Distributed structural dynamics control of flexible manipulators—II. Distributed sensor and active electromechanical actuator

Structural oscillation of lightweight robot arms can degrade the accuracy and precision of a robot's high-demanding performance. This paper is the second of two on vibration control of elastic or flexible robot structure. The proposed electromechanical device has both sensing and control capabilities. Effects of active damping treatment on elastic robot arms are discussed. The proposed active distributed sensor and controller is a layer, or multi-layer, of piezoelectric polymer directly attached to the flexible component which is required to be monitored and controlled. By utilizing direct and converse piezoelectric characteristics, respectively, the integrated piezeoelectric sensor/controller can monitor the vibration due to induced mechanical stress/strain in the polymer; and it can also actively and directly constrain the undesirable vibration of flexible component by injecting high voltages. Experimental results and finite element simulations of the electromechanical sensor/actuator are presented and discussed.     

Distributed structural identification and control of shells using distributed piezoelectrics: Theory and finite element analysis

Distributed dynamic identification and vibration control of high-performance flexible structures has drawn much attention in recent years. This article presents an analytical and finite-element study on a distributed piezoelectric sensor and distributed actuator coupled with flexible shells and plates. The integrated piezoelectric sensor/actuator can monitor the oscillation as well as actively control the structural vibration by the direct/converse piezoelectric effects, respectively. Based on Maxwell's equations and Love's assumptions, new theories on distributed sensing and active vibration control of a generic shell using the distributed piezoelectrics are derived. These theories can be easily simplified to account for plates, cylinders, beams, etc. A new piezoelectric finite element is also formulated using the variational principle and Hamilton's principle. A piezoelectric micropositioning device was first studied; analytical solutions are compared closely with experimental and finite-element results. Distributed vibration identification and control of a zero-curvature shell-a plate-are also investigated.     

Distributed structural dynamics control of flexible manipulators —I. Structural dynamics and distributed viscoelastic actuator

Reducing structural dead weight has become of increasing importance in the design of new generation lightweight and high-speed robot manipulators. However, due to the nature of structural flexibility, the dynamic oscillation associated with robot structures can affect the operation accuracy and precision. This work, in two parts, presents a study on the vibration control of elastic or flexible robot structures. Effects of distributed passive (Part I) and active (in Part II) actuators on elastic robot structures are studied. The proposed distributed passive viscoelastic actuator (in Part I) is a layer (or layers) of viscoelastic polymer directly attached to the flexible robot element, the oscillation of which is to be controlled. The passive actuator is activated by the oscillation of the robot structure and it automatically dissipates vibration energy and constrains the undesirable motion to eliminate the disturbance and to maintain a precise robot trajectory. A finite element program capable of analyzing flexible links is developed. Results obtained from the finite element simulation are presented.     

压电复合梁高阶有限元模型与主动振动控制研究

大型柔性空间结构的振动控制问题引起了广泛的关注.压电材料以其低质量、宽频带和适应性强等特点,非常适合于柔性空间结构的振动控制.本文针对上下表面粘贴有分布式压电传感器和作动器的智能层梁结构,提出了一种考虑压电材料对结构质量、刚度影响的高阶有限元模型.考虑到空间结构可能承受较大的热载荷,在模型中计及了压电材料的热电耦合效应.采用常增益负反馈控制方法、常增益速度负反馈控制方法、Lyapunov反馈控制方法和线性二次型调节器方法(LQR)设计主动控制器,实现了智能层梁结构脉冲激励下的振动主动控制.仿真结果表明,LQR方法更能有效的实现结构振动控制,并且具有更低的作动器峰值电压,但不能消除热载荷引起的结构静变形.     

