Input Shaping Research Articles

Residual vibration suppression in uncertain systems: A robust structural modification approach to trajectory planning

In this paper a novel method to improve the residual vibration suppression in underactuated uncertain flexible systems through motion planning is proposed. The proposed technique relies on the concurrent use of input shaping and on the alteration of the mechanical properties of the system, which enables the enhancement of the robustness to uncertain parameters. Robustness is formulated through the parametric sensitivities of the natural frequencies that provide an analytical and non-probabilistic tool, which is embedded in the eigenstructure assignment algorithm developed in this work. The effectiveness of the proposed method is assessed through a benchmark testbed composed by a triple pendulum attached to a delta robot, that should execute rest-to-rest, residual vibration-free motion. Hence, residual vibrations of the pendulum are used to measure the accuracy and the sensitivity of the proposed combined shaper-IDSM approach. Both the numerical and experimental results confirm the advantages of the proposed technique for the suppression of the residual vibrations in uncertain systems over traditional techniques. In particular, robustness of the dominant tuning frequency is increased with respect to variations of the tip-end mass of the pendulum, representing a varying payload transferred by a robotic system.

Input shaping for travelling wave generation

Travelling wave patterns observed in the movement of certain aquatic animals has motivated research in the modification of flow behavior, especially to deal with boundary layer separation in airplane wings. Research has shown that inducing travelling waves on the top surface of the wing can generate sufficient momentum to prevent boundary layer separation without increasing the drag. Due to this effect of propagating waves on the aerodynamics, generation of travelling waves on solid surfaces is being widely studied. Recently, methods such as two-mode excitation, active sink and impedance matching have shown promise in generation of uniform travelling waves in solids with the help of piezo electric actuators. Unfortunately, there are some challenges involved in the experimental application of these methods. Although these techniques have shown to be adequate in laboratory settings, they require laborious tuning procedures which do not guarantee desired trajectories and are followed in light of interference from unwanted modes and their transients. Some methods rely on selective mode excitation, which can cause interference from unwanted modes if the transient behavior of the system is not accounted for. Feed-forward input shaping control methods are proposed that augment the open-loop piezo actuation method (two-mode excitation) and provide a more robust method for generating uniform travelling waves. The input shaping control alters the reference signal such that the parasitic behavior of unnecessary modes is cancelled out. The combination of the mode suppression and selective mode excitation through input shaping is verified experimentally for generation of a smooth travelling waves in finite structures.

On reference trajectory generation for overhead crane travel movements

Abstract Input shaping is a well-established approach for suppressing oscillations in systems with flexible modes. When applying input shaping, it is common to assume the system to be at rest initially, i. e., the initial conditions of the oscillatory part of the system have to be at zero. In this paper, we propose a method that allows relaxing the aforementioned assumption for a large class of input signals. The approach relies on the standard input shaper structure but re-parameterizes the shaper such that non-zero initial conditions are cancelled out by the inputs, resulting in zero residual oscillation. Natural physical limitations of the concept are discussed and the application to overhead cranes is presented. The method is validated both in simulation as well as in experiments using a small scale crane. In addition, a simplified trajectory generator is presented that tailors a standard seven-segment jerk-limited motion profile such that zero residual vibrations are achieved without any dedicated input shaping.

Vibration Suppression with Use of Input Shaping Control in Machining.

This article discusses the problem of vibrations during machining. The manufacturing process of generator turbine blades is highly complex. Machining using Computerized Numerical Control (CNC) requires low cutting parameters in order to avoid vibration problems. However, even under these conditions, the surface quality and accuracy of the manufactured objects suffer from high levels of vibrations. Hence, the aim of this research is to counteract this phenomenon. Basic issues related to vibration problems will also be also discussed and a short review of currently available solutions for both active and passive vibration monitoring during machining will be presented. The authors developed a method which does not require any additional equipment other than modified CNC code. The proposed method can be applied to any CNC machine, and is especially suitable for lathes. The method seeks to eradicate the phenomenon of vibrations by providing enhanced control through Input Shaping Control (ISC). For this purpose, the authors present a method for modeling the machining process and design an ISC filter; the model is then implemented in the Matlab and Simulink environment. The last part of the article presents the results, together with a discussion, and includes a brief summary.

