Nonlinear adaptive robust backstepping force control of hydraulic load simulator: Theory and experiments

High performance robust force control of hydraulic load simulator with constant but unknown hydraulic parameters is considered. In contrast to the linear control based on hydraulic linearization equations, hydraulic inherent nonlinear properties and uncertainties make the conventional feedback proportional-integral-derivative (PID) control not yield to high performance requirements. Furthermore, the hydraulic system may be subjected to non-smooth and discontinuous nonlinearities due to the directional change of valve opening. In this paper, based on a nonlinear system model of hydraulic load simulator, a discontinuous projection-based nonlinear adaptive robust back-stepping controller is developed with servo valve dynamics. The proposed controller constructs a novel stable adaptive controller and adaptation laws with additional pressure dynamic related unknown parameters, which can compensate for the system nonlinearities and uncertain parameters, meanwhile a well-designed robust controller is also synthesized to dominate the model uncertainties coming from both parametric uncertainties and uncertain nonlinearities including unmodeled and ignored system dynamics. The controller theoretically guarantee a prescribed transient performance and final tracking accuracy in presence of both parametric uncertainties and uncertain nonlinearities; while achieving asymptotic output tracking in the absence of unstructured uncertainties. The implementation issues are also discussed for controller simplification. Some comparative results are obtained to verify the high-performance nature of the proposed controller.     

Robust adaptive precision motion control of hydraulic actuators with valve dead-zone compensation

This paper addresses the high performance motion control of hydraulic actuators with parametric uncertainties, unmodeled disturbances and unknown valve dead-zone. By constructing a smooth dead-zone inverse, a robust adaptive controller is proposed via backstepping method, in which adaptive law is synthesized to deal with parametric uncertainties and a continuous nonlinear robust control law to suppress unmodeled disturbances. Since the unknown dead-zone parameters can be estimated by adaptive law and then the effect of dead-zone can be compensated effectively via inverse operation, improved tracking performance can be expected. In addition, the disturbance upper bounds can also be updated online by adaptive laws, which increases the controller operability in practice. The Lyapunov based stability analysis shows that excellent asymptotic output tracking with zero steady-state error can be achieved by the developed controller even in the presence of unmodeled disturbance and unknown valve dead-zone. Finally, the proposed control strategy is experimentally tested on a servovalve controlled hydraulic actuation system subjected to an artificial valve dead-zone. Comparative experimental results are obtained to illustrate the effectiveness of the proposed control scheme.     

气动肌肉并联关节的位姿轨迹跟踪控制

针对多输入多输出的气动肌肉并联关节,建立包含任务空间负载动态方程、容腔压力动态方程和高速开关阀平均流量方程的多阶动态系统数学模型。为保证气动肌肉并联关节系统良好动态特性的同时具有高精度的位姿轨迹跟踪,采用基于非连续投影算法的自适应鲁棒控制策略。该策略通过自适应参数估计来消除因气动肌肉并联关节系统动态数学模型的参数未知而引起的较大参数不确定,通过鲁棒反馈来消除因气动肌肉的伸缩力模型误差、摩擦力时变和关节系统的不可知干扰等引起的严重非线性不确定,且控制器基于反推设计,对多输入多输出的多阶耦合动态系统具有很好的适用性。试验结果表明：所研究的气动肌肉并联关节阶跃响应的静态误差小于0.09°,连续轨迹跟踪的标准误差小于0.15°,且具有较强的自适应性和鲁棒性。     

非线性液压伺服系统的自适应控制

针对存在不确定参数的液压伺服系统,提出高性能位置跟踪控制器的设计方法。应用“反演”控制设计策略,给出了基于Lyapunov稳定的设计过程,其中系统负载、液压油缸及液压伺服阀的动力特性都包含于控制系统设计中。同时给出了基于液压系统不确定参数的自适应控制律,数值仿真表明了控制系统设计的正确性。     

Direct adaptive robust tracking control for 6 DOF industrial robot with enhanced accuracy

A direct adaptive robust tracking control is proposed for trajectory tracking of 6 DOF industrial robot in the presence of parametric uncertainties, external disturbances and uncertain nonlinearities. The controller is designed based on the dynamic characteristics in the working space of the end-effector of the 6 DOF robot. The controller includes robust control term and model compensation term that is developed directly based on the input reference or desired motion trajectory. A projection-type parametric adaptation law is also designed to compensate for parametric estimation errors for the adaptive robust control. The feasibility and effectiveness of the proposed direct adaptive robust control law and the associated projection-type parametric adaptation law have been comparatively evaluated based on two 6 DOF industrial robots. The test results demonstrate that the proposed control can be employed to better maintain the desired trajectory tracking even in the presence of large parametric uncertainties and external disturbances as compared with PD controller and nonlinear controller. The parametric estimates also eventually converge to the real values along with the convergence of tracking errors, which further validate the effectiveness of the proposed parametric adaption law.     

