BACKSTEPPING-BASED HYBRID ADAPTIVE CONTROL OF ROBOT MANIPULATORS INCORPORATING ACTUATOR DYNAMICS

By using the integrator backstepping technique, the control of rigid link, electrically driven robot manipulators is addressed in the presence of arbitrary uncertain manipulator inertia parameters and actuator parameters. The control scheme developed is computationally simple owing to the avoidance of the derivative computation of the regressor matrix. Semiglobal asymptotic stability of the controller is established in the Lyapunov sense. Simulation results are included to demonstrate the tracking performance. © 1997 by John Wiley & Sons, Ltd.     

Adaptive tracking control design of constrained robot systems

Both dynamic state feedback as well as output feedback tracking control designs are presented in this paper for constrained robot systems under parametric uncertainties and external disturbances. The previous studies on tracking control design, not considering the velocity measurements, address only the unconstrained robot design. In contrast, a dynamic output feedback controller based on a linear and reduced-order observer that uses only position measurements is proposed here for the first time to treat the trajectory tracking control problem of constrained robot systems. Both adaptive state feedback control schemes and adaptive output feedback control schemes with a guaranteed H^∞ performance are constructed. It is shown that all the variables of the closed-loop system are bounded and a pre-assigned H^∞ tracking performance is achieved, in the sense that the influence of external disturbance on the tracking motion error can be attenuated to any specified level. Moreover, it is also shown that the motion and force trajectories asymptotically converge to the desired ones as the dynamic model of robot systems is well-known and the external disturbance is neglected. Finally, simulation examples are presented to illustrate the tracking performance of a two-link robotic manipulator with a circular path constraint by the proposed control algorithms. © 1998 John Wiley & Sons, Ltd.     

新型随动系统的非线性控制和综合方法及实验验证

提出了一种新的电动机随动系统的非线性控制和综合方法.通过引进逆步式设计方法和流程,作者提出了新的随动系统非线性控制的算法和解析解,并且推证了系统的指数式稳定性.进而,作者将非线性控制算法和解析解演化为新的非线性控制系统结构图.在通过数字仿真验证了理论推导后,作者用了单片DSP(TMS320C32)来实现新的电动机随动系统的非线性数字控制.实验和仿真结果验证了新的控制结构和综合方法可以提高随动控制系统的外环频带宽度,减少对于斜坡给定信号的跟踪误差,和提高抗负荷干扰的性能.     

Online data‐driven composite adaptive backstepping control with exact differentiators

This paper presents an online data‐driven composite adaptive backstepping control for a class of parametric strict‐feedback nonlinear systems with mismatched uncertainties, where both tracking errors and prediction errors are utilized to update parametric estimates. Hybrid exact differentiators are applied to obtain the derivatives of virtual control inputs such that the complexity problem of integrator backstepping can be avoided. Closed‐loop tracking error equations are integrated in a moving‐time window to generate prediction errors such that online recorded data can be utilized to improve parameter adaptation. Semiglobal asymptotic stability of the closed‐loop system is rigorously established by the time‐scales separation and Lyapunov synthesis. The proposed composite adaptation can not only avoid the application of identification models and linear filters resulting in a simpler control structure, but also suppress parametric uncertainties and external perturbations via the time‐interval integral. Simulation results have demonstrated that the proposed approach possesses superior control performances under both noise‐free and noisy‐measurement environments. Copyright © 2015 John Wiley & Sons, Ltd.     

Output‐feedback adaptive tracking control of stochastic nonlinear systems using multi‐dimensional Taylor network

In this paper, an adaptive multi‐dimensional Taylor network (MTN) control scheme based on the backstepping and dynamic surface control (DSC) is developed to solve the tracking control problem for the stochastic nonlinear system with immeasurable states. The MTNs are used to approximate the unknown nonlinearities, and then based on the multivariable analog of circle criterion, an observer is first introduced to estimate the immeasurable states. By combining the adaptive backstepping technique and the DSC technique, an adaptive MTN output‐feedback backstepping DSC approach is developed. It is shown that the proposed controller ensures that all signals of the closed‐loop system are remain bounded in probability, and the tracking error converges to an arbitrarily small neighborhood around the origin in the sense of probability. Finally, the effectiveness of the design approach is illustrated by simulation results.     