Force impact suppression of contact transition state in robot grinding and polishing of industrial blades

When using robots to carry out grinding and polishing processing of industrial blades, due to factors such as non-zero approach speed and discontinuous dynamic characteristics, the robot grinding and polishing processing has contact force impact and oscillation problems during the contact transition process, which seriously affects the quality of the blade surface processing, contour accuracy, and control system stability. In order to solve the problem of large impact of contact force in robot grinding and polishing, this paper proposes an optimization method for impact suppression in the transition state of robot grinding and polishing. Taking the robot abrasive belt grinding and polishing as the research object, the adaptive weighted particle swarm algorithm is used to optimize the input shaper and realize the parameter self-tuning of the input shaping technology. The experimental results show that the stabilization time is shortened by about 86.5%, and the maximum overshoot of contact force is reduced by about 88.5% during contact transition. The method proposed in this paper can realize the smooth transition of the blade grinding and polishing process, does not need system modeling, effectively shorten the system stabilization time, reduce the maximum overshoot, and accelerate the system response speed, and it has strong stability and flexibility.

Residual Vibration Reduction of High-Speed Pick-and-Place Parallel Robot Using Input Shaping

Because of their elastic links and joints, high-speed parallel robots for pick-and-place operations inevitably suffer from residual vibrations that significantly degrade their positioning accuracy. An effective approach based on the input shaping technique is presented in this paper for suppressing the residual vibration in these parallel robots. After addressing the design principle of an input shaper for a parallel robot with flexible actuated joints, a robust optimal input shaper is developed by considering the configuration-dependent flexible modes and minimizing the maximum percentage of residual vibration at the end-effector. The input shaper allows a good overall performance to be achieved throughout the entire workspace. Experimental results on a 4-DOF SCARA-type parallel robot show that the residual vibration of the end-effector is dramatically reduced and the dynamic positioning accuracy of the robot significantly improved.

Application of Dynamic Input Shaping for a Dual-Mirror System

Abstract The task of trajectory planning for a dual-mirror optical pointing system greatly benefits from carefully designed dynamic input signals. This paper summarizes the application of multivariable input shaping (IS) for a dual-mirror system, starting from initial open-loop step-response data. The optical pointing system presented consists of two fast steering mirrors (FSM) for which dynamically coupled input signals are designed, while adhering to mechanical and input signal constraints. For the solution, the planned trajectories for the dual-mirrors are determined via (inverse) kinematic analysis. A linear program (LP) problem is used to compute the dynamic input signal for each of the FSMs, with one of the mirrors acting as an image motion compensation device that guarantees tracking of a planned trajectory within a specified accuracy and the operating constraints of the FSMs.

Equivalent Rope Length-Based Trajectory Planning for Double Pendulum Bridge Cranes with Distributed Mass Payloads

The hoisting form in which the payload is hung on the hook by two rigging ropes is widely used in the industry, but it also results in the complex double pendulum dynamic of the bridge crane, making the anti-swing trajectory planning full of challenges. In this paper, based on the concept of the equivalent rope length, an equivalent single pendulum model of the double pendulum bridge crane with the distributed mass payload is established. On this basis, the particle swarm optimization algorithm is adopted to solve the equivalent rope length and calculate the parameters of the anti-swing velocity trajectory based on the phase plane method. To evaluate the effectiveness of the proposed method, experiments with a laboratory double pendulum bridge crane are conducted. Experimental results demonstrate that the residual oscillation angle of the payload of the proposed method is smaller than those of the existing methods, such as the trajectory planning without the equivalent rope length, input shaping and command smoothing.

Global Sensitivity Analysis based Design of Input Shapers

This paper focuses on the development of a global sensitivity based design of robust input shapers. The Derivative-based Global Sensitivity Measure (DGSM) which consists of the expected value of the absolute value of the gradient of the terminal residual energy with respect to the uncertain parameters, is used to tradeoff performance to robustness. A multi-objective cost function which is a convex combination of the terminal residual energy for rest-to-rest maneuvers and the DGSM, is used to design robust input shapers. The proposed approach is illustrated on a single spring-mass-dashpot system and the benchmark floating oscillator. As compared to the traditional Zero Vibration Derivative Input Shaper, the proposed approach is demonstrated to reduce the average residual energy over the domain of uncertainty.

