基于压电陶瓷的柔性机器人主动抑振控制策略研究

柔性机器人因其轻质、高效、低能耗等优点已被广泛应用于航空航天,工业制造等诸多领域。然而,柔性机构易产生弯曲变形,引起系统振动而大大降低机器人的工作精度。为提高柔性机器人的工作性能,多种抑振策略得以研究与应用。提出了基于压电陶瓷（PZT）的柔性机器人振动主动抑制策略。其中,PZT传感器和PZT制动器分别被用来检测和抑制柔性臂的振动。本文构建了基于PZT材料的单自由度柔性机械臂的理论模型,并获得了传感电压与制动电压的传递函数。设计了一个可变控制方案的抑振器以抑制系统在不同频率下的振动。在COMSOL中进行仿真,获得了系统的抑振率。根据仿真结果显示,柔性臂在前三阶振动下,臂的末端位移分别得到了57.04%,57.76%与58.96%的抑制;系统的动能得到了57.95%,71.19%与87.81%的抑制。     

柔性机械臂的双时间尺度组合控制

本文研究柔性机械臂的轨迹跟踪和振动抑制问题. 首先, 利用Lagrange法和假设模态法建立柔性机械臂的动态模型, 进而利用奇异摄动理论得到柔性机械臂的双时间尺度模型. 然后, 基于慢时间尺度模型利用滑模控制理论设计轨迹跟踪控制器; 借助于快时间尺度模型利用自适应动态规划设计参数不精确已知情况下的最优振动抑制控制器; 将二者相结合, 构造双时间尺度组合控制器, 利用奇异摄动理论证明闭环系统稳定. 最后, 在Matlab/Simulink环境下进行实验, 与现有方法相比, 本文设计的控制器对柔性振动具有更好的振动抑制效果, 跟踪精度更高.     

Position/vibration control of two-degree-of-freedom arms having one flexible link with artificial pneumatic muscle actuators

A manipulator with a light and thus flexible link would be advantageous over a rigid link in the sense that it is physically safer when it comes into contact with its environment than a manipulator with a rigid and thus heavy link, even though it is harder for a flexible link manipulator to be robustly controlled. On the other hand, if an actuator can deliver enough force while maintaining proper compliance, it would be advantageous for the sake of safety. An artificial pneumatic muscle-type actuator is an adequate choice in this case. In this work, position control problem of a two-degree-of-freedom arm system having a flexible second link with artificial pneumatic muscle-type actuators is addressed. A composite controller design method is proposed in the framework of the singular perturbation method. Various robust control schemes are designed in order to meet with payload variation, parameter uncertainty, unmodeled vibration mode, actuator dynamics both in the slow and the fast subsystems.     

Boundary feedback stabilisation of a flexible robotic manipulator with constraint

In this paper, the flexible robotic manipulator is modelled as a distributed parameter system, represented by a group of partial differential equations and ordinary differential equations. Control is designed at the boundary of the robotic manipulator based on integral-barrier Lyapunov function to suppress the vibration of the elastic deflection and track the desired angular position. With the proposed boundary control, the manipulator can be driven to the desired set-point with angular position and elastic deflection stay under the former setting constraint. Uniformed boundedness of the closed-loop system under the unknown time-varying disturbance is achieved. Stability analysis of the closed-loop system is given by employing the Lyapunov stability theory. Simulation results illustrate the effectiveness of the proposed boundary controller for ensuring output constraint and suppressing vibrations.     

Adaptive neural network tracking control for manipulators with uncertain kinematics, dynamics and actuator model

A neural-network-based adaptive controller is proposed for the tracking problem of manipulators with uncertain kinematics, dynamics and actuator model. The adaptive Jacobian scheme is used to estimate the unknown kinematics parameters. Uncertainties in the manipulator dynamics and actuator model are compensated by three-layer neural networks. External disturbances and approximation errors are counteracted by robust signals. The actuator controller is designed based on the backstepping scheme. Compared with the existing work, the proposed method considers the manipulator kinematics uncertainty, does not need the “linearity-in-parameters” assumption for the uncertain terms in the dynamics of manipulator and actuator, and guarantees the tracking error to be as small as desired. Finally, the performance of the proposed approach is illustrated by the simulation example.     

