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.     

Adaptive robust boundary control of coupled bending‐torsional vibration of beams with only one axis of symmetry

In control design for vibration of beams in literature, the beam section is considered to have two axes of symmetry so that the bending and torsional vibrations are uncoupled; thus, the bending vibration is controlled independently without twisting the beam. However, if the cross section of a beam has only one axis of symmetry, the bending and torsional vibrations become coupled and the beam will undergo twisting in addition to bending. This paper addresses Lyapunov‐based boundary control of coupled bending‐torsional vibration of beams with only one axis of symmetry. The control strategy is based on applying a transverse force and a torque at the free end of the beam. The control design is directly based on the system partial differential equations (PDEs) so that spillover instabilities that are a result of model truncation are avoided. Three cases are investigated. Firstly, it is shown that when exogenous disturbances do not affect the beam, a linear boundary control law can exponentially stabilize the coupled bending‐torsional vibration. Secondly, a nonlinear robust boundary control is established that exponentially stabilizes the beam in the presence of boundary and spatially distributed disturbances. Thirdly, to rule out the need for prior knowledge of disturbances upper‐bound, the proposed robust control is redesigned to achieve an adaptive robust control that stabilizes the beam in the presence of disturbances with unknown upper‐bound. The efficacy of the proposed controls is illustrated by simulation results. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive robust control of a class of dynamic delay systems with unknown uncertainty bounds

In this paper, a robust adaptive controller is developed for a class of uncertain dynamic systems with time‐varying delays and subject to uncertainties whose bounds are unknown but their functional properties are known. It is shown that if a constraint on the norm of the matrix associated with the delayed state is met, then the adaptive controller designed guarantees that all solutions of the class of systems considered converge to a ball with any prespecified exponential convergence rate towards it. Finally, an example is included to illustrate the results developed in this paper. Copyright © 2001 John Wiley & Sons, Ltd.     

The robust adaptive control of chaotic systems with unknown parameters and external disturbance via a scalar input

This paper investigates the control of chaotic systems in the presence of unknown parameters, model uncertainties, and external disturbance. We first discuss the control of a class of chaotic systems and then investigate the control of general chaotic systems. Based on the adaptive control scheme, some novel criteria are proposed via a backstepping‐like procedure. As an example, the control of the Zhang hyperchaotic system is investigated via a single input. Some numerical simulations are given to demonstrate the robustness and efficiency of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.     

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 dynamic surface control with composite adaptation laws

This paper focuses on an adaptive robust dynamic surface control (ARDSC) with composite adaptation laws (CAL) for a class of uncertain nonlinear systems in semi‐strict feedback form. A simple and effective controller has been obtained by introducing dynamic surface control (DSC) technique and designing novel adaptation laws. First, the ‘explosion of terms’ problem caused by backstepping method in the traditional adaptive robust control (ARC) is avoided. Meanwhile, through a new proof philosophy the asymptotical output tracking that the ARC possesses is theoretically preserved. Second, when persistent excitation (PE) condition satisfies, true parameter estimates could be acquired via designing CALs which integrate the information of estimation errors. Finally, simulation results are presented to illustrate the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive control of Burgers' equation with unknown viscosity

In this paper, we propose a fortified boundary control law and an adaptation law for Burgers' equation with unknown viscosity, where no a priori knowledge of a lower bound on viscosity is needed. This control law is decentralized, i.e., implementable without the need for central computer and wiring. Using the Lyapunov method, we prove that the closed‐loop system, including the parameter estimator as a dynamic component, is globally H¹ stable and well posed. Furthermore, we show that the state of the system is regulated to zero by developing an alternative to Barbalat's Lemma which cannot be used in the present situation. Copyright © 2001 John Wiley & Sons, Ltd.     

风力发电系统最大功率跟踪自适应鲁棒控制

为了提高风力发电系统最大功率跟踪(MPPT)运行的工作性能,针对系统未知建模误差和外部扰动等不确定问题,提出了一种MPPT自适应鲁棒控制方法。该方法建立在基于广义扰动的风力发电系统角速度跟踪动态模型基础上,不依赖于系统模型参数和外部扰动辨识。利用MPPT跟踪偏差的非线性状态反馈和扰动边界值的在线实时估计,自适应地调整切换控制项增益,以加快系统收敛的速度。实际控制律经过一阶积分输出,进一步削弱控制输出信号幅值的抖振,平滑发电转矩,提高跟踪精度。通过构造Lyapunov函数,验证了闭环系统的全局稳定性。通过与常规线性PID控制和非线性动态状态反馈控制(SFC)进行仿真比较,验证了该控制器实现最大功率跟踪控制的良好效果,具有较强的鲁棒性和自适应性。     