Redefinition and re-evaluation of polydyne

The polydyne cam profile provides ‘perfect tracking’ with no transient vibrations and has been used in important mechanical applications like automotive valve cams. In this paper, the polydyne curve was redefined and re-evaluated as the feedforward control input. Firstly, the polydyne curve was redefined as an acceleration trajectory and it was shown that the feedforward control with polydyne input is equivalent to the vibration suppression perfect tracking controller (PTC) in terms of the nominal output (position of the control object). It was also clarified that the conditions of polydyne mean the pole-zero cancelation and continuity at the beginning and end of the input, and that the principle to suppress vibrations is different from the dead-beat control such as the input shaping. Secondly, the enhancements of polydyne were introduced. The sampled-data polydyne is the formulation in discrete-time domain. The condition of continuity in discrete-time domain can show the order of smoothness of sampled data. And it is available for generating low-vibration bang-bang trajectory, in which the acceleration is smoothly ramped between the acceleration and deceleration sections. Thirdly, the concept of polydyne was adapted to general functions like trigonometric functions. For example, the vibration manipulation function (VMF) satisfies the conditions of polydyne for the undamped system. In conclusions, feedforward control using the polydyne curve is a unique method to suppress the transient vibration completely and effective in high-speed and high-precision digital control like servo control in a hard drive.

Equilibrium Configuration Analysis and Equilibrium-Based Trajectory Generation Method for Under-Constrained Cable-Driven Parallel Robot

Under-constrained cable-driven parallel robots (UCCDPRs) manipulate the end-effector (EE) by employing fewer number of cables than the degree of freedom of the EE, which causes unwanted swaying motions and oscillations. These unwanted vibrations can be suppressed by using the regenerated EE trajectory through the input-shaper. However, in the case of the UCCDPR systems, generating the feasible EE trajectory and deriving the natural frequency for designing the input-shaper is not straightforward since finding the stable equilibrium configuration is challenging. This paper proposes a novel methodology to find the stable equilibrium configuration of the general UCCDPRs in the assigned EE position. With the proposed method, the EE trajectory can be reproduced as a vibration suppression trajectory through an input shaper designed based on the analysis of the natural frequencies, as well as generating feasible EE trajectories based on the equilibrium configuration. Also, even if the orientation trajectory is not given and only the position trajectory is given, the cable length to follow the given position trajectory of the EE can be obtained based on the equilibrium configuration corresponding to the given position trajectory. Computer simulations and hardware experiments were conducted to verify the effectiveness and performance of the proposed method.

Modelling and Oscillation Control of a Quadrotor with Cable-suspended Load

A quadrotor with cable-suspended load is a type of aerial transport vehicle to carry a payload attached with a cable to underside of the quadrotor. It has potential applications requiring transporting goods quickly, such as search-and-rescue and logistics. One important requirement is that the controller should be able to safely move the quadrotor and suppress excessive load swing which can be dangerous. This work presents a modelling of this system and a PID position controller with feedforward input shaping to suppress load swing. The model is formulated with Euler-Lagrange equations. This model assumes offset between quadrotor centre-of-mass and suspension point of the cable, as such is able to capture double-pendulum-like behaviour of the real system. Simulations are done to validate the model and controller to suppress the load, swing and its robustness to varying percentages of modelling errors.

