desired output is a set point.Simulation examples are provided for nonlinear systems to illustrate the better performance of the higher order learning adaptive control.