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In this paper, three control algorithms based on input shaping method are developed to suppress the residual vibration of a flexible beam. The flexible beam is modeled as an under-damped system. Three input shapers, ZV, ZVD, and ZVDD, are used to control the flexible beam. The three control algorithms are implemented by using the Mechatrolink-III motion system. The experiments are performed to verify the effectiveness of the three control algorithms.
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Journal of Computer Science and Cybernetics, V.32, N.1 (2016), 73–88
DOI: 10.15625/1813-9663/32/1/6765
1,2Head of Control and Automation Laboratory, Hochiminh City University of Technology;;
Abstract. In this paper, three control algorithms based on input shaping method are developed to
suppress the residual vibration of a flexible beam. The flexible beam is modeled as an under-damped
system. Three input shapers, ZV, ZVD, and ZVDD, are used to control the flexible beam. The three
control algorithms are implemented by using the Mechatrolink-III motion system. The experiments
are performed to verify the effectiveness of the three control algorithms.
Keywords. Flexible beam, input shaping, industrial network, motion control, Mechatrolink-III,
residual vibration.
For industrial motion system, the vibration suppression is one of key techniques which re-
searchers and engineers want to address the problem. Especially, with growth of accuracy
manufacturing system, a need for the development of residual vibration technique has there-
fore arisen. One of efforts to suppress residual vibrations has been tried by modifying the
motion profile. The proposed input motion design procedure in [1] was to define asymmetri-
cal S-curve velocity profiles with fast acceleration and slow deceleration of AC servo motors
which intermittently move the punching machine to desired positions with the reduced am-
plitude of residual vibrations. The authors in [2] developed an asymmetric S-curve profile
method with jerk bounded to obtain high precision and reduce the residual vibration. Ha et
al. [3] introduced a jerk ratio to scale down the jerks during the deceleration period. When
the jerk ratio increases, the residual vibration decreases in motion system. Particularly, the
high running speed can cause strong excitations in precision positioning machines. Thus,
in [4], a low-vibration motion profile generation method to lessen systematic excitations was
presented. The acceleration profile is designed by using a level-shifted sinusoidal waveform
to have an S-shape in order to control its change rate. In [5, 6] the constraints between
first natural frequency and deceleration time of motion profile was introduced. In these ex-
periments, the acceleration, constant velocity and deceleration time intervals of trapezoidal
velocity profile are selected by considering the lowest natural frequency at the stopping po-
sition. The root mean square (RMS) values are lowest if the inverse of the deceleration time
equals to the first natural frequency. It is highest if the inverse of the deceleration time
equals to the half of the first natural frequency.
Input shaping strategy is an attractive issue for reducing residual vibration in motion
control system due to the robustness and effectiveness. Since Singhose et al. in [7] described
a method for limiting vibration by adding constraints on the derivative of residual vibration
magnitudes, various approaches to suppress the residual vibrations has been achieved such
2015 Vietnam Academy of Science & Technology
as hybrid input shaping [8], a three-impulse sequence input shaper [9] or lookup table con-
trol method [10]. However, Singhose’s work performs the robustness to modeling errors and
effectiveness to apply in the industrial motion system. In this method, engineer needs to
determine the natural frequency and damping ratio in order to build an input shaping con-
troller. Recently, researchers in [11] studied the effect of natural frequency error to residual
vibration in three input shaping controller. ZVD and ZVDD shaper are more robust than
ZV shaper if the error in natural frequency of flexible beam exists.
Mechatrolink-III protocol is a real-time protocol that is based on Ethernet technology
and was developed by Yaskawa [12]. Mechatrolink-III is chosen to investigate because of their
advantages such as fast communication, high reliability and rapid design. The performance
of Mechatrolink-III was analyzed in [13] and slave station was designed in [14]. The protocol
guarantees the short cycle time which is considered as a typical factor in motion control
In this paper, the input shaper ZV, ZVD, and ZVDD are applied to suppress the residual
vibration of a flexible beam when the beam moves to the desired position. The control
algorithm is implemented using Mechatrolink-III. The experiments are carried out to verify
the effectiveness of the control algorithm.
This paper is organized as follows. In Section 2, the model formulation of flexible beam is
presented. Section 3 proposes the implementation of input shaper as an engineer solution. In
Section 4, the hardware development and software development of Mechatrolink-III motion
controller are shown. In Section 5, the experimental verifications and results are carried out.