Adaptive prescribed performance control of nonlinear systems with unknown dead zone

An alternative adaptive control with prescribed performance is proposed to address the output tracking of nonlinear systems with a nonlinear dead zone input. An appropriate function that characterizes the convergence rate, maximum overshoot, and steady‐state error is adopted and incorporated into an output error transformation, and thus the stabilization of the transformed system is sufficient to achieve original tracking control with prescribed performance. The nonlinear dead zone is represented as a time‐varying system and Nussbaum‐type functions are utilized to deal with the unknown control gain dynamics. A novel high‐order neural network with a scalar adaptive weight is developed to approximate unknown nonlinearities, thus the computational costs can be diminished dramatically. Some restrictive assumptions on the system dynamics and the dead‐zone are circumvented. Simulations are included to validate the effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive robust control of a class of nonlinear systems in semi‐strict feedback form with non‐uniformly detectable unmeasured internal states

This paper proposes a novel control method for a special class of nonlinear systems in semi‐strict feedback form. The main characteristic of this class of systems is that the unmeasured internal states are non‐uniformly detectable, which means that no observer for these states can be designed to make the observation error exponentially converge to zero. In view of this, a projection‐based adaptive robust control law is developed in this paper for this kind of system. This method uses a projection‐type adaptation algorithm for the estimation of both the unknown parameters and the internal states. Robust feedback term is synthesized to make the system robust to uncertain nonlinearities and disturbances. Although the estimation error for both the unknown parameters and the internal states may not converge to zero, the tracking error of the closed‐loop system is proved to converge to zero asymptotically if the system has only parametric uncertainties. Furthermore, it is theoretically proved that all the signals are bounded, and the control algorithm is robust to bounded disturbances and uncertain nonlinearities with guaranteed output tracking transient performance and steady‐state accuracy in general. The class of system considered here has wide engineering applications, and a practical example—control of mechanical systems with dynamic friction—is used as a case study. Simulation results are obtained to demonstrate the applicability of the proposed control methodology. Copyright © 2010 John Wiley & Sons, Ltd.     

带有逆向力补偿的Stewart平台自适应鲁棒控制

针对Stewart平台复杂的动力学特性以及参数不确定性,提出了带有逆向力补偿自适应鲁棒控制方法.依据对平台动力学特性的分析,采用Lagrange方法建立了上平台的前向动力学模型,同时利用Newton-Euler法对六连杆部分的动态特性进行逆向力补偿,得到了具有机械系统物理特征,且形式简单的误差动态系统.针对上平台参数摄动、逆向力补偿残量以及未建模动态等各种不确定性,依据耗散性理论设计自适应鲁棒控制器.由于平台动力学方程中形式最为复杂的六连杆动态特性被有效地加以补偿,从而控制器中动力学计算部分得以简化.平台动力学方程中上平台部分物理特征明显,可以方便地构造出合适的李雅普诺夫函数.仿真结果验证了该方法的有效性和分析的正确性.     

Adaptive control of systems with unknown non-smooth non-linearities

In this paper we unify our recent results in adaptive control of systems with unknown non-smooth non-linearities such as dead-zone, backlash and hysteresis characteristics at the input or output of a linear dynamics. Our adaptive inverse approach employs an adaptive controller structure consisting of an adaptive inverse for cancelling the effect of an unknown non-linearity and a fixed (or adaptive) linear control law for a known (or unknown) linear dynamics. Despite the bilinear dependence on the unknown parameters, a linearly parametrized error system is constructed which enables us to design robust adaptive laws for updating the controller parameters to ensure closed loop signal boundedness and improve system tracking performance. © 1997 by John Wiley & Sons, Ltd.     

Adaptive neural dynamic surface control of MIMO stochastic nonlinear systems with unknown control directions

In this paper, an adaptive neural output‐feedback control approach is considered for a class of uncertain multi‐input and multi‐output (MIMO) stochastic nonlinear systems with unknown control directions. Neural networks (NNs) are applied to approximate unknown nonlinearities, and K‐filter observer is designed to estimate unavailable system's states. Due to utilization of Nussbaum gain function technique in the proposed approach, the singularity problem and requirement to prior knowledge about signs of high‐frequency gains are removed, simultaneously. Razumikhin functional method is employed to deal with unknown state time‐varying delays, so that the offered control approach is free of common assumptions on derivative of time‐varying delays. Also, an adaptive neural dynamic surface control is developed; hence, explosion of complexity in conventional backstepping method is eliminated, effectively. The boundedness of all the resulting closed‐loop signals is guaranteed in probability; meanwhile, convergence of the tracking errors to adjustable compact set in the sense of mean quartic value is also proved. Finally, simulation results are shown to verify and clarify efficiency of the offered approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive fault-tolerant tracking control for nonlinear systems with unknown control coefficient and input saturation

