Minimum Residual Vibration Research Articles

Input Shaping for Flexible Systems with Non-Zero Initial Conditions

Input shaping is a finite-impulse response (FIR) filter whose coefficients are designed to produce a shaped input that avoids exciting lightly-damped modes. As a result, flexible systems can be commanded to move quickly from point to point with minimum residual vibration. However, traditional input shaping techniques assume zero initial conditions, limiting their usability for systems with non-zero initial conditions, such as, emergency stops of cranes. Besides, in practice, movement of flexible systems is often initiated when the systems are not completely stationary. In these situations, the performance of the input shaping technique deteriorates. In this paper, a modification of shaper’s impulse sequence at the beginning of the move is proposed to bring the moving flexible system to a stop before commencing movement. The modification utilizes the work and energy method to determine the distance and time as functions of the initial states for base excitation of flexible systems, rendering its application to nonlinear systems. By concatenating this modification with the existing input shapers, a novel shaper called the non-zero initial conditions zero-vibration-derivative (NI-ZVDk) input shaper is introduced. The NI-ZVDk input shaper effectively prevents the movement of flexible systems from their initial states. To demonstrate the effectiveness of the approach, a 2-mass system is utilized as a benchmark for general flexible systems with 2 degrees of freedom. Various types of motion, including pure translation, pure rotation, and combined translation-rotation, are considered. Extensive simulation results showed that, using the proposed NI-ZVDk input shaper, the flexible systems can move from non-zero initial conditions to their desired destinations with less time and less residual vibration. HIGHLIGHTS The Input Shaping (IS) technique is used to suppress residual vibrations by creating destructive interference in impulse responses This method presents a novel design modification for IS when initial conditions are non-zero This technique can be extended for use in various nonlinear vibratory systems For example, it can be used when a crane needs to stop abruptly from non-zero initial conditions without residual vibrations GRAPHICAL ABSTRACT

Research on vibration suppression of rigid flexible coupling manipulators based on genetic algorithm optimization

Aiming at the problem that the rigid flexible coupling manipulator generates elastic vibration during movement, which reduces the positioning accuracy and work efficiency, we propose a method of end vibration suppression based on cosine function superposition and multi population genetic algorithm. First, we get the relationship between the elastic vibration of the flexible arm and the joint trajectory motion according to the dynamic model of the system. Then, the cosine function superposition is used as the basis function to construct motion parameters of joints and the minimum residual vibration amplitude at the end of the flexible arm is used as the objective function. The undetermined coefficients in the basis function are optimized by multi population genetic algorithm to obtain the optimal trajectory. Finally, the simulation and experiment results show that the residual vibration amplitude is reduced by 60.6%. The proposed method can suppress the residual vibration at the end of the flexible arm and improve the work efficiency.

Discrete material optimization of composite structures subjected to initial excitation for minimum residual vibration

This work studies design optimization of laminated structures subjected to initial excitation for minimum residual vibration. The Discrete Material Optimization (DMO) method with solid isotropic material with penalization (SIMP) model is employed to perform the design optimization of stacking sequence, fiber angles, and selection of material for the composite structures. The transient vibration analysis of the composite structures excited by initial excitation can be performed via the finite element method, where the residual vibration is identified. The integration of squared displacement of residual vibration can be selected as the objective function, which can be greatly simplified by Lyapunov equation to reduce the computational time. A modal reduction method is employed to further improve the computational efficiency of vibration analysis. Since many linear constraints are included in the optimization formulation for discrete material optimization, sequential linear programming (SLP) algorithm with a trust region approach is used to conduct the optimization iteration with the help of the design sensitivities obtained by an adjoint method. Numerical examples are presented to illustrate the effectiveness of the proposed method. The influences of the distribution and magnitude of several initial excitations on the optimized solutions are discussed.