Adaptive fuzzy output feedback backstepping control of pure‐feedback nonlinear systems via dynamic surface control technique

In this paper, an adaptive fuzzy backstepping dynamic surface control approach is considered for a class of uncertain pure‐feedback nonlinear systems with immeasurable states. Fuzzy logic systems are first employed to approximate the unknown nonlinear functions, and then an adaptive fuzzy state observer is designed to estimate the immeasurable states. By the combination of the adaptive backstepping design with a dynamic surface control technique, an adaptive fuzzy output feedback backstepping control approach is developed. It is proven that all the signals of the resulting closed‐loop system are semi‐globally uniformly ultimately bounded, and the observer and tracking errors converge to a small neighborhood of the origin by choosing the design parameters appropriately. Simulation examples are provided to show the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Unifying adaptive control with the nonlinear PI methodology: Designs for unknown strict‐feedback nonlinear systems with nonsmooth actuator nonlinearities

In this paper, we extend the nonlinear PI control methodology within an adaptive control framework. An adaptive nonlinear PI controller is proposed for output tracking of strict‐feedback nonlinear systems with nonsmooth actuator nonlinearities and unknown control directions. The current approach relaxes the standard assumption of known bounds for the associated system nonlinearities made in earlier nonlinear PI schemes. New theoretical boundedness results have been proved that enable the successful combination of backstepping and linear parametric approximators with the nonlinear PI approach and ensure semiglobal approximate tracking of the output to some reference trajectory. Following recent extensions of the nonlinear PI method to strict‐feedback systems, the intermediate virtual control laws are derived through suitable integral equations. Simulation results are also presented in this paper that verify our theoretical analysis.     

Nonlinear control of interior permanent-magnet synchronous motor

This paper presents a novel speed control technique for an interior permanent-magnet synchronous motor (IPMSM) drive based on newly developed adaptive backstepping technique. The proposed stabilizing feedback law for the IPMSM drive is shown to be globally asymptotically stable in the context of Lyapunov theory. The adaptive backstepping technique takes system nonlinearities into account in the control system design stage. The detailed derivations of the control laws have been given for controller design. The complete IPMSM drive incorporating the proposed backstepping control technique has been successfully implemented in real-time using digital signal processor board DS1102 for a laboratory 1-hp motor. The performance of the proposed drive is investigated both in experiment and simulation at different operating conditions. It is found that the proposed control technique provides a good speed tracking performance for the IPMSM drive ensuring the global stability.     

基于dSPACE PMSM伺服控制器自适应反步法设计

针对永磁同步电机(Permanent Mmagnet Synchronous Motor，PMSM)绕组相电流和转速强耦合特性和参数的不确定性，利用非线性Backstepping方法设计了自适应积分反步控制器，在补偿参数不确定性影响的同时实现PMSM高性能位置跟踪控制。借助于dSPACE平台，将系统模型下载到实时硬件中进行在线仿真。实时在线仿真结果表明，设计的PMSM控制系统可以获得满意的跟踪效果，其滤波跟踪误差迅速以指数特性收敛到零，具有较好的位置伺服控制特性。     

Adaptive backstepping repetitive learning control design for nonlinear discrete‐time systems with periodic uncertainties

This paper addresses a tracking problem for uncertain nonlinear discrete‐time systems in which the uncertainties, including parametric uncertainty and external disturbance, are periodic with known periodicity. Repetitive learning control (RLC) is an effective tool to deal with periodic unknown components. By using the backstepping procedures, an adaptive RLC law with periodic parameter estimation is designed. The overparameterization problem is overcome by postponing the parameter estimation to the last backstepping step, which could not be easily solved in robust adaptive control. It is shown that the proposed adaptive RLC law without overparameterization can guarantee the perfect tracking and boundedness of the states of the whole closed‐loop systems in presence of periodic uncertainties. In addition, the effectiveness of the developed controller is demonstrated by an implementation example on a single‐link flexible‐joint robot. Copyright © 2014 John Wiley & Sons, Ltd.     

Neural adaptive robust output feedback control of wheeled mobile robots with saturating actuators

This paper addresses the output feedback tracking control problem of electrically driven wheeled mobile robots subjected to actuator constraints. The main drawback of previously proposed controllers is the actuator saturation problem, which degrades the transient performance of the closed‐loop control system. In order to alleviate this problem, a saturated tracking controller has been proposed using the hyperbolic tangent function. A new nonlinear observer is introduced in order to leave out the velocity sensors in the robot system to decrease the cost and weight of the system for practical applications. A dynamic surface control strategy is effectively used to reduce the design complexity when considering actuator dynamics. In addition, neural network approximation capabilities and adaptive robust techniques are also adopted to improve the tracking performance in the presence of uncertain nonlinearities and unknown parameters. Semi‐global stability of the closed‐loop system is presented using direct Lyapunov method. Simulation results are provided to illustrate the effectiveness of the proposed control system for a differential drive mobile robot in practice. Copyright © 2014 John Wiley & Sons, Ltd.     