Finally, this paper ends with conclusions in Section 6.
Consider a mass mounted on the end of flexible beam as Fig.1 (a). Both of the beam and the
mass of the tip end are made from aluminum alloy. The material parameters of the beam
are as follows. The beam has length Land mass per unit length ρ, as shown in Fig.1 (a).
The modulus of elasticity is E, and the internal bending moment of the beam is I.
Assuming that the end-mass is much greater than the mass of the beam. Define mtas
the total mass at the tip end of the beam. It should be noted that mtcan be computed as
mt=mbeam +m, (1)
where mbeam is the effective mass of the beam, and mis the mass of the tip end. Define the
effective mass of the beam mbeam as
mbeam =ρZL
dx. (2)
Using the first mode, the shape function of the beam (without the mass of the tip end
m) can be obtained as follows.
Figure 1. (a) Cantilever beam model; (b) free-body diagram; (c) a section of beam
y(x) = ρLg
EI x3
where y(x) is the deflection of the static beam.
Substituting Eq. (3) to Eq. (2) yields.
mbeam = 0.23357ρL. (4)
The free-body diagram of beam is described in Fig.1 (b). Let Rbe the reaction force,
and MRbe the reaction bending moment. Applying Newton’s law for static equilibrium
point, the following equations can be obtained.
Rmtg= 0,(5)
MRmtgL = 0.(6)
In Fig.1 (c), at the left boundary of the flexible beam, the sum of bending moments M
at the right side can be as follows.
M=MRRx. (7)
Based on the differential equations for the elastic curve of a beam [13, Eq. (9.12), p.
297], the relation of the bending moment Mand the deflection y(x) of the flexible beam can
be obtained as follows.
M=EI d2y(x)
It should be noted that the curvature is negative. Substituting Eq. (8) into Eq. (7),
results in the following equation at the right boundary.
EI (Lx).(9)
Integrating Eq. (9) twice with the zero boundary conditions
dy(L, 0)
dx = 0,(10)
y(L, 0),(11)
The following equation that describes the deflection of the tip of the beam (at right
boundary) is obtained.
y(L) = mtgL3
3EI .(12)
In this paper, the flexible beam with total mass mtat the end is assumed to be a linear
spring with the stiffness.
The natural frequency ωnof the cantilever beam at the tip end can be computed as.
Theoretically, the damping ratio ζof an under-damped system in the time domain can
be identified by using logarithmic decrement method in Fig. 2. The amount of logarithmic
decrement δis the natural logarithm of the ratio between the two amplitudes consecutive
peaks xiand xi+1.
nln xi
Then, the damping ratio is defined as follows.
In this paper, the control objective is to suppress the residual vibration while the beam is
driven to the desired angle. It is assumed that the flexible beam system can be considered
as an under-damped second order system, which can be expressed as the transfer function
G(s) = Y(s)
s2+ 2ζωns+ω2
In the time domain, the impulse response of the system is given as
y(t) = n
p1ζ2eζωn(tt0)sin ωnp1ζ2(tt0),(18)
where Aand t0are the amplitude and the time of impulse, respectively. Basic technical point
of input shaping is described in Fig. 3. When first impulse is applied, it results in vibration
to a system (solid line). Then, if we continue to apply second impulse with appropriate
amplitude and time location, this
Figure 2. Illustration of logarithmic decrement method to calculate the damping ratio
Figure 3. Basic concept of input shaping [7]
impulse generates vibration (dash line), which can suppress the vibration caused by first
impulse. This effect results in zero vibration of the system. A sequence of impulses that
caused no vibration when applying to system is called input shaper.
The percentage residual vibration between the single unity-magnitude sequences is given
as [7]
V(ωn, ξ) = eξωntnpC(ωn, ξ)2+S(ωn, ξ)2,(19)
C(ωn, ξ) =
C(ωn, ξ) =
In the Eqs. (20) and (21) Aiandtiis the amplitude and time location of the i-th impulse,
nis the number of impulses in the impulse sequence, ωnis natural frequency, ζis damping
ratio, and ωd=ωnp1ζ2is defined as damped natural frequency.