Optimization Process for Polynomial Motion Profiles to Achieve Fast Movement With Low Vibration

Since fast and accurate motion profiles are directly related to the productivity of manufacturing, many studies have been performed to optimize such motion profiles. However, previous research has not provided an appropriate solution regarding which motion profile is the best for a given situation. Therefore, in this article, we propose an optimization process for polynomial-function-based motion profiles to achieve fast movement with low vibration. The proposed process describes a method of optimizing an $n$ th-order polynomial motion profile to achieve a fast transfer time and minimal residual vibration characteristics with extra robustness to system uncertainty for a given moving distance and given actuator capacities. Then, we describe how to determine the best order of the optimized motion profile for given conditions, such as the allowable computational load, the required residual vibration bound, and the required robustness against system uncertainties. The performance of the optimized motion profile is demonstrated, and the suggested process for obtaining the best order of the optimal motion profile is applied to a practical example of a wafer transfer robot.

Topology optimization of damping layers in shell structures subject to impact loads for minimum residual vibration

This paper studies optimum distributions of damping material in shell structures subject to impact loads by topology optimization. The optimization aims at reducing the residual vibration responses after the application of impact loads. In particular, the dependence of both structural forced vibration and residual vibration on the damping layer distribution is considered by transient dynamic responses based optimization approach. Until now, optimum distributions of damping material are always carried out based on frequency domain responses or structural dynamic characteristics. But for the studied problem, transient responses based optimization is more straightforward when the impact loads are known. When involving transient responses, the calculations of structural responses and sensitivities are always difficult and time-consuming. To deal with these problems, we use an integrated square performance measure of residual vibration as the objective function, which can be greatly simplified by Lyapunov equation, and use an efficient adjoint method to calculate the sensitivities. The topology optimization is implemented using the common solid isotropic material with penalization (SIMP) method. Numerical examples are carried out to illustrate the validity and utility of the proposed approach, and the numerical results also show the advantages of transient dynamic responses based optimization for the studied problem.

The Design of Input Shapers Which Eliminate Nonzero Initial Conditions

Input shaping is widely used in the control of flexible systems due to its effectiveness and ease of implementation. Due to its open-loop nature, it is often overlooked as a control method in systems where parametric uncertainty or force disturbances are present. However, if the disturbances are known and finite in duration, their effect on the flexible mode can be approximated by formulating an initial condition control problem. With this knowledge, an input shaper can be designed, which cancels the initial oscillation, resulting in minimal residual vibration. By incorporating Specified Insensitivity robustness constraints, such shapers can be designed to ensure good performance in the presence of modeling uncertainty. This input shaping method is demonstrated through computer and experimental methods to eliminate vibration in actuator bandwidth-limited systems.

Trajectory planning with residual vibration suppression for space manipulator based on particle swarm optimization algorithm

Space manipulator suffers from vibration problems mainly due to the flexibility of joints and links in a microgravity environment. This article presents a new optimization method of trajectory planning with minimum residual vibration for space manipulator system which is modeled by absolute coordinate-based method. First, absolute nodal coordinate formulation, which can describe large rotation and large deformation of flexible bodies precisely, is used to describe the deformation of flexible links, and natural coordinate formulation with nonlinear torsion stiffness function is used to model flexible joints. Then, joint rotation trajectory resulting from the planned end-effector trajectory by inverse kinematics theory is discrete through the proposed cosine-based function that has been validated to suppress the residual vibration. The particle swarm optimization algorithm is employed to achieve minimum residual vibration by optimizing redundant coefficients of movement derived from inverse kinematics theory. The effectiveness of the proposed method is illustrated via simulation of a planar three-link manipulator taking large deformation and large rotation into account. Results show that the optimized method can exhibit better features for the residual vibration suppression as compared to those of the original cosine-based trajectory.

