Dynamic surface control-backstepping based impedance control for 5-DOF flexible joint robots

A new impedance controller based on the dynamic surface control-backstepping technique to actualize the anticipant dynamic relationship between the motion of end-effector and the external torques was presented.Comparing with the traditional backstepping method that has "explosion of terms" problem,the new proposed control system is a combination of the dynamic surface control technique and the backstepping.The dynamic surface control(DSC) technique can resolve the "explosion of terms" problem that is caused by differential coefficient calculation in the model,and the problem can bring a complexity that will cause the backstepping method hardly to be applied to the practical application,especially to the multi-joint robot.Finally,the validity of the method was proved in the laboratory environment that was set up on the 5-DOF(degree of freedom) flexible joint robot.Tracking errors of DSC-backstepping impedance control that were 2.0 and 1.5 mm are better than those of backstepping impedance control which were 3.5 and 2.5 mm in directions X,Y in free space,respectively.And the anticipant Cartesian impedance behavior and compliant behavior were achieved successfully as depicted theoretically.

Backstepping adaptive control of hydraulic Stewart platform using dynamic surface

Hydraulic Stewart platform is characterized by nonlinearity for driving system in essence,severe load coupling among the legs,which bring a great difficulty for controller design and performance improvement.Afore controller research is either low in tracking performance and movement smoothness when it ignores the nonlinearity and dynamics coupling,or complex in algorithm and has the need of acceleration feedback or observer when the dynamics coupling and nonlinearity is included.To solve the dilemma,a new controller,backstepping adaptive control of hydraulic Stewart platform using dynamic surface is put forward based on the complete dynamics including the upper platform dynamics and hydraulic nonlinearity in driving system.Asymptotic stability of the whole system is proved by Lyapunov method.The proposed algorithm is simple by avoiding the use of acceleration.The simulation results indicate that the control algorithm performs better than the normal PID controller in control precision,dynamic response and depression of the cross coupling.

Adaptive Fuzzy Dynamic Surface Control for Uncertain Nonlinear Systems

In this paper, a robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems is proposed. A novel adaptive fuzzy dynamic surface model is built to approximate the uncertain nonlinear functions by only one fuzzy logic system. The approximation capability of this model is proved and the model is implemented to solve the problem that too many approximators are used in the controller design of uncertain nonlinear systems. The shortage of ＂explosion of complexity＂ in backstepping design procedure is overcome by using the proposed dynamic surface control method. It is proved by constructing appropriate Lyapunov candidates that all signals of closed-loop systems are semi-globally uniformly ultimate bounded. Also, this novel controller stabilizes the states of uncertain nonlinear systems faster than the adaptive sliding mode controller （SMC）. Two simulation examples are provided to illustrate the effectiveness of the control approach proposed in this paper.

Serret-Frenet frame based on path following control for underactuated unmanned surface vehicles with dynamic uncertainties

The path following problem for an underactuated unmanned surface vehicle(USV) in the Serret-Frenet frame is addressed. The control system takes account of the uncertain influence induced by model perturbation, external disturbance, etc. By introducing the Serret-Frenet frame and global coordinate transformation, the control problem of underactuated system(a nonlinear system with single-input and ternate-output) is transformed into the control problem of actuated system(a single-input and single-output nonlinear system), which simplifies the controller design. A backstepping adaptive sliding mode controller(BADSMC)is proposed based on backstepping design technique, adaptive method and theory of dynamic slide model control(DSMC). Then, it is proven that the state of closed loop system is globally stabilized to the desired configuration with the proposed controller. Simulation results are presented to illustrate the effectiveness of the proposed controller.