Adaptive robust motion trajectory tracking control of pneumatic cylinders with LuGre model-based friction compensation

Friction compensation is particularly important for motion trajectory tracking control of pneumatic cylinders at low speed movement. However, most of the existing model-based friction compensation schemes use simple classical models, which are not enough to address applications with high-accuracy position requirements. Furthermore, the friction force in the cylinder is time-varying, and there exist rather severe unmodelled dynamics and unknown disturbances in the pneumatic system. To deal with these problems effectively, an adaptive robust controller with LuGre model-based dynamic friction compensation is constructed. The proposed controller employs on-line recursive least squares estimation（RLSE） to reduce the extent of parametric uncertainties, and utilizes the sliding mode control method to attenuate the effects of parameter estimation errors, unmodelled dynamics and disturbances. In addition, in order to realize LuGre model-based friction compensation, the modified dual-observer structure for estimating immeasurable friction internal state is developed. Therefore, a prescribed motion tracking transient performance and final tracking accuracy can be guaranteed. Since the system model uncertainties are unmatched, the recursive backstepping design technology is applied. In order to solve the conflicts between the sliding mode control design and the adaptive control design, the projection mapping is used to condition the RLSE algorithm so that the parameter estimates are kept within a known bounded convex set. Finally, the proposed controller is tested for tracking sinusoidal trajectories and smooth square trajectory under different loads and sudden disturbance. The testing results demonstrate that the achievable performance of the proposed controller is excellent and is much better than most other studies in literature. Especially when a 0.5 Hz sinusoidal trajectory is tracked, the maximum tracking error is 0.96 mm and the average tracking error is 0.45 mm. This paper constructs an adaptive robust controller     

变刚度电液力负载模拟器自适应反步控制

某电液力负载模拟系统以钢丝绳为传递介质,其特性随钢丝绳刚度大范围变化而改变,针对定常控制策略难以实现其大范围控制难题,提出采用自适应反步控制策略。结合间接自适应方法和反步控制方法的优点,通过反步设计方法获得与系统模型参数直接相关的控制器,通过参数预估实时更新刚度值并修正控制器参数,从而补偿刚度变化对闭环控制系统性能的影响。仿真结果表明：在所设计的力加载范围内,该控制算法能够准确预估钢丝绳刚度值,可以实现变刚度电液力负载模拟系统大范围高精度控制,并且可以消除多余力对负载模拟精度的影响。     

Neural network adaptive position tracking control of underactuated autonomous surface vehicle

The present study investigates the position tracking control of the underactuated autonomous surface vehicle, which is subjected to parameters uncertainties and external disturbances. In this regard, the backstepping method, neural network, dynamic surface control and the sliding mode method are employed to design an adaptive robust controller. Moreover, a Lyapunov synthesis is utilized to verify the stability of the closed-loop control system. Following innovations are highlighted in this study: (i) The derivatives of the virtual control signals are obtained through the dynamic surface control, which overcomes the computational complexities of the conventional backstepping method. (ii) The designed controller can be easily applied in practical applications with no requirement to employ the neural network and state predictors to obtain model parameters. (iii) The prediction errors are combined with position tracking errors to construct the neural network updating laws, which improves the adaptation and the tracking performance. The simulation results demonstrate the effectiveness of the proposed position tracking controller.

     

Design of adaptive backstepping congestion controller for TCP networks with UDP flows based on minimax

The congestion control problem of TCP network systems with user datagram protocol (UDP) flows is investigated in this paper. A nonlinear TCP network model with strict-feedback structure is first established. The unknown UDP flow is regarded as the external disturbance, and the maximum UDP flow is calculated by using the minimax approach. And then, a congestion control algorithm is proposed by using the adaptive backstepping approach. Meanwhile, the adaptive law is employed to estimate the unknown link capacity. The design of the adaptive law is to introduce a parameter mapping mechanism to limit the parameter identification range to a specified interval, thereby improving the estimation efficiency of the parameters. Furthermore, a state-feedback congestion controller is presented to make sure that the output of the system tracks the desired queue. The simulation results show the superiority and feasibility of the proposed method.     