Input shaping control of a nuclear power plant’s fuel transport system

In this paper, the residual vibration control problem of a nuclear power plant’s fuel-transport system is discussed. The purpose of the system is to transport fuel rods to the target position within the minimum time. But according to observations, the rods oscillate at the end of the maneuver, causing an undesirable delay in the operation and affecting the system’s performance in terms both of productivity and of safety. In the present study, a mathematical model of the system was developed to simulate the under-water sway response of the rod while keeping in view the effects of the hydrodynamic forces imposed by the surrounding water. Experiments were performed to validate the model’s correctness. Further, simulation results were used to design the input shaping control that generates shaped velocity commands for transport of the fuel rods to the target position with the minimum residual vibration. It was observed that due to the under-water maneuvering, the fuel-handling system behaves as a highly damped process and that the generated shaped velocity commands fail to effect the desired suppression of the residual vibration. Therefore, keeping in view the highly damped nature of the system, a modified shaped command was generated that transported the fuel rods to the target position with the minimum residual vibration.

Minimum Residual Vibration Sliding Mode Servo Control for Computer Disk Drives

This paper presents a discrete time design of sliding mode servo control with minimum residual vibration that significantly affects settling of the disk drive head to a target track. By optimizing the acceleration rate, the convergence rate to the sliding hyperplane for seek is determined for minimum residual vibration at the end of track seek. The scheme retains the intrinsic nature of the sliding mode servo control enforcing the actuator to slide along the optimally designed reference profile such that no substantial seek performance degradation occurs at all. Simulation and experiment results are also presented to demonstrate utility of the proposed minimum residual vibration sliding mode controller.

Design and optimization of input shapers for liquid slosh suppression

The need for fast maneuvering and accurate positioning of flexible structures poses a control challenge. The inherent flexibility in these lightly damped systems creates large undesirable residual vibrations in response to rapid excitations. Several control approaches have been proposed to tackle this class of problems, of which the input shaping technique is appealing in many aspects. While input shaping has been widely investigated to attenuate residual vibrations in flexible structures, less attention was granted to expand its viability in further applications. The aim of this work is to develop a methodology for applying input shaping techniques to suppress sloshing effects in open moving containers to facilitate safe and fast point-to-point movements. The liquid behavior is modeled using finite element analysis. The input shaper parameters are optimized to find the commands that would result in minimum residual vibration. Other objectives, such as improved robustness, and motion constraints such as deflection limiting are also addressed in the optimization scheme. Numerical results are verified on an experimental setup consisting of a small motor-driven water tank undergoing rectilinear motion, while measuring both the tank motion and free surface displacement of the water. The results obtained suggest that input shaping is an effective method for liquid slosh suppression.

INPUT SHAPING TECHNIQUES FOR LIQUID SLOSH SUPPRESSION

ABSTRACTThe need for fast maneuvering and accurate positioning of flexible structuresposes a control challenge. The inherent flexibility in these lightly damped systemscreates large undesirable residual vibrations in response to rapid disturbances. Severalcontrol approaches have been proposed to tackle this class of problems, of which theinput shaping technique is appealing in many aspects.While input shaping has been widely investigated to attenuate residual vibrations inflexible structures, less attention was granted to expand its viability in furtherapplications. The aim of this work is to develop a methodology for applying inputshaping techniques to suppress sloshing effects in open moving containers to facilitatesafe and fast point-to-point movements. The liquid behavior is modeled using finiteelement analysis. The input shaper parameters are optimized to find the commandsthat would result in minimum residual vibration. Other objectives, such as improvedrobustness, and motion constraints such as deflection limiting are also addressed in theoptimization scheme. Numerical results are verified on an experimental setupconsisting of a small motor-driven water tank undergoing rectilinear motion, whilemeasuring both the tank motion and free surface displacement of the water. Theresults obtained suggest that input shaping is an effective method for suppressingresidual liquid vibrations.