Partial differential equation modeling and vibration control for a nonlinear 3D rigid‐flexible manipulator system with actuator faults

In this paper, modeling and controlling problem for a two‐link rigid‐flexible manipulator in three‐dimensional (3D) space is studied under actuator faults. For modeling, the dynamics of the 3D mechanical system is represented by nonlinear partial differential equations, which is first derived in infinite dimension form. Based on the nonlinear model, the controller is proposed, which can achieve joint angle control and vibration suppression control in the presence of actuator faults. The stability analysis of the closed‐loop system is given based on LaSalle invariance principle. Numerical simulations illustrate the effectiveness of the proposed controller. This study will promote the development of nonlinear flexible manipulator systems in 3D space.     

A Computed Torque/Time Delay Approach to the End-Point Control of a One-Link Flexible Manipulator

The problem of modelling end point control of a one-linkflexible manipulator has been considered. The assumed mode methodas well as the Lagrangian dynamics are used to develop the dynamicmodel. It has been shown that a conventional computed torquecontroller cannot deal with the end point vibrations of flexiblelinks. The non-minimum phase characteristic of the end pointcontrol of a one link flexible manipulator has been demonstratedby choosing the absolute angle of a point along the link as thecontrolled output. In order to introduce active damping intothe system, a computed torque/delayed deflection approach hasbeen proposed. In this approach, the actuator torque is computedfrom the joint angle and a delayed deflection of a point alongthe link. The choice of the delay time depends on the point atwhich the deflection is measured. Simulation results are presentedto demonstrate the effectiveness of the proposed controller.     

欠驱动TORA系统的自耦PID控制策略

针对欠驱动旋转激励平移振荡器(translational oscillations with a rotational actuator,TORA)系统的控制问题,使用一种自耦PID(self-coupling proportional-integral-differential,SCPID)控制方法.该方法首先利用坐标变换使TORA系统的质心映射为Huygens振动中心,以实现新系统控制输入解耦,避免零动态不稳定问题;然后对Huygens振动中心设计平移位置的SCPID控制器,同时获得小球偏转角度的虚拟指令,进而设计小球偏转角度的SCPID控制器,从而实现TORA系统的平衡点跟踪控制;最后在复频域对闭环控制系统的稳定性进行严格的数学分析和证明.仿真及与其他方法的结果对比表明,所设计的控制算法简单高效,在欠驱动控制系统领域具有实际的应用价值.     

VIBRATION CONTROL OF A SMART STRUCTURE USING PERIODIC OUTPUT FEEDBACK TECHNIQUE

Active vibration control is an important problem in structures. One of the ways to tackle this problem is to make the structure smart, adaptive and self‐controlling. The objective of active vibration control is to reduce the vibration of a system by automatic modification of the system's structural response. This work features the modeling and design of a Periodic Output Feedback (POF) control technique for the vibration control of a smart flexible cantilever beam system for a Single Input Single Output case. A POF controller is designed for the beam by bonding patches of piezoelectric layer as sensor/actuator to the master structure at different locations along the length of the beam. The entire structure is modeled in state space form using the Finite Element Method by dividing the structure into 3, 4, 5 elements, thus giving rise to three types of systems, viz., system 1 (beam divided into 3 finite elements), system 2 (4 finite elements), system 3 (5 finite elements). POF controllers are designed for the above three types of systems for different sensor/actuator locations along the length of the beam by retaining the first two vibratory modes. The smart cantilever beam model is developed using the concept of piezoelectric bonding and Euler‐Bernouli theory principles. The effect of placing the sensor/actuator at various locations along the length of the beam for all the three types of systems considered is observed and the conclusions are drawn for the best performance and for the smallest magnitude of the control input required to control the vibrations of the beam. The tip displacements with the controller is obtained. Performance of the system is also observed by retaining the first 3 vibratory modes and the conclusions are drawn.     

Analytical development of dynamic equations of motion for a three-dimensional flexible link manipulator with revolute and prismatic joints

In this paper, a mathematical model capable of handling a three-dimensional (3D) flexible n-degree of freedom manipulator having both revolute and prismatic joints is considered. This model is used to study the longitudinal, transversal, and torsional vibration characteristics of the robot manipulator and obtain kinematic and dynamic equations of motion. The presence of prismatic joints makes the mathematical derivation complex. In this paper, for the first time, prismatic joints as well as revolute joints have been considered in the structure of a 3D flexible n-degree of freedom manipulator. The kinematic and dynamic equations of motion representing longitudinal, transversal, and torsional vibration characteristics have been solved in parametric form with no discretization. In this investigation, in order to obtain an analytical solution of the vibrational equations, a novel approach is presented using the perturbation method. By solving the equations of motion, it is shown that mode shapes of the link with prismatic joints can be modeled as the equivalent clamped beam at each time instant. As an example, this method is applied to a three degrees of freedom robot with revolute and prismatic joints. The obtained equations are solved using the perturbation method and the results are used to simulate vibrational behavior of the manipulator.     