基于自适应反演的超细金刚线张力控制系统

针对多线切割机张力控制系统存在库仑摩擦和摆角耦合等较强非线性特征,以及收放卷轮直径变化引起的参数不确定问题,提出了一种基于自适应反演的非线性补偿控制方法。该方法结合实验辨识和自适应参数控制器设计方法分别对多线切割机的多轴电机同步运动控制系统和不确定系统参数进行简化分析和在线估计,使用李雅普诺夫稳定性理论保证了系统全局渐近稳定性以及系统状态的有界性。仿真和实验结果表明,所设计的自适应控制器可以实现多轴同步运动,并将张力摆角控制在较小的范围内,获得更高的张力控制精度。     

基于Backstepping的电液伺服系统多级自适应滑模控制

针对电液伺服系统的非线性特性、系统参数及外部负载的非匹配不确定性,在电液伺服系统的位置跟踪控制中,提出了基于Backstepping逆向递推技术的多级自适应滑模控制方法,应用Backstepping的逆向递推方法有效地解决了高阶系统的控制问题,并结合了自适应方法和滑模控制方法各自优良的抗干扰特点。仿真结果显示,该控制方法具有较强的鲁棒性及良好的跟踪性能。     

Adaptive integral LOS path following for an unmanned airship with uncertainties based on robust RBFNN backstepping

This paper investigates the path following control problem for an unmanned airship in the presence of unknown wind and uncertainties. The backstepping technique augmented by a robust adaptive radial basis function neural network (RBFNN) is employed as the main control framework. Based on the horizontal dynamic model of the airship, an improved adaptive integral line-of-sight (LOS) guidance law is first proposed, which suits any parametric paths. The guidance law calculates the desired yaw angle and estimates the wind. Then the controller is extended to cope with the airship yaw tracking and velocity control by resorting to the augmented backstepping technique. The uncertainties of the dynamics are compensated by using the robust RBFNNs. Each robust RBFNN utilizes an nth-order smooth switching function to combine a conventional RBFNN with a robust control. The conventional RBFNN dominates in the neural active region, while the robust control retrieves the transient outside the active region, so that the stability range can be widened. Stability analysis shows that the controlled closed-loop system is globally uniformly ultimately bounded. Simulations are provided to validate the effectiveness of the proposed control approach.     

Spatial curvilinear path following control of underactuated AUV with multiple uncertainties

This paper investigates the problem of spatial curvilinear path following control of underactuated autonomous underwater vehicles (AUVs) with multiple uncertainties. Firstly, in order to design the appropriate controller, path following error dynamics model is constructed in a moving Serret–Frenet frame, and the five degrees of freedom (DOFs) dynamic model with multiple uncertainties is established. Secondly, the proposed control law is separated into kinematic controller and dynamic controller via back-stepping technique. In the case of kinematic controller, to overcome the drawback of dependence on the accurate vehicle model that are present in a number of path following control strategies described in the literature, the unknown side-slip angular velocity and attack angular velocity are treated as uncertainties. Whereas in the case of dynamic controller, the model parameters perturbations, unknown external environmental disturbances and the nonlinear hydrodynamic damping terms are treated as lumped uncertainties. Both kinematic and dynamic uncertainties are estimated and compensated by designed reduced-order linear extended state observes (LESOs). Thirdly, feedback linearization (FL) based control law is implemented for the control model using the estimates generated by reduced-order LESOs. For handling the problem of computational complexity inherent in the conventional back-stepping method, nonlinear tracking differentiators (NTDs) are applied to construct derivatives of the virtual control commands. Finally, the closed loop stability for the overall system is established. Simulation and comparative analysis demonstrate that the proposed controller exhibits enhanced performance in the presence of internal parameter variations, external unknown disturbances, unmodeled nonlinear damping terms, and measurement noises.     

6 DOF synchronized control for spacecraft formation flying with input constraint and parameter uncertainties

This paper treats the problem of synchronized control of spacecraft formation flying (SFF) in the presence of input constraint and parameter uncertainties. More specifically, backstepping based robust control is first developed for the total 6 DOF dynamic model of SFF with parameter uncertainties, in which the model consists of relative translation and attitude rotation. Then this controller is redesigned to deal with the input constraint problem by incorporating a command filter such that the generated control could be implementable even under physical or operating constraints on the control input. The convergence of the proposed control algorithms is proved by the Lyapunov stability theorem. Compared with conventional methods, illustrative simulations of spacecraft formation flying are conducted to verify the effectiveness of the proposed approach to achieve the spacecraft track the desired attitude and position trajectories in a synchronized fashion even in the presence of uncertainties, external disturbances and control saturation constraint.     

Adaptive backstepping sliding mode control of flexible ball screw drives with time-varying parametric uncertainties and disturbances

This paper presents a method to model and design servo controllers for flexible ball screw drives with dynamic variations. A mathematical model describing the structural flexibility of the ball screw drive containing time-varying uncertainties and disturbances with unknown bounds is proposed. A mode-compensating adaptive backstepping sliding mode controller is designed to suppress the vibration. The time-varying uncertainties and disturbances represented in finite-term Fourier series can be estimated by updating the Fourier coefficients through function approximation technique. Adaptive laws are obtained from Lyapunov approach to guarantee the convergence and stability of the closed loop system. The simulation results indicate that the tracking accuracy is improved considerably with the proposed scheme when the time-varying parametric uncertainties and disturbances exist.     