ZV is the simplest and earliest input shaper, it can be obtained by solving following
constraints [7]:
1) V(ω, ζ ) = 0;
2) PAi= 1;
3) Ai>0;
4) t1= 0;
5) min(tn).
ZV input shaper is given as the following matrix.
1 + K
1 + K
0 0.5Td
where Td=2π/ωdis the damped period of vibration, andK= exp(ξπ/p1ξ2).
In this paper, the robust input shaper ZV D [15] is also used to improve the control
performance of the flexible beam system.
JZV D = 1 + 2K+K2.(25)
To achieve more robustness than ZVD, the input shaper ZVDD [15] is introduced as
0 0.5TdTd1.5Td
J=K3+ 3K2+ 3K+ 1.(27)
Figure 4. Block diagram of hardware design
In this paper, the controller of the flexible beam system is built by using the Mechatronlink-
III network components, which includes one C1 master and various slaves which can be
servo drive, stepping motor and I/O module. They can be connected in cascade, star or mix
topology if using hub. In the network, C1 master receives command profiles from slaves and
determines the kind of devices. After master sends commands, slaves receive and execute
commands, and later slaves reply their monitoring information. The speed of network to
transmit data is at 100 Mbps. The Mechatrolink-III protocol supports both synchronous
and asynchronous communication modes. In synchronous mode, master station sends the
command data at any required timing and the slave station responds to the sent command
data. Asynchronous communication can be used in a system where synchronous operation
is not needed, i.e., collecting necessary information for synchronous communication from
4.1. Hardware development
In this section, the design of Mechatrolink-III master device is introduced. Figure 4 presents
the block diagram of hardware design. The controller communicates with host PC by PCI
interface. Then, FPGA chipset is used for timing synchronization of controller. Based
on the powerful and fast computation, motion generator and other calculations of signals
are embedded into DSP. In this diagram, ARM CPU plays an important role. It handles
data between internal controller and Mechatrolink-III network. Finally, ASIC JL-100A chip
control Mechatrolink-III sending/receiving frame inside network. In Table 1, specifications
of Mechatrolink-III controller are listed.
4.2. Software development
In Windows platform, the static library 32-bit is programmed to input data from end-user.
The essential parameters to apply input shaping are shown.
where lAxis is the number of axis to control; dFreq and dDampingRatio are natural frequency
and damping ratio of motion system. dImpulseCount displays the number of impulse to
dImpulseCount = 2: ZV control scheme
dImpulseCount = 3: ZVD control scheme
dImpulseCount = 4: ZVDD control scheme
The value TRUE of dEnable is to activate the input shaping technology, otherwise normal
motion is execute. Once, natural frequency and damping ratio are input, amplitude and time
cycle of impulse are known. A number of impulses depend on input shaping modes. When
input shaping control is activated, a reference data from profile generator is driven into ZV,
ZVD or ZVDD shaper scheme.
In low level, in Fig. 5, a loop which is responsible for the real-time control of data
exchange is defined. The firmware includes the main program and interrupts service routine.
In the first stage, PLL clock, timer, system control register, interrupt service routine and
motion parameters are predetermined. Later, ASIC JL-100A is initialized in three times.
If error still occurs, LED displays to notify. Otherwise, infinite loop that switches between
asynchronous and synchronous mode is used to update data. As shown in Fig. 6, the input
shaping strategies are implemented in ISR. After confirming the error system is in a range,
motion profile is generated. Value of time is computed and compared with sampling time
in system to determine the period of impulse. Then, a mathematical operation is convolved
between two signals as an output of input shaper. The result is transmitted to slave station
in Mechatrolink-III network in order to execute command profile.
Table 1. Specifications of Mechatrolink-III controller
Form Factor PCI (32 bit/33 MHz)
Protocol Communication Mechatrolink-III
Speed 100 Mbps
Transmission Cycle 250 us
Data Frame 48 byte
Support Communication Cyclic, Event-driven
Mechatrolink-III Chipset JL100A
The input shaping for S-curve motion profile is illustrated in Fig. 7. In fact, the con-
ventional motion controller generating S-curve trajectory to drive AC Servo motor yield
vibrations of the beam. In the case of the input shaping applied, the convolution product
between S-curve profile and two-pulse command yield the better results, i.e., the dynamic
Figure 5. Flowchart of main program
response is smoother, and the residual vibration is suppressed when the motion is completed.