Trajectory tracking control for underactuated unmanned surface vehicles with dynamic uncertainties

The trajectory tracking control problem for underactuated unmanned surface vehicles(USV) was addressed, and the control system took account of the uncertain influences induced by model perturbation, external disturbance, etc. By introducing the reference, trajectory was generated by a virtual USV, and the error equation of trajectory tracking for USV was obtained, which transformed the tracking problem of underactuated USV into the stabilization problem of the trajectory tracking error equation. A backstepping adaptive sliding mode controller was proposed based on backstepping technology and method of dynamic slide model control. By means of theoretical analysis, it is proved that the proposed controller ensures that the solutions of closed loop system have the ultimate boundedness property. Simulation results are presented to illustrate the effectiveness of the proposed controller.

高阶系统变增益固定时间动态面Backstepping控制

为解决一类存在未知建模误差、外部扰动的非线性系统控制在快速性、准确性、鲁棒性方面的问题,提出变增益固定时间动态面Backstepping控制器。首先,为每一层子系统设计具备新型结构的固定时间Backstepping控制器和固定时间动态面滤波器,使系统状态跟踪误差和滤波误差可在固定时间内完成收敛,收敛时间上界仅与设计参数有关。然后,为控制器和滤波器设计变增益函数,兼顾了大误差阶段的收敛快速性与小误差阶段的收敛准确性。仿真结果表明,所提方案可使系统在1.76 s内完成收敛,快于对比方案的5.51 s和3.68 s,证明了所提方案的优越性和有效性。

超机动飞行的动态面Backstepping控制

设计了一种超机动飞行的动态面Backstepping控制方法。新控制律在保留Backstepping"递归"设计步骤的基础上,放弃了参数自适应律;通过构造滑动面变量并根据能达条件,来设计中间虚拟控制信号和最终控制信号;通过在"递归"过程中增加一低通动态滤波器,避免了设计过程中对某些非线性信号的微分,减小了控制律的计算量。数值仿真结果表明,新控制律较简单地实现了超机动飞行时良好的飞机操纵指令信号跟踪,且易于工程实现。

高阶非线性液压辊缝系统的Backstepping动态面控制

针对某四辊冷轧机的液压辊缝系统,考虑系统干扰的情况下,建立了高阶非线性系统数学模型,利用Backstepping动态面算法设计了辊缝闭环控制器。该方法由于在逆递推设计过程中结合使用了一阶低通滤波器,无需对模型的非线性部分重复微分,从而避免了因"微分项的膨胀"而引起的算法复杂性。理论分析和仿真结果均表明所设计的控制器能够保证系统的半局稳定性,输出渐近跟踪期望轨迹,使系统对于给定位置跟踪具有良好的动态性能,对外部干扰也有较强的鲁棒性。

固定时间收敛动态面Backstepping控制

针对传统Backstepping动态面控制中滤波器跟踪误差及控制误差在靠近原点阶段收敛较慢、收敛时间无限大、控制器增益存在脆弱性等问题,设计了适用于具有不确定和外干扰的高阶多输入多输出非线性系统的固定时间收敛动态面Backstepping控制。首先提出并证明一种新的固定时间收敛的李雅普诺夫定理;基于此结论,将每一层子系统的虚拟控制器和滤波器均设计为固定时间收敛的新型结构。相对现有方案,新方案的优点是:1)加快了跟踪误差轨迹在远离和靠近平衡点两个阶段的收敛速度,即全论域的快速化;2)避免了参数脆弱性的问题;3)跟踪误差和控制误差都是固定时间收敛的,即不论初始误差多大,收敛时间不仅有限而且存在与初始误差无关的固定上界;4)虚拟控制器和控制器均为非奇异的。

基于发电单元完整模型的backstepping控制

针对发电单元高阶非线性完整数学模型(锅炉、汽轮机和发电机模型),结合系统参数的不确定性,采用backstepping动态面控制方法设计了一种鲁棒自适应控制器。在反推设计过程中引入了虚拟控制器和一阶低通滤波器,从而避免了对模型非线性进行多次微分而引起的算法复杂性,使设计方法简化。理论分析和仿真结果均表明,该控制器能够保证闭环系统的半全局渐近稳定性,对系统参数的不确定性具有较强的鲁棒性,在系统发生故障时能够使系统稳定运行。