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。     

Vibration Control of a Planar Parallel Manipulator Using Piezoelectric Actuators

This paper presents an active damping control approach applied to piezoelectric actuators attached to flexible linkages of a planar parallel manipulator for the purpose of attenuation of unwanted mechanical vibrations. Lightweight linkages of parallel manipulators deform under high acceleration and deceleration, inducing unwanted vibration of linkages. Such vibration must be damped quickly to reduce settling time of the manipulator platform position and orientation. An integrated control system for a parallel manipulator is proposed to achieve precise path tracking of the platform while damping the undesirable manipulator linkage vibration. The proposed control system consists of a PD feedback control scheme for rigid body motion of the platform, and a linear velocity feedback control scheme applied to piezoelectric actuators to damp unwanted linkage vibrations. In this paper, we apply the proposed vibration suppression algorithm to two different types of piezoelectric actuators and evaluate their respective performances. The two piezoelectric actuators are (i) a PVDF layer applied to the flexible linkage and (ii) PZT actuator segments also applied to the linkage. Simulation results show that both piezoelectric actuators achieve good performance in vibration attenuation of the planar parallel manipulator. The dynamics of the planar parallel platform are selected such that the linkages have considerable flexibility, to better exhibit the effects of the vibration damping control system proposed.     

Control of flexible manipulators via singular perturbations and distributed vibration damping

A composite control strategy for a two-link flexible manipulator is analyzed which combines hub actuation with distributed vibration control. The hub actuation is based upon an integral manifold approach in which the system dynamics are approximately linearized to any order of a small parameter E representing stiffness of the robot arms. A polymer film is proposed as a distributed actuator to dampen vibrations due to elasticity in the links. Simulation results are provided which show that the addition of the distributed actuator significantly reduces the displacement and velocity of the first flexible mode in each link compared to hub actuation alone. Editor: T. Vincent     

Dynamics and Noncollocated Model‐Free Position Control for a Space Robot with Multi‐Link Flexible Manipulators

In this paper, both the dynamics and noncollocated model‐free position control (NMPC) for a space robot with multi‐link flexible manipulators are developed. Using assumed modes approach to describe the flexible deformation, the dynamic model of the flexible space robotic system is derived with Lagrangian method to represent the system dynamic behaviors. Based on Lyapunov's direct method, the robust model‐free position control with noncollocated feedback is designed for position regulation of the space robot and vibration suppression of the flexible manipulators. The closed‐loop stability of the space robotic system can be guaranteed and the guideline of choosing noncollocated feedback is analyzed. The proposed control is easily implementable for flexible space robot with both uncertain complicated dynamic model and unknown system parameters, and all the control signals can be measured by sensors directly or obtained by a backward difference algorithm. Numerical simulations on a two‐link flexible space robot are provided to demonstrate the effectiveness of the proposed control.     

Simultaneous optimization of piezoelectric actuator topology and polarization

This article addresses the problem of piezoelectric actuator design for active structural vibration control. The topology optimization method using the Piezoelectric Material with Penalization and Polarization (PEMAP-P) model is employed in this work to find the optimum actuator layout and polarization profile simultaneously. A coupled finite element model of the structure is derived assuming a two-phase material, and this structural model is written into the state-space representation. The proposed optimization formulation aims to determine the distribution of piezoelectric material which maximizes the controllability for a given vibration mode. The optimization of the layout and poling direction of embedded in-plane piezoelectric actuators are carried out using a Sequential Linear Programming (SLP) algorithm. Numerical examples are presented considering the control of the bending vibration modes for a cantilever and a fixed beam. A Linear-Quadratic Regulator (LQR) is synthesized for each case of controlled structure in order to compare the influence of the polarization profile.     

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.     

Experimental Comparison Research on Active Vibration Control for Flexible Piezoelectric Manipulator Using Fuzzy Controller

Space manipulators are flexible structures. Vibration problem will be unavoidable due to motion or external disturbance excitation. Model based control methods will not maintain the required accuracy because of the existence of nonlinear factors and parameter uncertainties. To solve these problems, fuzzy logic control laws with different membership function groups are adopted to suppress vibrations of a flexible smart manipulator using collocated piezoelectric sensor/actuator pair. Also, dual-mode controllers combining fuzzy logic and proportional integral control are designed, for suppressing the lower amplitude vibration near the equilibrium point significantly. Experimental comparison research is conducted, using fuzzy control algorithms and the dual-mode controllers with different membership functions. The experimental results show that the adopted fuzzy control algorithms can substantially suppress the larger amplitude vibration; and the dual-mode controllers can also damp out the lower amplitude vibration significantly. The experimental results demonstrate that the proposed fuzzy controllers and dual-mode controllers can suppress vibration effectively, and the optimal placement is feasible.     