The difference between the conventional and the proposed methods is the suppression of the
vibration at the end of the motion. In the case of the conventional method, the vibration
suppression is based on the viscous damping of the system. This can be considered as a
passive vibration suppression method. In the case of the proposed control method, the vi-
bration eliminated at the time the motion is completed. Therefore, the proposed control
method may yields two advantages: (i) The vibration is suppressed quickly; (ii) The time
for vibration suppression can be predicted.
Experiments were conducted with proposed Mechatrolink-III controller and slave servo drive
as shown in Fig. 8 and its corresponding parameters can be seen in Table 2. An aluminum
thin beam is used as flexible beam. Two bolts are hanged in each side of beam as mass or
load. Then the beam is directly mounted with motor shaft which is vertically suspended on
In order to identify exact natural frequency of beam, a laser sensor is used to measure
the vibration the flexible beam. The flexible beam rotates around vertical direction and
then, laser sensor detects residual vibration of beam. In Figs. 9 and 10, spectrum frequency
and system vibration that measured by laser sensor are displayed. The measured natural
frequency is 33.3 Hz. Hence, the calculated damping ratio based on logarithmic decrement
Figure 6. Flowchart of interrupt service routine
method is 0.008. These parameters are used in all tests. However, depending on each kind
of input shapers, impulse counts are selected as 2, 3 or 4
Table 2. Parameters of experimental motion system
Young’s modulus of beam 70 GPa
Density 2.7 g/cm3
Length of beam 85 mm
Width of beam 15 mm
Height of beam 1.8 mm
Mass of two bolts 1.2 g
The experimental results of the case of ZV, ZVD and ZVDD shapers and of the conven-
Figure 7. Input shaping for S-curve profile
Figure 8. Experiment system is set-up
tional method are described in Figs. 11, 12, 13 and 14 correspondingly. To illustrate visually,
speed and position of servo motor are plotted on left and right side of vertical axis. Their
units are revolutions per minute (rpm) and the number of rotations (rev) around motor
shaft. In these experiments, angle of the beam is obtained by using the 17-bit incremental
Figure 9. Spectrum frequency measured by laser sensor
encoder in the servo motor. Based on a motion planning trajectory, controller generates the
reference (command) speed to drive AC servo motor and obtains the actual speed. Fig. 11
shows the results in the case of the conventional method applied. There is the oscillation in
the actual speed, especially in period of constant velocity and deceleration. When the ZV
shaper is applied, the oscillation appears in the speed signal is decreased in comparison to
the case of the conventional method, as shown in Fig. 12. The ZVD and ZVDD shapers
yield the better results than ZV, as shown in the Figs. 13 and 14, where the oscillations
are suppressed completely. Fig. 15 shows experimental data of torque control in the case
of ZV, ZVD and ZVDD input shapers and of the conventional method. It is obvious that
there is the torque of the conventional method oscillates with a big amplitude There are still
small residual vibrations with the ZV and ZVD shapers, but residual vibrations are zero in
the case of the ZVDD shaper applied The experiments show that input shapers yield good
performance in Mechatrolink-III motion control system
Table 3. Comparison of RMS tracking errors and reduction ratios in test cases
Control Scheme RMS Reduction %
Without Input Shaper 1.4721e-3 -
With ZV Input Shaper 1.0572e-3 28.18
With ZVD Input Shaper 0.7233e-3 50.86
With ZVDD Input Shaper 0.2615e-3 82.23
The comparison of the control performance of the three proposed control methods, which
has been illustrated, is shown in Table 3. It should be noted that the tracking error is an
important factor to evaluate motion control systems. In the case of the conventional control,
the experimental result shows large RMS tracking error. The input shaper ZV, ZVD, and
ZVDD, yield the reduction of the RMS tracking error, where ZVDD generates the best
Figure 10. System vibration measured by laser sensor
Figure 11. Experimental speed profile without input shaper
control performance.
The three input shaping algorithms for a flexible beam have been presented. A mathematical
model of beam has been used to analyze natural frequency and damping ratio. According
Figure 12. Experimental speed profile with ZV shaper
Figure 13. Experimental speed profile with ZVD shaper
to the experimental results, the motion profiles are smooth and reduced residual vibration.