考虑铁损的永磁同步电动机模糊自适应约束控制

针对考虑铁损的永磁同步电动机位置伺服控制中的状态约束问题,本文提出了一种基于势垒Lyapunov函数的模糊自适应反步控制策略。首先,选取模糊逻辑系统处理电动机系统中的未知非线性函数项;然后,将势垒Lyapunov函数与反步法结合对状态变量幅值进行约束,保证电动机系统的转子角速度、定子电流等状态量被限制在给定的区间内;最终构建基于势垒Lyapunov函数的模糊自适应反步控制器。仿真结果表明所设计的控制器不仅实现了有效的位置跟踪,并且将控制量和状态量都限制在合理区间内,避免了因违反状态约束而引发的安全性问题。     

Adaptive fuzzy output‐feedback tracking control for switched stochastic pure‐feedback nonlinear systems

This paper considers the problem of adaptive fuzzy output‐feedback tracking control for a class of switched stochastic nonlinear systems in pure‐feedback form. Unknown nonlinear functions and unmeasurable states are taken into account. Fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy observer is designed to estimate the immeasurable states. Based on these methods, an adaptive fuzzy output‐feedback control scheme is developed by combining the backstepping recursive design technique and the common Lyapunov function approach. It is shown that all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded in mean square in the sense of probability, and the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing appropriate parameters. Finally, a simulation result is provided to show the effectiveness of the proposed control method.     

基于观测器的异步电机随机系统模糊反步位置跟踪控制

提出了一种基于观测器的异步电机随机系统模糊反步位置跟踪控制方法:通过构造降维观测器估计转子角速度;采用模糊逻辑系统逼近系统模型中的未知随机非线性函数。利用动态面控制技术解决传统反步设计中存在的"计算爆炸"问题。仿真结果表明:所提出的控制方法可以克服随机扰动的影响,并且确保跟踪误差收敛到足够小的原点邻域内。     

Learning‐based iterative modular adaptive control for nonlinear systems

In this paper, we study the problem of adaptive trajectory tracking control for a class of nonlinear systems with structured parametric uncertainties. We propose to use an iterative modular approach: we first design a robust nonlinear state feedback that renders the closed‐loop input‐to‐state stable (ISS). Here, the input is considered to be the estimation error of the uncertain parameters, and the state is considered to be the closed‐loop output tracking error. Next, we propose an iterative adaptive algorithm, where we augment this robust ISS controller with an iterative data‐driven learning algorithm to estimate online the parametric uncertainties of the model. We implement this method with two different learning approaches. The first one is a data‐driven multiparametric extremum seeking method, which guarantees local convergence results, and the second is a Bayesian optimization‐based method called Gaussian Process Upper Confidence Bound, which guarantees global results in a compact search set. The combination of the ISS feedback and the data‐driven learning algorithms gives a learning‐based modular indirect adaptive controller. We show the efficiency of this approach on a two‐link robot manipulator numerical example.     

Cooperative adaptive neural partial tracking errors constrained control for nonlinear multi‐agent systems

This paper considers the problem of partial tracking errors constrained for high‐order nonlinear multi‐agent systems in strict‐feedback form. In the control design, radial‐based function neural networks are utilized to identify uncertain nonlinear functions, and a cooperative adaptive dynamic surface control is proposed to avoid the explosion of complexity in the backstepping technique. Based on the minimal learning parameter technique and the predefined performance approach, a novel cooperative adaptive neural network control method is developed. The proposed controller is able to guarantee that all the closed‐loop network signals are cooperative semi‐globally uniformly ultimately bounded, and partial tracking errors confine all times within the predefined bounds. Finally, simulation example and comparative example with previous methods are given to verify and clarify the effectiveness of the new design procedure. Copyright © 2016 John Wiley & Sons, Ltd.     

多关节机器人的反演自适应模糊滑模控制

针对二关节机器人轨迹跟踪问题,设计了一种新的反演自适应模糊滑模控制器.该方法设计了反演滑模控制器和自适应模糊控制器,通过设计合适的自适应律,采用模糊控制器在线估计不确定性上界值,实现了对建模误差和干扰的自动跟踪,削弱了抖振.利用李亚普诺夫定理证明了系统的稳定性.仿真结果表明该方法的有效性.     

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.     

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.     

基于 PSO-BP 神经网络的分拣机器人视觉反馈跟踪

针对分拣机器人视觉反馈跟踪精度差、耗时较长的问题,研究基于粒子群算法-反向传播(particle swarm optimization-back propagation, PSO-BP)神经网络的分拣机器人视觉反馈跟踪方法,以提升视觉反馈跟踪效果。依据分拣机器人的视觉反馈信息,建立分拣机器人运动学模型,并求解分拣机器人机械臂输出位置和输入位置的误差函数;利用PSO算法优化BP神经网络的权值与偏置;在权值与偏置优化后的BP神经网络内,输入误差函数,预测分拣机器人视觉反馈跟踪控制量;利用预测视觉反馈跟踪控制量,在线调整增量式比例-积分-微分(proportional-integral-derivative, PID)的参数,输出高精度的分拣机器人视觉反馈跟踪控制量,实现分拣机器人视觉反馈跟踪。实验结果表明,该方法可有效视觉反馈跟踪分拣机器人机械臂的关节角;存在干扰情况下,在运行时间为10 s左右时,阶跃响应趋于稳定;有干扰情况下,视觉反馈跟踪的平均误差为0.09 cm,耗时平均值为0.10 ms;无干扰情况下,平均误差为0.03 cm,耗时平均值为0.04 ms。