Approximate Inertial Manifold-Based Model Reduction and Vibration Suppression for Rigid-Flexible Mechanical Arms

The dynamic characteristics of the mechanical arm with a rigid-flexible structure are very complex. The reason is that it is a complex DPS (distributed parameter system) with infinite dimension and nonlinearity in essence due to the rigid-flexible coupling. So, accurately positioning and controlling the rigid-flexible mechanical arms could be difficult. Therefore, a model reduction method of rigid-flexible mechanical arms based on the approximate inertial manifold is put forward. To repress the residual vibration of the end of the mechanical arm, a feedforward control strategy is designed. The high-dimensional solution of the vibration equation of the rigid-flexible mechanical arms is projected into the complete space composed of orthogonal decomposition modes. By using Galerkin’s method, the system is simplified and the approximate solution is obtained through the interaction between high-order and low-order modes. The truncated finite mode is also used to construct a lowest-order dynamic model on the basis of approximate inertia manifold. Given the reduced-order rigid-flexible mechanical arms dynamic model, dynamic response analysis is conducted to optimize the target position error and end residual vibration. A limited number of sinusoidal signals approximately combine the input signal, by using the particle swarm optimization algorithm to optimize the input signal, and the amplitude of the sinusoidal signal is corrected. The simulation results depict the superiority of the proposed method, which greatly suppresses the end residual vibration of the mechanical arm and realizes the accurate positioning of the end of the mechanical arm. In addition, the hardware experimental device of the rigid-flexible mechanical arms is constructed, and the experimental verification of the above method is put into effect. The simulation results of angular displacement and end vibration of the reduced model are accordant which is shown by the experimental results of the hardware platform.

An improved IDA-PBC method with link-side damping injection and online gravity compensation for series elastic actuator

Elastic elements in series elastic actuator (SEA) will cause residual vibration in position control. Incorporating link-side damping injection and friction compensation, we propose an improved interconnection and damping assignment passivity-based control (IDA-PBC+) method to suppress residual vibration. Damping on the motor side and link side can be adjusted simultaneously. In addition, the desired motor-side trajectory planning and online gravity compensation are also introduced to improve control performance and steady-state accuracy. The effectiveness of the proposed method in suppressing residual vibration is experimentally verified with a two-degree-of-freedom SEA device.

Robust Vibration Control Based on Rigid-Body State Observer for Modular Joints

The vibration caused by resonance modes frequently occurs during acceleration and deceleration of the modular joint integrated with flexible harmonic drive. The conventional equivalent rigid-body velocity method with observer can suppress the residual vibration induced by resonant frequency but has poor robustness to model uncertainties and external disturbances. Moreover, it cannot eliminate the torque ripple caused by the harmonic drive during low-speed uniform motion, reducing the velocity tracking accuracy. Hence, a velocity controller with a rigid-body state observer and an adjustable damper is designed to improve the robust performance and velocity tracking accuracy. The designed rigid-body state observer allows a higher gain so that the bandwidth of the observer can increase, and the equivalent rigid-body velocity can be acquired more accurately. Notably, the high gain observer reduces the sensitivity to model uncertainties and exotic disturbances, especially near the resonant frequency. In addition, the observer combined with an adjustable damper can suppress the residual vibration and torque ripple simultaneously. The proposed method is compared experimentally with a PI method and two other rigid-body velocity methods, such as the conventional equivalent rigid-body observer method and the self-resonance cancellation method, to verify its advantages.

Research on intelligent vibration suppression control of high-speed lightweight Delta robot

Lightweight Delta robot is typical high-speed and high-precision industrial parallel robot. However, under high-speed condition, because of the lightweight components, it will inevitably lead to the vibration of Delta robot, which reduces the position accuracy and positioning efficiency. To solve this problem comprehensively, this article considers the process vibration and residual vibration of Delta robot, and the intelligent shaping vibration suppression control system is designed by using trajectory planning method of improved trapezoidal mode, shaping control method, and fast terminal sliding mode controller, and the detailed experimental analysis is carried out. The experimental results show that the proposed intelligent shaping vibration suppression control method can well suppress the process vibration and residual vibration of Delta robot, which can effectively improve the operation stability, work efficiency, and position accuracy of Delta robot.