基于动态面backstepping控制的高超声速飞行器自适应故障补偿设计

针对带有冗余舵面的高超声速飞行器纵向模型,考虑舵面出现卡死故障情况下,分别设计了基于backstepping的高度容错控制器与基于动态逆的速度跟踪控制器.在运用backstepping自适应设计高度控制器时,采用动态面设计方法,引入一阶滤波器,避免了设计中对虚拟信号求导带来的复杂计算问题.针对舵面出现未知故障(不确定故障模式、大小、发生时间)的情况,设计容错控制器结构,给出实现故障补偿控制的匹配条件,根据Lyapunov稳定性理论设计的控制器参数自适应律保证系统的稳定性与指令跟踪性能.针对舵面出现卡死故障的情况,仿真对控制算法进行了验证,得到了较理想的控制效果.

基于Backstepping的板球系统自适应神经网络H_(∞)控制

针对一个同时考虑了小球离心加速度及小球与板之间的未知摩擦力的非严格反馈形式的板球系统模型,基于Backstepping方法和H_(∞)控制理论首次研究了系统受到外部扰动时的H_(∞)跟踪控制问题。提出了一种自适应神经网络H_(∞)控制方法,获得了板球系统的自适应神经H_(∞)控制器。在控制器设计中,先借助一种变量分离方法对板球系统数学模型中的非严格反馈项进行处理,而后对于设计过程中出现的未知函数用神经网络进行近似逼近,并借助动态面技术避免了Backstepping方法的计算复杂性。所设计的控制器能够保证闭环板球系统内所有信号半全局一致最终有界,且系统具有对外部干扰的抑制能力。系统仿真实验证明了所设计控制器的有效性。

A robust output-feedback adaptive dynamic surface control for linear systems with input disturbance

In this paper, a robust output-feedback adaptive control is proposed for linear time-invariant （LTI） single- input single-output （SISO） plants with unmeasurable input disturbance. Using dynamic surface control （DSC） technique, it is shown that the explosion of complexity problem in backstepping control can be eliminated. Furthermore, the proposed adaptive DSC scheme has the following merits： 1） by introducing an initialization technique, the L~ performance of system tracking error can be guaranteed even if the plant high-frequency gain is unknown and the input disturbance exists, and 2） the adaptive law is necessary only at the first design step, which significantly reduces the design procedure. It is proved that with the proposed scheme, all the closed-loop signals are semiglobally uniformly ultimately bounded. Simulation results are presented to demonstrate the effectiveness of the proposed scheme.

Adaptive NN Dynamic Surface Control for a Class of Uncertain Non-affine Pure-feedback Systems with Unknown Time-delay

Adaptive neural network （NN） dynamic surface control （DSC） is developed for a class of non-affine pure-feedback systems with unknown time-delay. The problems of ＂explosion of complexity＂ and circular construction of the practical controller in the traditional backstepping algorithm are avoided by using this controller design method. For removing the requirements on the sign of the derivative of function f~, Nussbaum control gain technique is used in control design procedure. The effects of unknown time-delays are eliminated by using appropriate Lyapunov-Krasovskii functionals. Proposed control scheme guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Two simulation examples are presented to demonstrate the method.

Robust Tracking Control of Uncertain MIMO Nonlinear Systems with Application to UAVs

In this paper, we consider the robust adaptive tracking control of uncertain multi-input and multi-output(MIMO) nonlinear systems with input saturation and unknown external disturbance. The nonlinear disturbance observer(NDO)is employed to tackle the system uncertainty as well as the external disturbance. To handle the input saturation, an auxiliary system is constructed as a saturation compensator. By using the backstepping technique and the dynamic surface method,a robust adaptive tracking control scheme is developed. The closed-loop system is proved to be uniformly ultimately bounded thorough Lyapunov stability analysis. Simulation results with application to an unmanned aerial vehicle(UAV) demonstrate the effectiveness of the proposed robust control scheme.