The implementation of the three input shapers is performed by using the Mechatrolink-III
network. It is indicated that the input shapers have provided good control performance.
With large buffer enough in Mechatrolink-III, this successful implementation provides an
opportunity to apply the input shaper for multi-axes in industrial network motion system.
Figure 14. Experimental speed profile with ZVDD shaper
Figure 15. Experimental torque control with ZV, ZVD shaper, ZVDD shaper and without
This research is funded by Vietnam National Foundation for Science and Technology
Development (NAFOSTED) under grant number 107.04-2012.37 and by Vietnam National
University Hochiminh City (VNU-HCM) under grant number C2013-20-01.
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Received on August 24 - 2015
Revised on May 13 - 2016
... Banerjee ve Singhose [20,21] esnek iki bağlantılı manipülatörün minimum zaman kontrolü için girdi kontrolcü konfigürasyonunu incelemişlerdir. Sıfır titreşim (ZV) şekillendirici, sıfır titreşim türevi (ZVD) şekillendirici ve sıfır titreşim türevinin türevi (ZVDD) şekillendirici gibi çeşitli girdi şekillendiriciler yaygın olarak kullanılır [22,23]. Bu üç girdi şekillendirici yöntemi, esnek bir kirişin titreşim genliklerini bastırmak için Nguyen ve Ngo [22] tarafından kullanılmış ve sonuçlar deneylerle karşılaştırılmıştır. ...
... Sıfır titreşim (ZV) şekillendirici, sıfır titreşim türevi (ZVD) şekillendirici ve sıfır titreşim türevinin türevi (ZVDD) şekillendirici gibi çeşitli girdi şekillendiriciler yaygın olarak kullanılır [22,23]. Bu üç girdi şekillendirici yöntemi, esnek bir kirişin titreşim genliklerini bastırmak için Nguyen ve Ngo [22] tarafından kullanılmış ve sonuçlar deneylerle karşılaştırılmıştır. İki eksenli sarkaç sistemi dış etkilerin zorlaması altında girdi şekillendirici yöntemi ve geri-beslemeli kontrol kullanılarak kontrol edilmiştir [24]. ...
... The established model can be used for many purposes such as providing vibration control of the system. There are many studies in the literature about vibration attenuation in the system by using model information [21][22][23][24][25][26][27][28][29][30]. It is studied that in a robotic-manipulator, if input is in trapezoidal velocity profile, the deceleration time parameter can be chosen by considering the lowest natural frequency. ...
... This approach can be performed to planar or curved flexible manipulators with cycloidal and triangular motion profiles [30]. Also input-shaper filter techniques such as zero vibration (ZV), zero vibration derivative (ZVD), and zero vibration derivative-derivative (ZVDD) can be performed to suppress the residual vibration of a flexible robotic manipulator and this method can be applied by microcontrollers for mechatronic applications [23][24][25] In this study, the finite-element-method-generated system is transformed from nodal coordinates to modal coordinates using the mode summation technique. After deformation mode selection is applied, the ROM is realized in state-space form. ...
This paper introduces a modified reduced-order model with aim to use in the dynamic analysis of flexible robot-manipulators. The model structure is firstly discussed theoretically, then numerically, and finally experimentally in terms of efficiency, utility and robustness. Due to the deterministic structure of the model, which is formed by taking into account the specific features of the system, a successful model can be created without the need for wide range of training data such in probabilistic methods. Because of the simplicity of the model, it is able to realize a dramatic decrease in the analysis period compared to FEA programs. The model is also quite successful in reflecting the robot’s nonlinear trigonometric position responses. Besides, an open loop model-associative vibration control method was used to show the utility and satisfactory results were achieved in the actual system. Furthermore, the ability of the model to perform multiple scenarios in a short time allowed the case-study of the control input parameters.
... We consider two input shaping techniques, a zero vibration (ZV) input shaper and a zero vibration derivative (ZVD) input shaper [13][14][15][16]. Addition of an input shaper to the seeking process adds a delay to the seeking process. ...