Suppression of Residual Vibration in Nonlinear Systems with Temporal Variation and Uncertainty in Parameters by Elimination of the Natural Frequency Component

A systematic approach is developed for determining a control input for the point-to-point control of an overhead crane that exhibits temporal variation of rope length in addition to damping and nonlinearity, without inducing residual vibration. Complete suppression of the residual vibration is achieved by eliminating the natural frequency component of the cargo from the apparent external force, which is defined to include the effects of damping, nonlinearity, and parameter variation. Furthermore, an effective technique previously proposed by the authors for improving robustness to the modeling error of the natural frequency is extended. Numerical simulation results show that, even when cargo is hoisted up or down during operation, the proposed method realizes accurate positioning of the cargo without inducing residual vibration and sufficiently improves robustness. To the best of the authors' knowledge, this is the first frequency-domain robust open-loop control strategy that ensures a theoretical zero amplitude for residual vibration in the absence of modeling error in nonlinear crane hoisting operation. The developed method is not only a contribution to the realization of low-cost and efficient crane hoisting operation, but is also applicable to the control of other nonlinear damped systems that include time-varying parameters.

Multi-degree-of-freedom vibration reduction strategy of the solar array drive system

The operation disturbance induced by the solar array drive system (SADS) and the residual vibration of solar array following the attitude adjustment of the spacecraft obviously affect the dynamics environment, quick stabilization, and attitude stability of the high-precision spacecraft. However, these two kinds of vibration disturbance are characterized by distinct vibration categories, direction of vibration, and modal shapes. A multi-degree-of-freedom vibration reduction strategy (VRS) was presented to improve the dynamic characteristics of SADS and then to weaken these disturbances synthetically in this paper. SADS applying this VRS was modeled based on the virtual work principle, and the influence of the stiffness and damping parameters of this VRS on the SADS dynamic characteristics was analyzed. Then a prototype of vibration reduction device (VRD) was designed and verified by disturbance characteristic and modal experiments. The results indicate that the equivalent stiffness of VRD is critical to the natural frequency of SADS and thus should be carefully deliberated to avoid resonance. The equivalent damping of VRD always has positive correlation with modal damping. A good performance up to 40% in terms of operation disturbance suppression and a greater than 56% decrease of the damping time for 99% residual vibration have been obtained.

A smooth optimized input shaping method for two-dimensional crane systems using Bezier curves

Conventional input shaping commands have been successfully employed to suppress residual vibration in the payload rest-to-rest transportation process. Most of these methods introduce an impractical large and sudden variation on the acceleration profile. This paper presents a new smooth command input with adjustable time length and limited jerks. The command input is generated from the trolley displacement using a Bezier curve function by adjusting the position of the control points, which were divided into boundary and intermedium points. The boundary control points are selected to accurately move the trolley to its desired position with zero velocity and acceleration at the closing motion. The positions of the intermedium points were optimized using a particle swarm scheme for reducing maneuvering time while suppressing the payload oscillations at the end of the process and satisfying physical system constraints. Several cases were discussed for fixed cable length, variable cable involving single and multi-hoisting mechanisms, and different maneuver times. Simulated results were validated experimentally on a laboratory size crane. The results demonstrated that the proposed input Bezier-curve shaper provides an effective, reliable, and practical technique to be used for the payload transportation process. Moreover, the proposed method can generate asymmetrical acceleration and deceleration motions, which cannot be achieved using existing smoother commands.

A Review on Disturbance Analysis and Suppression for Permanent Magnet Linear Synchronous Motor

In high-end testing and manufacturing equipment, a trend exists whereby the traditional servo feed system with a ball screw and rotary motor will gradually be replaced by a direct drive system. The precision motion system driven by a permanent magnet linear synchronous motor (PMLSM) offers several advantages, including high speed, high acceleration, and high positioning accuracy. However, the operating precision of the feed device will be affected by the PMLSM robustness to nonlinear and uncertain disturbances, such as cogging force, friction, thermal effects, residual vibration, and load disturbance. The aim of this paper was to provide a survey on disturbance analysis and suppression approaches to improve the dynamic performance of PMLSM motion systems. First, the origin and inhibition methods of thrust ripple and friction are presented. Second, the mechanisms, modeling approaches, and mitigation measures of thermal effects are introduced. Additionally, the residual vibration characteristics and suppression methods are discussed. Finally, disturbance observers of periodic and aperiodic loads are introduced. These suppression methods from structural design and control compensation are then discussed in order to improve the dynamic response and steady-state accuracy of PMLSM.