基于递推最小二乘法的阀控缸液压系统控制策略

阀控缸液压系统存在建模不准确、动态控制精度较低和控制算法调试困难的问题,为此,提出了一种基于递推最小二乘法(RLS)的反步法动态面控制策略,并采用半实物仿真平台对其控制算法进行了调试验证。首先,建立了阀控缸液压系统非线性状态空间模型,推导了该系统的最小二乘矩阵形式和递推算法公式;然后,基于李雅普诺夫稳定性理论和动态面控制技术,建立了阀控非对称缸系统的控制模型,设计了一种基于RLS的反步法动态面控制器;最后,基于半实物仿真平台,对改造后的Linux操作系统进行了实时性验证,完成了阀控非对称缸系统参数辨识和基于RLS的反步法动态面控制试验任务。试验结果表明:RLS算法不仅能用于准确地估计系统模型参数,更能有效地适应系统模型参数的变化;相比于常规PID控制方法,基于RLS反步法动态面控制策略在阀控非对称缸系统稳定状态和换向的过程中,其动态控制精度分别提高了72.9%和20.3%,可为今后阀控缸液压系统建模及非线性控制策略研究提供较高的理论参考。

Adaptive backstepping control for a class of semistrict feedback nonlinear systems using neural networks

This paper addresses a neural adaptive backstepping control with dynamic surface control technique for a class of semistrict feedback nonlinear systems with bounded external disturbances.Neural networks (NNs) are introduced as approximators for uncertain nonlinearities and the dynamic surface control (DSC) technique is involved to solve the so-called 'explosion of terms' problem.In addition,the NN is used to approximate the transformed unknown functions but not the original nonlinear functions to overcome the possible singularity problem.The stability of closed-loop system is proven by using Lyapunov function method,and adaptation laws of NN weights are derived from the stability analysis.Finally,a numeric simulation validates the results of theoretical analysis.

Observer-based adaptive sliding mode backstepping output-feedback DSC for spin-stabilized canard-controlled projectiles

This article presents a complete nonlinear controller design for a class of spin-stabilized canard-controlled projectiles.Uniformly ultimate boundedness and tracking are achieved,exploiting a heavily coupled,bounded uncertain and highly nonlinear model of longitudinal and lateral dynamics.In order to estimate unmeasurable states,an observer is proposed for an augmented multiple-input-multiple-output（MIMO） nonlinear system with an adaptive sliding mode term against the disturbances.Under the frame of a backstepping design,an adaptive sliding mode output-feedback dynamic surface control（DSC） approach is derived recursively by virtue of the estimated states.The DSC technique is adopted to overcome the problem of ‘‘explosion of complexity＂ and relieve the stress of the guidance loop.It is proven that all signals of the MIMO closed-loop system,including the observer and controller,are uniformly ultimately bounded,and the tracking errors converge to an arbitrarily small neighborhood of the origin.Simulation results for the observer and controller are provided to illustrate the feasibility and effectiveness of the proposed approach.

基于DM-DSC的舰载机着舰自动复飞控制算法

针对理想复飞轨迹已知条件下的舰载机自动复飞控制问题,提出一种基于偏差模型的动态面控制(DM-DSC)算法。基于Radau伪谱法给出了舰载机着舰的最优复飞轨迹;根据得到的最优复飞轨迹及其所对应的控制方案,分别给出了速度子系统和高度子系统的偏差控制模型和反演(Backstepping)控制器,并通过引入动态面结构来获得虚拟控制量的微分信号,避免了Backstepping控制律求解过程中的“微分膨胀”问题;考虑到气动参数的不确定性及舰尾流场的干扰,采用线性扩张状态观测器(LESO)对控制模型中的干扰项进行估计和补偿,并设计抗饱和辅助系统来抑制控制饱和的不利影响;最后,基于Lyapunov方法证明闭环系统信号的有界性。仿真结果表明:所提算法具有良好的控制性能。