Controller Design Procedure for Two-Mass Systems With Single Flexible Mode

Many manufacturing machines must execute motions as quickly as possible to achieve profitable high-volume production. Most of them exhibit some flexibility, which makes the settling time longer and controller design difficult. This paper develops a control strategy that combines feedforward and feedback control with command shaping for systems with collocated actuator and sensor. First, a feedback controller is designed to increase damping and eliminate steady-state error. Next, an appropriate reference profile is generated using command-shaping techniques to ensure fast point-to-point motions with minimum residual vibration. Finally, a feedforward controller is designed to speed up the transient response. The proposed proportional-integral-derivative (PID) controller design ensures that two important resonant frequencies nearly match, making the design of the input commands much simpler. The resulting control strategy is successfully demonstrated for a generic dimensionless system that incorporates some modeling errors to assess robustness.

Suppression of motion-induced residual longitudinal vibration of an elastic rod by input shaping

Various input-shaping schemes such as the “zero-vibration” (ZV), “zero-vibration-and-derivative” (ZVD), “negative ZV” (NZV), and “negative ZVD” (NZVD) schemes have previously been proposed to suppress motion-induced residual vibration of lightly damped structures. In such schemes, the input command of the dynamical system in question is properly administered (i.e., shaped), so that the dominant induced vibration modes are annihilated through destructive interference. Here we are concerned with the effects of system payload on the vibration reduction capabilities of the aforementioned input-shaping schemes, especially when they are applied to continuous systems. By use of the simple structure of a linearly elastic rod as a specific example, it is demonstrated that both the minimum achievable residual vibration amplitude and the tolerance of detuning parameter errors of the input-shaping schemes are sensitive to the amount of payload on the system. It is therefore imperative to take the factor of system payload into account in the design of practical input shapers.

Settling control with reference redesign for dual actuator hard disk drive systems

This paper considers settling control of a recording head for a dual actuator system for hard disk drives consisting of a coarse actuator (voice coil motor, VCM) and a fine actuator (peizoelectric transducer, PZT). The design method proposed in this paper is called the dual actuator reference trajectory re-design (RTRD). In this method, the design is divided into three steps. In the first step, the coarse actuator loop is designed to achieve stability and basic performance. In the second step, the fine actuator path is designed by loop shaping for superior performance of the overall system. Finally, the reference signals are generated for both the coarse and fine actuators by minimizing the square integral of jerk during the transition. The reference signals are updated or redesigned in real time as the recording head approaches the target track for smooth landing and minimal residual vibration. The “soft switching” technique is applied for gradually introducing the fine actuator (PZT actuator), which may shorten the settling time and achieve a smooth settling response. The effectiveness of the proposed approach is evaluated by simulations.

Flexible robot manipulator path design to reduce the endpoint residual vibration under torque constraints

In this work, a new method is presented for generating the path that significantly reduces residual vibration under the torque constraints. The desired path is optimally designed so that the required movement can be achieved with minimum residual vibration. From the previous research works, the dynamic model has been established including both the link and the joint flexibilities. The performance index is selected to minimize the maximum amplitude of residual vibration. The path to be designed is developed by a combined Fourier series and polynomial function to satisfy both the convergence and boundary condition matching problem. The concept of correlation coefficients is used to select the minimum number of design variables, i.e., Fourier coefficients, the only ones which have a considerable effect on the reduction of residual vibration. A two-link manipulator is used to evaluate this method. Results show that residual vibration can be drastically reduced by selecting an appropriate path in both cases of unlimited and torque-limited.

Path design of redundant flexible robot manipulators to reduce residual vibration in the presence of obstacles

A method is presented for generating the path that significantly reduces residual vibration of the redundant, flexible robot manipulator in the presence of obstacles. The desired path is optimally designed so that the system completes the required move with minimum residual vibration, avoiding obstacles. The dynamic model and optimal path are effectively formulated and computed by using a special moving coordinate, called VLCS, to represent the link flexibility. The path to be designed is developed by a combined Fourier series and polynomial function to satisfy both the convergence and boundary condition matching problems. The concept of correlation coefficients is used to select the minimum number of design variables. A planar three-link manipulator is used to evaluate this method. Results show that residual vibration can be drastically reduced by selecting an appropriate path, in the presence of obstacles.

