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.     

Inverse optimal sliding mode control of spacecraft with coupled translation and attitude dynamics

This paper proposes two robust inverse optimal control schemes for spacecraft with coupled translation and attitude dynamics in the presence of external disturbances. For the first controller, an inverse optimal control law is designed based on Sontag-type formula and the control Lyapunov function. Then a robust inverse optimal position and attitude controller is designed by using a new second-order integral sliding mode control method to combine a sliding mode control with the derived inverse optimal control. The global asymptotic stability of the proposed control law is proved by using the second method of Lyapunov. For the other control law, a nonlinear H_∞ inverse optimal controller for spacecraft position and attitude tracking motion is developed to achieve the design conditions of controller gains that the control law becomes suboptimal H_∞ state feedback control. The ultimate boundedness of system state is proved by using the Lyapunov stability theory. Both developed robust inverse optimal controllers can minimise a performance index and ensure the stability of the closed-loop system and external disturbance attenuation. An example of position and attitude tracking manoeuvres is presented and simulation results are included to show the performance of the proposed controllers.     

空间三关节机器人模糊积分滑模控制

研究提高关节机器人轨迹跟踪控制的性能,由于关节机器人运动中产生振动,影响系统的稳定性能。为解决上述问题,提出了一种反馈线性化的自适应模糊积分滑模控制方法。在上述方法的基础上,对机器人非线性动力学模型反馈线性化。为了进一步提高滑模控制的精度,设计了一种积分滑模面的滑模控制器,可以减弱积分滑模控制的抖振。通过设计一个模糊控制器,根据积分滑模面的大小自适应地调节积分滑模控制的切换部分,达到削弱抖振的目的。利用李亚普诺夫定理证明了控制系统的稳定性。仿真结果表明,改进方法有效地提高了关节机器人跟踪控制性能。     

Nonlinear robust sliding mode control of a quadrotor unmanned aerial vehicle based on immersion and invariance method

We present an asymptotic tracking controller for an underactuated quadrotor unmanned aerial vehicle using the sliding mode control method and immersion and invariance based adaptive control strategy in this paper. The control system is divided into two loops: the inner‐loop for the attitude control and the outer‐loop for the position. The sliding mode control technology is applied in the inner‐loop to compensate the unmatched nonlinear disturbances, and the immersion and invariance approach is chosen for the outer‐loop to address the parametric uncertainties. The asymptotic tracking of the position and the yaw motion is proven with the Lyapunov based stability analysis and LaSalle's invariance theorem. Real‐time experiment results performed on a hardware‐in‐the‐loop‐simulation testbed are presented to validate the good control performance of the proposed scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Model reference adaptive impedance control in Cartesian coordinates for physical human–robot interaction

In this paper, a nonlinear model reference adaptive impedance controller is proposed and tested. The controller provides asymptotic tracking of a reference impedance model for the robot end-effector in Cartesian coordinates applicable to rehabilitation robotics or any other human–robot interactions such as haptic systems. The controller uses the parameters of a desired stable reference model which is the target impedance for the robot’s end-effector. It also considers uncertainties in the model parameters of the robot. The asymptotic tracking is proven using Lyapunov stability theorem. Moreover, the adaptation law is proposed in joint space for reducing the complexity of its calculations; however, the controller and the stability proof are all presented in Cartesian coordinates. Using simulations and experiments on a two DOFs robot, the effectiveness of the proposed controller is investigated.     

A new continuous high‐gain controller scheme for a class of uncertain nonlinear systems

In this study, we present a new robust continuous controller mechanism for the tracking problem of uncertain nonlinear systems. The proposed strategy is based on a Lyapunov‐type stability argument and only requires the uncertainties of the dynamical system to be the first‐order differentiable to achieve asymptotic practical tracking. For the ease of presentation, the controller formulation is presented on a general, second‐order dynamical system, extension to higher order versions are also possible with a considerably small effort. Simulation studies comparing the performance of the proposed method with the classical Sliding mode and robust integral of the sign of the error controller are presented to illustrate the performance and the feasibility of the proposed strategy. Experimental validation on a two link direct drive robot manipulator are also included to illustrate the implementability of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

基于光滑二阶滑模的可重复使用运载器有限时间再入姿态控制

针对可重复使用运载器(reusable launch vehicle,RLV)的六自由度再入模型,考虑模型不确定和外界干扰对再入姿态控制的影响,提出了一种非线性鲁棒控制策略.首先,根据多时间尺度特性将RLV的再入姿态模型分为姿态角子系统和姿态角速率子系统.其次,对每个子系统分别设计光滑二阶滑模控制器和滑模干扰观测器实现子系统的有限时间稳定.利用干扰观测器可以实现对不确定和外界干扰的精确估计,从而对控制器进行有效的补偿.进而,基于Lyapunov理论证明了整个系统的有限时间稳定.最后,通过仿真验证了提出的控制策略具有良好的控制性能和鲁棒性.     

Finite‐Time Sliding Mode Trajectory Tracking Control of Uncertain Mechanical Systems

The problem of finite‐time tracking control is studied for uncertain nonlinear mechanical systems. To achieve finite‐time convergence of tracking errors, a simple linear sliding surface based on polynomial reference trajectory is proposed to enable the trajectory tracking errors to converge to zero in a finite time, which is assigned arbitrarily in advance. The sliding mode control technique is employed in the development of the finite‐time controller to guarantee the excellent robustness of the closed‐loop system. The proposed sliding mode scheme eliminates the reaching phase problem, so that the closed‐loop system always holds the invariance property to parametric uncertainties and external disturbances. Lyapunov stability analysis is performed to show the global finite‐time convergence of the tracking errors. A numerical example of a rigid spacecraft attitude tracking problem demonstrates the effectiveness of the proposed controller.     

非完整移动机器人的神经网络鲁棒自适应控制

在非完整移动机器人轨迹跟踪问题中,针对机器人运动学与动力学模型的参数和非参数不确定性,提出了一种混合神经网络鲁棒自适应轨迹跟踪控制器,该控制器由运动学控制器和动力学控制器两部分组成;其中,采用了参数自适应的径向基神经网络对运动学模型的未知部分进行了建模,并采用权值在线调整的单层神经网络和自适应鲁棒控制项构成了动力学控制器;基于Lyapunov方法的设计过程保证了系统的稳定性和收敛性,仿真结果证明了算法的有效性。     

Robust attitude tracking control of flexible spacecraft for achieving globally asymptotic stability

The three‐axis attitude tracking control problem in the presence of parameter uncertainties and external disturbances for a spacecraft with flexible appendages is investigated in this paper. Novel simple robust Lyapunov‐based controllers that require only the attitude and angular velocity measurement are proposed. The first controller is a discontinuous one composed of a nonlinear PD part plus a sign function, whereas the second one is continuous or even smooth by modifying the discontinuous part of the first one. For a general desired trajectory, both controllers can achieve globally asymptotic stability of the attitude and angular velocity tracking errors instead of ultimate boundedness. By using a two‐step proof technique, the partial stability of the proposed controllers for the resulting closed‐loop systems in the face of model uncertainties and unexpected disturbances is proven theoretically. To further enhance the control performance, a continuous controller is presented that utilizes the tracking errors for estimating the external disturbances. In addition, stability analysis is done. For all the developed controllers, numerical simulation results are provided to demonstrate their performance. Copyright © 2008 John Wiley & Sons, Ltd.