Adaptive backstepping-based tracking control design for nonlinear active suspension system with parameter uncertainties and safety constraints

This paper proposes a novel constraint adaptive backstepping based tracking controller for nonlinear active suspension system with parameter uncertainties and safety constraints. By introducing the virtual control input and reference trajectories, the adaptive control law is developed to stabilize both of the vertical and pitch motions of vehicle body using backstepping technique and Lyapunov stability theory, and further to track the predefined reference trajectories within a finite time, which not only ensure the safety performance requirements, but also achieve improvements in riding comfort and handling stability of vehicle active suspension system. Next, the stability analysis on zero dynamics error system is conducted to ensure that all the safety performance indicators are all bounded and the corresponding upper bounds are estimable. Finally, a numerical simulation is provided to verify the effectiveness of the proposed controller and to address the comparability between the classical Barrier–Lyapunov Function based adaptive tracking controller and the proposed controller.     

基于NDO的ROV滤波反步轨迹跟踪控制

针对作业型遥控水下机器人(ROV)在轨迹跟踪过程中存在模型非线性、强耦合、模型参数不确定和外界干扰不确定等问题,提出一种基于非线性干扰观测器(NDO)的滤波自适应反步控制策略。使用NDO观测模型的不确定性和外界干扰,通过指令滤波器避免了直接对虚拟控制量解析求导的过程,利用自适应律补偿观测器观测残量。通过Lyapunov稳定性理论证明了跟踪误差系统的渐进稳定。仿真实验表明,设计的控制器能够实现精确的轨迹跟踪,具有较好的鲁棒特性。     

Anti-disturbance backstepping control for air-breathing hypersonic vehicles based on extended state observer

In this paper, we propose an anti-disturbance backstepping control approach with extended state observer (ESO) for tracking control of air-breathing hypersonic vehicles. Considering the large uncertainties, the external disturbances, and especially the lack of aerodynamic knowledge, several ESOs are introduced in the backstepping controller. With the total disturbance estimation ability of ESOs, almost no aerodynamic knowledge is needed for the controller design. Meanwhile, ESOs are also used to estimate the derivatives of the virtual control signals. The problem of “explosion of terms” is avoided. A key strategy of the controller is that each step of backstepping is activated successively. Consequently, the closed-loop system has time-scale structure. Rigorous stability proof can be obtained. At last, compared simulation results verify the superior tracking performance of the proposed controller.     

Intelligent fractional-order backstepping control for an ironless linear synchronous motor with uncertain nonlinear dynamics

This study aims to develop an intelligent fractional-order backstepping controller to control the mover position of an ironless permanent magnet linear synchronous motor. First, we investigated the operating principle and dynamic modeling of the linear synchronous motor based on the field-oriented control method. Next, to improve the convergence speed and control accuracy of the conventional backstepping controller, we designed a fractional-order backstepping controller that has more degrees of freedom in the control parameters. However, designing the switching control gain is difficult owing to the unknown degree of uncertainty. To address this problem, we proposed an intelligent fractional-order backstepping controller to further enhance the adaptiveness and robustness of the fractional-order backstepping controller. In this intelligent controller, we proposed a Hermite-polynomial-based functional-link fuzzy neural network as an uncertainty estimator that can directly estimate system uncertainty, thereby improving the disturbance rejection ability and requiring no uncertainty bound information. Additionally, to compensate for the estimation error introduced by the estimator, we designed an exponential compensator that employs a smooth exponential self-regulation mechanism. We utilized the Lyapunov theorem to derive estimation laws for the online tuning of the control parameters. Experimental results demonstrate the effectiveness and high positioning performance of the proposed intelligent fractional-order backstepping controller in comparison with the backstepping controller and fractional-order backstepping controller in the linear synchronous motor control system.     

电液马达伺服系统积分鲁棒自适应高精度位置控制

电液马达伺服系统中存在各种类型的扰动,包括参数不确定性和不确定非线性,制约着其高精度位置控制。针对电液马达伺服系统高精度位置跟踪控制,考虑系统的黏性摩擦特性以及外干扰等建模不确定性,提出了一种基于鲁棒自适应的电液马达伺服系统高精度位置控制策略。所提出的全状态控制器通过自适应对模型不确定性进行估计及前馈补偿,提高了系统的低速伺服性能;通过自适应对未建模干扰等不确定性的上界进行估计并前馈补偿,提高了系统对外干扰的鲁棒性。所设计的闭环控制器还能保证系统获得渐近跟踪性能,对比仿真验证了其可行性。