Estimation of the Flexural States of a Macro–Micro Manipulator Using Point-Acceleration Data

The work reported here was motivated by the development of manipulator systems comprising one long-reach, flexible-link subsystem, termed the macromanipulator, and a short-reach, rigid-link subsystem, called the micromanipulator. The flexural states of the macromanipulator, needed for controlling such systems effectively, are not usually measurable directly. For this reason, a state-estimation algorithm is proposed which uses the velocity and angular-velocity data of the micromanipulator base to estimate the flexural states of the macromanipulator. The velocity data are inferred from the acceleration signals delivered by a kinematically redundant set of triaxial accelerometers. The accelerometer signals are also utilized to calculate the translational and angular accelerations of the micromanipulator base, which are, in turn, used along with the dynamics equations of the micromanipulator to obtain the reaction force and moment acting between the two subsystems. Treating the force and the moment as inputs, the dynamics equations of the macromanipulator alone are used in the observer, thus reducing the order of the dynamics model. The state–output relations, on the other hand, are linearized in closed form to lower the computational cost. The relations thus obtained are then used in an extended Kalman filter to estimate the flexural states of the system.     

Constrained motion control of flexible robot manipulators based on recurrent neural networks

In this paper, a neural network approach is presented for the motion control of constrained flexible manipulators, where both the contact force everted by the flexible manipulator and the position of the end-effector contacting with a surface are controlled. The dynamic equations for vibration of flexible link and constrained force are derived. The developed control, scheme can adaptively estimate the underlying dynamics of the manipulator using recurrent neural networks (RNNs). Based on the error dynamics of a feedback controller, a learning rule for updating the connection weights of the adaptive RNN model is obtained. Local stability properties of the control system are discussed. Simulation results are elaborated on for both position and force trajectory tracking tasks in the presence of varying parameters and unknown dynamics, which show that the designed controller performs remarkably well.     

A new controller design for a flexible one-link manipulator

A novel controller design for noncollocated flexible one-link manipulator arm tip position control based on variable structure sliding mode control is presented. Using the assumed-mode method, the plant model is derived. The discontinuous control law based on the variable structure system theory for the noncollocated manipulator tip position control is then designed. The position state variables are obtained directly from the inversion of the output submatrix multiplied by the sensor measurements. The velocity state variables are estimated through decoupled estimators-a separate first-order observer for each of the system's modes under consideration. Different sampling periods are used for the estimator and the controller. The performance of the controller is evaluated through a series of simulations, followed by an analysis of the designed control system     

Fault Diagnosis and Fault Tolerant Control for Manipulator with Actuator Multiplicative Fault

In this paper, a new fault diagnosis and fault tolerant control algorithm for manipulators with actuator multiplicative fault is proposed. The dynamic model of the manipulator with disturbance is taken as the research object. When faults occur in the actuator, a nonlinear observer based on radial basis function (RBF) neural network is used to estimate the fault information. After the fault information is obtained, an adaptive back-stepping sliding mode controller is used to control the manipulator to reach the desired trajectory. At last, an illustrated example is given to demonstrate the efficiency of the proposed algorithm, and satisfactory results have been obtained.

     

受时变约束柔性臂鲁棒RBF神经网络力/位置控制

研究了受时变约束的柔性臂系统，建立了分布参数模型，通过奇异摄动方法将该模型划分为表征系统刚性运动的集中参数子系统和表征系统振动的分布参数子系统．设计了集中参数子系统的鲁棒RBF神经网络力／位置控制算法和分布参数子系统的鲁棒自适应振动抑制控制算法．理论分析及仿真结果验证了该方法的有效性．     

Adaptive fault-tolerant vibration control of a wind turbine blade with actuator stuck

ABSTRACT

This paper proposes an adaptive fault-tolerant boundary vibration control method designed to resolve unknown failure and stuck actuator problems in the wind turbine blade control process. The blade is modelled as a distributed parameter system described by two coupled partial differential equations. The proposed boundary control achieved the fact that the vibration of the blade can still be suppressed even when the actuator fails, and the bending and torsional deformation is eventually reduced to zero. Based on the Lyapunov direct method, a fact has been confirmed that the stability of the system is guaranteed under the boundary controller. The effectiveness of the controllers is demonstrated by numerical simulations.     