Model-based trajectory planning for flexible-link mechanisms with bounded jerk

This paper deals with the model-based development of optimal jerk-limited point-to-point trajectories for flexible-link robotic manipulators. In the proposed approach, an open-loop optimal control strategy is applied to an accurate dynamic model of flexible multi-body planar mechanisms. The model, which has already been fully validated through experimental tests, is based on finite element discretization and accounts for the main geometric and inertial non-linearities of the linkage. Exploiting an indirect variational solution method, the necessary optimality conditions deriving from Pontryagin's minimum principle are imposed, and lead to a differential Two-Point Boundary Value Problem (TPBVP); numerical solution of the latter is accomplished by means of collocation techniques. The resulting motion and control profiles can be used as feedforward reference signals for a position and vibration control. Considering a lightweight RR robot, simulation results are provided for rest-to-rest, jerk-limited trajectories with minimum actuator jerks and vibrations. However, the strategy under investigation has general validity and can be applied to other types of mechanisms, as well as with different objective functions and boundary conditions. Numerical evidence clearly indicates that the use of a composite cost functional and the imposition of jerk constraints can greatly reduce vibration phenomena during high-speed motion of flexible-link manipulators.     

Active vibration control of smart piezoelectric beams: Comparison of classical and optimal feedback control strategies

This paper presents a numerical study concerning the active vibration control of smart piezoelectric beams. A comparison between the classical control strategies, constant gain and amplitude velocity feedback, and optimal control strategies, linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) controller, is performed in order to investigate their effectiveness to suppress vibrations in beams with piezoelectric patches acting as sensors or actuators. A one-dimensional finite element of a three-layered smart beam with two piezoelectric surface layers and metallic core is utilized. A partial layerwise theory, with three discrete layers, and a fully coupled electro-mechanical theory is considered. The finite element model equations of motion and electric charge equilibrium are presented and recast into a state variable representation in terms of the physical modes of the beam. The analyzed case studies concern the vibration reduction of a cantilever aluminum beam with a collocated asymmetric piezoelectric sensor/actuator pair bonded on the surface. The transverse displacement time history, for an initial displacement field and white noise force disturbance, and point receptance at the free end are evaluated with the open- and closed-loop classical and optimal control systems. The case studies allow the comparison of their performances demonstrating some of their advantages and disadvantages.     

Self-learning active vibration control of a flexible plate structure with piezoelectric actuator

In this paper, an active vibration control (AVC) incorporating active piezoelectric actuator and self-learning control for a flexible plate structure is presented. The flexible plate system is first modelled and simulated via a finite difference (FD) method. Then, the validity of the obtained model is investigated by comparing the plate natural frequencies predicted by the model with the reported values obtained from literature. After validating the model, a proportional or P-type iterative learning (IL) algorithm combined with a feedback controller is applied to the plate dynamics via the FD simulation platform. The algorithms were then coded in MATLAB to evaluate the performance of the control system. An optimized value of the learning parameter and an appropriate stopping criterion for the IL algorithm were also proposed. Different types of disturbances were employed to excite the plate system at different excitation points and the controller ability to attenuate the vibration of observation point was investigated. The simulation results clearly demonstrate an effective vibration suppression capability that can be achieved using piezoelectric actuator with the incorporated self-learning feedback controller.     