The multi actuator drive technology was unveiled by Seagate in December 2017, a breakthrough that can almost double the data performance of the future generation hard disk drives. This technology will equip drives with dual actuators operating on the same pivot point. Each actuator will control half of the drive's arms. Since two actuators operate independently on the same pivot timber, the control forces and torques generated by one actuator can affect the operation of the other actuator. We will have a scenario when one actuator is track seeking and the other actuator is in the track following mode. The track seeking actuator will impart vibration disturbances to the track following actuator. Previously, we presented a single-input single-output (SISO) data driven feedforward control design method [1] to obtain feedforward controllers for the voice coil motor and the micro actuator sequentially. The design was based on multiple frequency response measurements of the actuators. In this paper, firstly, we present a single-input multi-output (SIMO) data driven feedforward control design technique to simultaneously obtain feedforward controllers for the voice coil motor and the micro actuator. This methodology will obtain a common controller for multiple drives. We will compare the performance of this algorithm with the sequential SISO design technique [1]. Secondly, we present an add-on input shaping technique to suppress the residual vibration.
... An alternative robustness shaper was known as Extra-Insensitive (EI) shaper, which was used by Singhose et al. 22 to put residual vibration into acceptable tolerance while the derivative of residual vibration converged to zero. Nguyen et al. 23 designed the input shaping control to minimize the vibration of a rotational beam. Sadat-Hoseini et al. 24 derived an optimal-integral feedforward control scheme to control vibrations of aircraft wings enabling the auto-landing of aircraft. ...
Full-text available
Introduction: A cantilever beam is a well-known structural element in engineering, which is only fixed at one end. This structure can be used to describe a manipulator, whose stiffness is large to ensure rigidity and stability of the system. A flexible cantilever beam provides a light-weight structure and high cost efficiency but generates vibration under high-speed positioning. In this paper, we aim to control the vibratory behavior of a flexible cantilever beam attached to a moving hub. Method: The mathematical model of the flexible beam is described by partial differential equations (PDEs) using Euler-Bernoulli beam theory. Then, The PDE model is approximated by using the Galerkin method, which is resulted in a set of ordinary differential equations (ODEs). Experiment is used to determine unknown parameters of the system to complete the model. The ODE model enables the control design of three input shapers: (i) Zero-Vibration (ZV), (ii) Zero-Vibration-Derivative (ZVD), and (iii) Zero-Vibration-Derivative-Derivative (ZVDD), which are employed to drive the flexible beam to the desired position and to reduce vibrations of the beam. Results and conclusion: The dynamic model is obtained in term of ordinary differential equations. Unknown parameters of the system are determined by experimental process. Various controllers are designed to eliminate the vibration of the beam. The simulation is applied to predict the dynamic response of the beam to verify the designed controllers numerically. Experiment shows the validity of the mathematical model through the consistency between the simulation and experimental data and the effectiveness of the controllers for the real system. These controllers show several advantages such as no need of extra equipment; the positioning controller is intact, which means it may be applied to many existing systems.
This paper presents an improved vibration control method that controls the amplitudes of residual vibrations of a flexible non-uniform shaped manipulator with higher suppression ratio. The proposed new method suppresses the residual vibrations that occur after motion by shaping the velocity input. By considering the parameters of the experimental system, an analytical model is established according to the natural frequency of the system which is effective in the vibrations that occur in the direction of motion. To demonstrate the accuracy of the established model, transient analysis is performed by the Fast Fourier Transform (FFT) method and the resulting dynamic response is compared with the response of the experimental system. The motivation of this study is to add the shaped exponential-harmonic velocity input to the end of the trapezoidal or triangular velocity input to suppress the velocity response that is in the region of the residual vibrations. The effects of changes in the amplitude, frequency, exponential decay factor, phase angle and application time parameters of the exponential-harmonic input on the control of the residual vibration amplitudes are examined. The obtained results are compared with the experimental results and it is observed that the proposed vibration control method has succeeded in suppressing the residual vibrations by up to 99%. Thanks to the proposed method, the time needed for the manipulator to reach the steady-state time at the end of the motion was reduced from 18 seconds to the motion time.
This paper presents the vibration control problem of the single-link flexible composite manipulators. Two different materials of composite which are epoxy-glass and carbon-fiber are considered for both simulation and experimental analyses. Manipulators are obliged to perform a job such as pick and place applications and machining a workpiece. Therefore, a payload is attached to the manipulators. If the system is suitable for loading applications, the improved vibration control method is used to suppress the residual vibrations of the manipulators. The simulation results are verified with experimental results and it is observed that the proposed vibration control method significantly reduces the residual vibrations compared to passive vibration control method in literature. Additionally, the stresses during motion are analyzed for both simulation and experiment and the effectiveness of the proposed method on the stresses is investigated. Results showed that only the carbon-fiber manipulator is suitable for payload applications and its utilization efficiency can be greatly improved by the proposed method.