In this article, the tracking control problem is investigated for a class of nonlinear systems in the presence of unknown disturbance, input saturation, actuator fault, and unknown control coefficient. A novel disturbance observer-based adaptive fault-tolerant tracking control strategy is proposed with regard to nonlinear systems. Based on the Gaussian error function, the auxiliary dynamic system is designed to offset effects caused by the input saturation. Moreover, the Nussbaum-type function is employed to avert control singularity and deal with the unknown control coefficient. A theoretical analysis indicates that the boundedness of all signals in the closed-loop system can be guaranteed. Finally, two examples with one concerning the dynamic point-the-bit rotary steerable drilling tool system are given to confirm the validity of the method.     

一类非线性系统模糊自适应鲁棒控制

针对一类不确定性非线性系统的传统模糊自适应控制方案存在的缺陷,利用第一类模糊逻辑系统直接作为非线性系统控制器,提出了一种模糊自适应鲁棒控制策略.在传统方案的基础上加入鲁棒补偿项,取消监督控制项,进一步放宽稳定条件到最小近似误差有界,利用Lyapunov稳定性理论证明了系统的全局稳定性.通过对二阶混沌对象仿真结果表明,鲁棒控制有效地补偿了稳态误差,解决了单一模糊自适应控制寻优空间有限问题.     

一类机器人系统的非线性鲁棒控制

分析了一类具有完全非线性特性的不确定机器人系统,基于非线性设计方法,给出了该类机器人系统鲁棒指数稳定化的非线性控制方案。仿真实例说明了结论的有效性和可行性。     

多机电力系统自适应鲁棒Terminal滑模励磁控制

设计了多机电力系统发电机励磁的自适应鲁棒Terminal滑模控制器,将L2增益干扰抑制、自适应逆推法、Terminal滑模控制相结合,可以自适应估计发电机的不确定阻尼系数,对扰动具有鲁棒性。给出了控制器的设计过程。针对2区域4机系统的仿真结果表明,所设计的自适应鲁棒Terminal滑模励磁控制器能够快速抑制功率振荡,有效提高电力系统的暂态稳定性,并保持机端电压的恒定。     

Robust adaptive constrained boundary control for a suspension cable system of a helicopter

In this article, the problems of modeling and controlling are investigated for a suspension cable system of a helicopter with input saturation, system parameter uncertainties, and external disturbances by using the boundary control method. In accordance with the Hamilton's principle, the model of the suspension cable system of a helicopter is established by using a set of partial differential and ordinary differential equations. Considering nonsymmetric saturation constraint, the auxiliary systems are designed to handle with the effect of input saturation. Considering Lyapunov's direct method and the designed auxiliary systems, two robust adaptive boundary controllers are provided by the actuators at the helicopter and the box. Under the proposed controllers, the error between the bottom payload and the target location and the vibration range are uniformly ultimately bounded. Moreover, they will converge to a small neighborhood of zero by selecting the suitable parameters. Meanwhile, to guarantee the validity of the proposed adaptive boundary control laws, some sufficient conditions are raised. Simulation results are provided to verify that the effectiveness of the designed controllers in this paper.     

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     

Adaptive output feedback control for a class of nonlinear systems with unknown virtual control coefficients signs

This paper presents a global output-feedback control scheme for a class of nonlinear systems that are transformed via a parameter-independent change of co-ordinates into a form in which there exist three kinds of unknown parameters: one is the unknown virtual control coefficients, one is the unknown parameters that multiply output nonlinearities and the other kind is the unknown parameters that multiply affine functions of the derivative of the measured output with coefficients that are smooth nonlinear functions of the measured output. We use two parameter-dependent changes of co-ordinates to transform the system considered into parametric output-feedback form. One transformation is used to eliminate the difficulty in dealing with unknown virtual control coefficients and the other transformation is used to remove the nonlinearities which are affine functions of the derivative of the measured output with coefficients that are smooth nonlinear functions of the measured output. Then the scheme presented by Ye (IEEE Trans. Automat. Control 2001; 46 :112–115) can be applied to the new system. Global results can be obtained for the overall closed-loop systems without any constraints on the nonlinear terms. Copyright © 2006 John Wiley & Sons, Ltd.