A Case Study of a Hydraulic Servo Drive Flexibly Connected to a Boom Manipulator Excited by the Cyclic Impact Force Generated by a Hydraulic Rock Breaker

This study deals with the mathematical modeling, dynamic analysis, hybrid control structure, and experimental tests of a hydraulic servo drive (HSD) flexibly connected by a vibration isolator as a spring damping device (SDD) to a boom manipulator excited by the cyclic impact force generated by a rock breaker. Based on the dynamic model of the HSD-SDD system, the frequency ratios of the rigid and flexible connections to the mass load were determined. The HSD-SDD model was saved as a Hammerstein model with unknown parameters. The dynamic linear part of the HSD-SDD model was adopted as an autoregressive model with an exogenous input (ARX) model. The online proportional integral derivative (PID) controller parameter-tuning algorithm was implemented in several steps. The PID controller tuning process occurs in real time, and the optimal setting of the PID controller depends on the critical ultimate gain and period set at the stability limit. A hybrid control structure consisting of a feedback controller and feedforward controller was proposed. A combination of input shaping and feedforward filters is used, thus the badly damped vibrations are more effectively compensated, resulting in better control accuracy of the HSD-SDD system. The goal of optimizing the hybrid control structure is to determine a feedforward filter coefficient that minimizes the objective function. Finally, the global minimum is calculated from the control error based on the measurement of the input and output signals. The highlight of this study is the development of a new hybrid control structure to compensate for badly damped vibrations.

Automatic parameter selection ZVD shaping algorithm for crane vibration suppression based on particle swarm optimisation

Abstract This work introduces the foundation of a new class of input shaping algorithm, designed based on the particle swarm optimisation. This algorithm is utilised to control the residual vibrations in the crane system. The motivation is the development of simple algorithms and architecture for controlling the motion in under-actuated nonlinear systems with minimal modelling effort. By recording the payload swing signal of the crane only once, the approach can automatically calculate the optimisation amplitude and time locations of the impulses required by a common zero-vibration-derivative (ZVD) technique. In this work, we use this algorithm to design a ZVD shaper for controlling the motion of an under-actuated nonlinear crane model system. We validate the approach using experiments. If this algorithm is implanted into the embedded system and applied to the actual crane, which will solve the problem of the traditional ZVD parameter adjustment and improve the vibration suppression effect of the ZVD Algorithm.

Hybrid vibration control of an industrial CFRP composite robot-manipulator system based on reduced order model

This paper introduces a novel hybrid vibration control of an industrial flexible link manipulator (FLM) with carbon-fiber reinforced polymer (CFRP) composite material. The hybrid controller consists of a closed-loop direct strain feedback controller (DSFC) and a new open-loop input shaper (OLIS), and its performance is examined and compared by numerical simulation and experiment. Vibration attenuation is also verified by a spare sensor, an accelerometer. Thanks to the design of an analog isolator circuit, data acquisition of the real-time experiments are carried out noise-free from the servo driver. Reduced-order-model (ROM) is generated for the composite link with three different loading conditions and model for servo system is derived via system identification. Impulse force test hammer (IFTH) equipment is used to excite the system with force input and the results of the experiments/simulations confirm that the controller is robust against the impulse disturbances. As a result, a decrease of 88 ± 6.9 percent in vibration amplitudes and a decrease of 90 ± 7 percent in vibration duration confirms that the proposed controller is effective for vibration control of the flexible arm even under disturbance. Controller performance also enabled the FLM to work with payloads 16 times of its own weight.

Payload oscillation control of tower crane using smooth command input

This paper presents a smooth command (SC) input shaper for suppressing payload oscillations in rest-to-rest simultaneous radial and tangential motions of a tower crane. The radial and tangential acceleration profiles of the compound motions are represented by multi-sine wave functions with independent and variable maneuvering time. The proposed SC is designed using a nonlinear mathematical model of the tower crane while the parameters of the acceleration profiles and maneuvering times were optimized using a particle swarm algorithm (PSO). The simulated results were verified experimentally on a laboratory scale tower crane. The results confirm that the proposed SC input effectively canceled residual vibrations of the payload compound motions with a time length comparable to zero vibrations (ZV) shaper. Moreover, sensitivity analysis to variations in cable length reveals that the proposed command input is robust over a wide range of cable lengths.