Task-specific optimal simultaneous kinematic, dynamic, and control design of high-performance robotic systems

A task-specific optimal simultaneous kinematic, dynamic and control design approach is proposed for high-performance computer-controlled machines, such as robots. This mechatronics design approach is based on the trajectory pattern method and a fundamentally new design philosophy that such machines, in general, and ultrahigh-performance machines, in particular, must only be designed to perform a class or classes of motions effectively. In the proposed approach, given the structure of the manipulator, its kinematic, dynamic, and control parameters are optimized simultaneously with the parameters that describe a selected trajectory pattern with which the desired class(es) of task(s) can best be performed. In one example, a weighted sum of the norms of the higher harmonics appearing in the actuating torques and the integral of the position and velocity tracking errors are used to form the optimality criterion. The selected optimality criterion should yield a system that is optimally designed to accurately follow the specified trajectory at high speed. Other objective functions can be readily formulated to synthesize systems for optimal performance. Based on the developed design methodology, a two-degrees-of-freedom robot manipulator with a closed-loop chain is optimally designed and constructed for point-to-point motions. The preliminary results of experiments indicate that the robot can, in fact, execute point-to-point motions rapidly and with minimal residual vibration. The potentials of the developed method and its implementation for generally defined motion patterns are discussed.

Study on Positioning Control Algorithm for Stacker Cranes.

Recently, many types of automatic logistics systems have been developed in order to meet various requirements. A stacker crane functions as a key component in the automatic warehouse system and is required to move quickly with minimum residual vibration. The driving motor is controlled by the controller which cannot control its speed in low speed region. So, in the last stage of motion control, the motor is driven at the lowest controllable speed and is stopped by the mechanical and electric brake. In this paper, we consider the problem of how to realize the best residual vibration settling characteristics for the horizontal motion axis by the optimization of three proposed braking parameters (creep velocity, creep motion distance, delay time between electric braking and mechanical braking). This research led to the following conclusion and proposal. (1) The optimal onset timing of the mechanical braking is the time when the phase of the acceleration at the upper part of the crane reaches 90∼180°. (2) We proposed "soft braking control" which means that electric braking is applied earlier than mechanical braking and reduced the settling time 70% compared with the case which used only mechanical braking.

Trajectory synthesis and inverse dynamics model formulation and control of tip motion of a high performance flexible positioning system

A new method to synthesize tip-point trajectory for mechanical system with structural flexibility and formulate the inverse dynamics model is presented. The inverse dynamics models are derived for selected trajectory patterns in parametric form [1–3]. The trajectories are synthesized such that the natural modes of vibration are not excited and minimal residual vibration is achieved. The structure of the inverse dynamics models permits the construction of tracking controllers with minimal on-line and off-line computations. The results of computer simulation for a high-performance positioning system are presented.

Fourier-based optimal design of a flexible manipulator path to reduce residual vibration of the endpoint

SUMMARYA method is presented for generating the path which significantly reduces residual vibration. The desired path is optimally designed so that the system completes the required move with minimum residual vibration. The dynamic model and optimal path are effectively formulated and computed by using special moving coordinates, called virtual rigid link coordinates, to represent the link flexibilities. Also joint compliances are included in the model. Characteristics of residual vibration are identified from the linearized equations of motion. From these results, the performance index is selected to reduce residual vibration effectively. The path to be designed is developed by a combined Fourier series and polynomial function to satisfy both the convergence and boundary condition matching problems. The concept of correlation coefficients is used to select the minimum number of design variables, i.e. Fourier coefficients, the only ones which have a considerable effect on the reduction of residual vibration. A two-link manipulator is used to evaluate this method. Results show that residual vibration can be drastically reduced by selecting an appropriate manipulator path.