Inverse dynamics of spatial open-chain flexible manipulators with lumped and distributed actuators

This article addresses the problem of inverse dynamics for three-dimensional flexible manipulators with both lumped and distributed actuators. A recursive procedure is presented for computing the lumped inverse dynamic torques and the distributed piezoelectric actuator inputs for simultaneously tracking a prescribed end-point trajectory and reducing induced vibrations in the manipulator. The procedure sequentially solves for the non-causal inverse dynamic torques and piezoelectric voltages applied to each link in the manipulator, starting from the last element in the chain and proceeding to the base element. The method allows trajectory tracking wherein controllability of the structural vibrations is assured in all possible configurations through the use of only one motor at each intermediate joint and three motors at the ground. Numerical simulation shows that the elastic vibrations can be reduced significantly through the use of distributed actuators while at the same time satisfying the trajectory tracking requirement through the use of inverse dynamics. © 1994 John Wiley & Sons, Inc.     

主动约束层阻尼梁有限元建模与动态特性研究

基于弹性、粘弹性和压电材料的本构关系,利用Hamilton原理,推导了主动约束层阻尼梁的有限元动力学模型．结合压电材料的机电耦合特性,采用自感电压的位移反馈,研究了主动约束层阻尼梁的闭环控制特性．求解了主动约束层阻尼简支梁的动态特性如固有频率、模态损耗因子及频率响应特性等．对被动控制、主动控制和主被动混合控制的控制效果进行了分析比较．研究了粘弹性层与约束层厚度等参数对减振控制效果的影响．     

欠驱动柔性机器人的振动可控性分析

欠驱动柔性机器人的可控性分析是对其进行有效控制的关键问题. 本文以具有柔性杆的3DOF平面欠驱动机器人为例, 分两步分析系统的可控性. 首先,忽略杆件的弹性变形, 研究欠驱动刚性系统在不同驱动电机位置的状态可控性；然后, 考虑柔性因素, 研究欠驱动柔性系统的结构振动可控性. 结果表明振动可控性是随机器人关节位形和驱动电机位置而变化的, 并且欠驱动刚性机器人的状态可控性对相应的柔性系统的振动可控性有很重要的影响. 最后, 将上述研究方法扩展到具有一个被动关节的N自由度平面欠驱动柔性机器人.     

A flexible-arm as manipulator position and force detection unit

This paper presents a self-sensory robot arm to two basic sensing problems in control of flexible manipulators: detection of the position and orientation variations due to structural deformation and detection of the contact force of end-effector when manipulator interacts with its environment. Taking advantage of structural flexibility, a flexible robot arm with strain gauges distributed on it acts as a sensing unit. The position and orientation of flexible arm are expressed as a function of curvature of the arm. An interpolation technique gives this continuous curvature function from a finite set of measurements made with strain gauges. A relation between strain measurements and endpoint force of flexible arm is developed and the contact force of end-effector is then determined using a force propagation algorithm. The proposed technique and algorithm were implemented and evaluated in a laboratorial flexible arm. Experimental validations using a vision system and two force sensors have shown that the self-sensory flexible arm can provide accurate endpoint position and force in both static and dynamic loading situations.     

Development of a sensor system for collecting tactile information

This paper presents the development of a sensor system for collecting tactile information. An active sensing system using the piezoelectric effect and the pyroelectric effect of a PVDF (Polyvinylidene fluoride) film is proposed. The active sensing is designed with human motions for tactile perception in mind. First, as the pretest, the distinction examination of six fabrics with different textures is carried out through human tactile perception. Next, the proposed sensor system is assembled. The sensor is composed of a PVDF film and a soft rubber. The surface of the sensor can be heated through temperature control. The sensor is attached on the tip of a robot finger driven by a piezoelectric bimorph strip and the root of the finger is mounted on a linear slider. Two kinds of active sensing are introduced. First, the heated sensor is contacted with an object and pyroelectric output signals are collected in order to obtain the information on tactile warmth. Next, the heated sensor is slid over the object and piezoelectric output signals are collected in order to obtain the information on feelings of vibration. Through the discussion about each sensing, three indexes representing features of the collected data are extracted and proposed as the sensor outputs for the evaluation of tactile sensation. The measurement using the sensor system is done on the samples used in the distinction examination. Comparison with the results shows that the sensor system extracts features on feelings of vibration and warmth.