失重环境下可控柔性臂的模态特性

在非重力场中,考虑控制器动态反馈的影响,对存在控制器定位约束的柔性臂系统进行动力分析,研 究其在相对平衡位置的模态特性．以具有柔性关节和弹性臂杆的可控柔性臂为研究对象,分析了控制器作用下的反 馈约束特性,将控制器位置和速度增益引入力边界条件,得到了耦合控制器参量的模态特征方程,证明了反馈约束 的存在使得系统特征频率为复频率,且模态主振型是复变函数．通过数值仿真,明确了可控柔性臂的模态特性与控 制器增益之间的关系,得到了不同于经典振动理论的结论．设计了可控柔性臂的仿失重实验平台,试验模态结果证 明了理论分析的有效性．     

FAULT TOLERANT CONTROL OF FLEXIBLE SMART STRUCTURES USING ROBUST DECENTRALIZED FAST OUTPUT SAMPLING FEEDBACK TECHNIQUE

This paper presents the modeling, design and simulation of a Robust Decentralized Fast Output Sampling (RDFOS) feedback controller for the vibration control of a smart structure (flexible cantilever beam) when there is actuator failure. The beam is divided into 8 finite elements and the sensors / actuators are placed at finite element positions 2, 4, 6, and 8 as collocated pairs. The smart structure is modeled using the concepts of piezoelectric theory, Euler‐Bernoulli beam theory, Finite Element Method (FEM) techniques and the state space techniques. Four multi‐variable state‐space models of the smart structure plant are obtained when there is a failure of one of the four actuators to function. The effect of failure of one of the piezo actuators to function during the vibration of the beam is observed. The tip displacements, open and closed loop responses with and without the controller are observed. For all of these models, a common stabilizing state feedback gain F is obtained. A robust decentralized fast output sampling feedback gain L which realizes this state feedback gain is obtained using the LMI approach. In this designed control law, the control inputs to each actuator of the multi‐model representation of the smart structure is a function of the output of that corresponding sensor only and the gain matrix has got all off‐diagonal terms zero and this makes the control design a robust decentralized one. Then, the performance of the designed smart system is evaluated for Active Vibration Control (AVC). The robust decentralized FOS controller obtained by the designed method requires only constant gains and hence may be easier to implement in real time.     

Adaptive actuator fault compensation control for a rigid-flexible manipulator with ODEs-PDEs model

In this paper, the actuator fault problem is studied for a two-link rigid-flexible manipulator system in the presence of boundary disturbance and state constraint. The system consists of a rigid beam, a flexible beam and a payload at the end, which are described by hybrid ordinary differential equations–partial differential equations. The novel controller includes a proportional-derivative feedback structure, a disturbance observer and a fault-tolerant algorithm, which can regulate the joint positions and eliminate vibration of flexible beam, on circumstance of boundary disturbance and actuator fault. With the help of Barrier Lyapunov Function, the states will not be violated. It is proved that the closed-loop system has asymptotic stability by LaSalle Invariance Principle. Simulations are provided to demonstrate the effectiveness of the proposed controller.     

双连杆刚柔机械臂无残余振动位置控制

针对双连杆刚柔机械臂,提出一种基于轨迹规划的无残余振动位置控制方法,在将机械臂的末端执行器从任意初始位置移动到目标位置的同时,确保系统没有残余振动产生.首先,建立系统的动力学模型,并通过分析该模型得到系统的状态约束方程.其次,基于状态约束方程,运用双向轨迹规划方法规划一条系统前向轨迹和一条系统反向轨迹.然后,利用时间倒转方法及基于遗传算法的轨迹优化方法对两条轨迹进行拼合,得到一条从系统初始状态到目标状态的期望轨迹.最后,设计轨迹跟踪控制器使系统沿期望轨迹到达目标状态,实现系统的无残余振动位置控制目标.仿真结果验证了本文所提方法的有效性.