Research On Dynamic Analysis And Vibration Control Of Flexible Robot Mechanism

In order to improve dynamic performance and quality of mechanism, we must pay more attention to mechanism dynamic as modern machinery is developing into high-speed, precise, lightweight and low-noise one. Especially for a high-speed operating robot, the elastic deformation of its component is not ignored under the external force and inertia force. The elastic deformations not only affect trajectory accuracy and positioning precision, destroy the system stability and reliability, but also reduce productivity and machine life. It is an important issue for mechanism dynamic to reduce its hazardous dynamic response. In the paper, theory and methods on the dynamical modeling, optimization, and active vibration control of flexible robot mechanism is systematically analyzed and studied. The main contributions in this thesis are listed as follows:A sub-structure modeling method is presented for a general flexible parallel robot. The main idea of the method is that according to the structure character of parallel robot comprised by some independent moving chain, static platform and moving platform, the kinematic substructure is treated as flexible one, the static and moving platform is rigid. Its dynamic equations are established, respectively, and then the system motion equations are obtained by combining all the motion equations of the sub-structure. The characters of the method are as follows: rigid substructure is introduced; the geometric and motion constraint relationship between rigid substructure and flexible one is derived. The model is simplified by using the micro-displacement and micro rotation of the moving platform center as system generalized coordinates to reduce its degrees of freedom and calculate conveniently them. The dynamic analysis results of two examples show the validity of the model.For a novel 2-DoF flexible parallel manipulator, the optimal design of sectional parameters is carried out in order to acquire the best dynamic characteristics within the category of elastodynamic. The finite element method is applied to obtain the dynamic equations of the system. The sensitivity analysis of the first order natural frequency with respect to sectional parameters is investigated to determine the optimization design variables. Fundamental frequency or weight is selected as objective function respectively; the final optimization results can meet the design requirements, that is, the manipulator have less weight and a relatively high natural frequency. Ideas and methods presented in the paper can be applied to optimize the design of other mechanisms.For a novel 2-DoF flexible parallel manipulator, the dynamic equations of the system were derived by using assumed mode method and Langrange multiplier method. It is a differential algebraic equation. In order to design a controller, the coordinate-partitioned method is used to convert the differential algebraic equations into a second-order differential equations. Beacause the equations are non-linear and time-varying the variable structure control method is applied to design the controller in order to acquire desired trajectory and attenuate the elastic deformation of flexible parts by selecting the appropriate joint control law. The simulation results show the feasibility and effectiveness of the controller.Mode theory and variable structure control are applied to design active vibration controller for a novel 2-DoF flexible parallel manipulator with piezoelectric actuators and sensors. The sliding surface is determined by using optimization method according to the performance demand of the system, and sliding controller is designed by applying Lyapunov direct method, and taking account of actuator input voltage limits. The simulation results show the controller can effectively attenuate elastic vibration caused by flexible parts, and reduce the displacement errors of mobile platform of the parallel manipulator, and it is feasible and effective.Linear quadratic Gaussian optimal control is applied the active vibration control of the flexible five-link manipulator. The optimum positions of the actuators and sensors are determined by applying a controllable and observable indicator characterized by the energy of actuator and measurement signal. The state variables and the output response are used as the performance index in the calculation of the linear quadratic feedback gain matrix. The external force and inertia force in modal coordinate is treated as white noise, a Kalman state estimator is constructed and connects the state estimator and feedback gain matrix to obtain quadratic Gauss controller. The simulation results show the two controllers can effectively suppress the vibration of flexible manipulator, and through comparative analysis, the controller with output performance can obtain better control effects.Model predictive control is applied to suppress elastic vibration response of a flexible five–link robot. According to the system state space equation, its prediction model is derived so as to obtain the future output value of prediction model. The modal force and measurement noise is non-deterministic external disturbance, and are treated as white noise, a Kalman filter estimator to estimate the system states. Considering the control voltages and its change rates as constraints, the system performance index and the constraints is formed into a quadratic programming optimization problem, and finally the optimal control outputs are acquired. The simulation results show that it is effective of the model predictive control method to attenuate vibration response of flexible manipulator, and achieve satisfactory control effects.H_∞control theory andμsynthesis is applied to design robust controller to suppress elastic vibration response of a flexible five–link robot. During the design of H_∞controller, the modal force and measurement noise is uncertain external disturbances, modal displacement signal and output response signals are selected as the evaluation signal respectively, and using amplitude and frequency characteristics of actual signal select the appropriate weighting function to form a minimum sensitivity problem. Considering the uncertainty of structural parameters, such as natural frequency, damping ratio and actuator parameters, theμcontroller is designed by usingμsynthesis approach. In order to verify the validity of the controller, the analysis from the frequency domain and time domain are carried out, respectively. Analysis results show that: The two controllers are designed to inhibit the influence of mode force on output strain; The controllers can meet control requirements with uncertainty, and denote that all controllers have some robustness; The control performance and robustness ofμcontroller is better than the H_∞controller. Finally, the comparative analysis of the sliding mode variable structure control, linear quadratic Gaussian control, model predictive control, H_∞control andμcontrol are performed. The advantages and disadvantages, and the similarities and differences of these control method apllied to active vibration control of flexible robot mechanism are analyzed respectively. The control performance compariatve analysis of these controllers is carried out from the point of view of time domain and frequency domain.In order to verify the validity of the designed controller, the experiment on active vibration control of a flexible five-link manipulator is carried out. The experiment is divided into three parts: The first part is the rigid motion control of the manipulator; The second part is experimental modal testing to access to natural frequency and damping ration of the system, and modify the theoretical model; The third part is the experiment for the vibration control. The experimental data shows the designed controller can effectively suppress the elastic vibration of the manipulator.