A fuzzy logic-based intelligent decision support system for the selection of an appropriate input-shaping technique for controlling flexible link systems

ABSTRACT Most robotic systems consist of heavy machine elements that help reduce the vibrations generated by motion and that support good positional accuracy. Large-sized actuators are needed for such systems. Energy consumption significantly increases in oversized robotic systems. The proposed solution to which is to design robotic systems in lightweight and flexible forms. This makes possible smaller overall structure and actuator sizes. However, such systems suffer from residual vibrations. One well-known control solution to residual vibration problem could be input shaping techniques. In this study, a new Fuzzy Logic-based intelligent input shaping selection technique has been proposed. With this proposed approach, it is possible to set optimum settling time, positioning accuracy of robotic systems, and minimum residual vibrations by implementing the crucial open-loop control approach. Comprehensive experience is needed to overcome design issues on command shaping and system modeling. Based on these design criteria constraints and extensive knowledge requirements, the recommended solution is a Fuzzy Logic-based intelligent input shaping technique for accurate modeling and parameter estimation of the systems. The proposed approach is a Fuzzy Logic-based intelligent input shaper selection and input shaper setting determination algorithm. The applicability of the proposed method was verified on the Quanser Flexible Link experimental setup.

A cascade vibration-free trajectory planning method and its application in the FAST feed support system

In order to solve the vibration problem of low-damping flexible mechanism in motion, a cascade vibration suppression (CVS) trajectory planning method combining the advantages of the optimal double S-curve trajectory planning method and the input shaping method is proposed. The CVS method can effectively suppress the vibration in the period of uniform motion. The correctness of this method is proved by theoretical analysis and digital simulation. Finally, the application results of the proposed method in the FAST feed support system show that it can effectively improve the motion accuracy of the parallel cable mechanism, especially when the motion speed is constant, improving the position tracking accuracy by over 20%.

Precision open-loop control of piezoelectric actuator

Due to space constraints, some micro-assemblies and micro-operating systems cannot install sensors, so it is challenging to achieve closed-loop control. For this reason, a precision open-loop control strategy for piezoelectric actuators is proposed. Firstly, based on the PI model and the proposed threshold partition method, the hysteresis model of the piezoelectric actuator with rate-dependent and few operators is established. Then the hysteresis error of the piezoelectric actuator is compensated by the inverse model obtained. Secondly, the creep model of the logarithmic piezoelectric actuator with simple expression and few parameters is established. Then, a creep controller without demand inverse is designed to compensate for the creep error of the piezoelectric actuator. Finally, a ZVD (Zero Vibration Derivative) input shaping method with good robustness is given to eliminate the oscillation generated by the piezoelectric actuator under the action of the step signal. The experimental results show that the displacement error of piezoelectric actuator is reduced from −9.07 to 9.46 μm to −1.22 to 1.78 μm when the maximum displacement is 120 μm after hysteresis compensation; after creeping compensation, within the action time of the 1200 s, the displacement creep of the piezoelectric actuator was reduced from 5.5 μm before compensation to 0.3 μm; after the oscillation control, the displacement overshoot of the piezoelectric actuator is reduced to 0.6% of that before control.

Performance analysis of shapeable-maximum power point tracking technique from thermoelectric-solar hybrid energy harvesting sources on mobile devices

ABSTRACT In this study, the performance analysis of the thermoelectric-solar (TEM-SA) hybrid energy harvesting system is presented. The proposed system is analyzed for continuous and discontinuous load condition and mobile devices as a load. In this feed forward type of controller, Inverse Dynamic Analysis Input Shaper (IDAIS) is introduced to shape the unsteady response behavior to become stable input and is named as Shapeable MPPT (SMPPT). The experimental analysis is done to verify the performance of the new arrangement proposed circuit of HEHS which is used only one MPPT board. An initial test is made in determining which energy-efficient sources are capable to produce the highest output. Then the device that produces the highest output is connected to the new arrangement proposed circuit incorporated SMPPT unit, the converter, and the energy storage. With constant source supply, full charging time obtained for mobile phone is 4 hours and 30 minutes which is equivalent to the charging period using the normal alternating current sources. Greater focus is then given to the charging time for some types of mobile phones that have different battery capacity mAH. From the verification results, it is found that the load that having lowest mAh values steadily able to reach the full charging period faster than the others.