Lighter manipulators are used due to reducing power consumption and reaching higher speeds for applications. Composite manipulators can be more desirable for this purpose because they are light weight and have high strength. As it is well known that using flexible manipulators causes high amplitude vibrations and this affects the accuracy of end-point positioning. In this study, a single-link flexible glass fabric reinforced epoxy-glass composite manipulator is analyzed in ANSYS and the residual vibrations are controlled with a new method. The finite element vibration analysis is performed and an experimental system is introduced to verify simulation results. [0/90] lay-up and two different velocity profiles are studied for different case studies. An exponential-harmonic velocity excitation is applied after the end of the trapezoidal velocity profile to control the residual vibrations. It is known that the vibration amplitudes of a system decrease when the system is excited at higher frequency than the natural frequencies. The effect of the amplitude, frequency, the duration of the application and the exponential decay factor on the suppression of the residual vibration are analyzed. Both simulation and experimental analyses are performed and the results are in good agreement. It is concluded that the residual vibration amplitudes of the flexible composite manipulator are suppressed with the proposed method up to 99% for all velocity inputs.
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This paper describes a method for limiting vibration in flexible systems by shaping the input to the system. Unlike most previous input shaping strategies, this method does not require a precise system model or lengthy numerical computation; only estimates of the system natural frequency and damping ratio are required. The effectiveness of this method when there are errors in the system model is explored and quantified. Next, an algorithm is presented, which, given an upper bound on acceptable residual vibration amplitude, determines a shaping strategy that is insensitive to errors in the estimate of the natural frequency. Finally, performance predictions are compared to hardware experiments.
Conference Paper
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In this paper, we propose the asymmetric S-curve motion profile that enables easy manipulation of jerks during the arrival time in order to effectively reduce the residual vibration. To derive the complete closed form solution to the asymmetric S-curve, a design parameter the so-called jerk ratio is introduced to scale down the jerks during the deceleration period so that the velocity profile is in an asymmetric S-curve. Thanks to the jerk ratio, the motion parameters are remarkably simplified in analytic forms for short, medium and long distances. The effectiveness of the proposed approach is validated by experiments with the AC motor control system. As the jerk ratio increases, the residual vibration decreases, but, the motion profile is lengthened as expected by simulations.
The use of lighter manipulators reduces the power consumption and increases payload-to-weight ratio. Composite manipulators can be preferred for this aim due to their properties such as light weight and high strength. Using lighter manipulators causes vibrations due to their flexibility. Flexibility affects the end-point positioning accuracy and repeatability of manipulators in high speed engineering applications. In this study, a single-link flexible composite manipulator is considered to analyze in ANSYS and reduce end-point vibrations. The finite element vibration analysis is performed and an experimental system is introduced to verify simulation results. [0/90] and [45/-45] lay-ups, trapezoidal and triangular velocity profiles are studied by creating cases for different stopping positions and motion times. The time intervals of the motion profiles are determined from the natural frequency of the composite manipulator. Residual vibrations which occur after stopping the movement of the manipulator are obtained and the root-mean-square (RMS) values of these signals are calculated. It is observed from the results that the first vibration mode dominates to reduce the residual amplitudes. The lowest RMS values are achieved for various cases if the time interval is selected so that the deceleration time equals to the inverse of the first natural frequency.
In this study, a two-link manipulator with flexible members is considered. The end point vibration signals are simulated by developing a MatLAB code based on the finite element theory and Newmark solution. Experimental results are also presented and compared with simulation results. The mass and stiffness matrices are time dependent because the angular positions of the links change during the motion. Trapezoidal velocity profiles for the actuating motors are used. The time dependent inertia forces are calculated by using the rigid body dynamics. The inertia forces are due to the motors, end point payload mass and distributed masses of the links. The acceleration, constant velocity and deceleration time intervals of the trapezoidal velocity profile are selected by considering the lowest natural frequency of the manipulator structure at the stopping position. Various starting and stopping positions are considered. The root mean square (RMS) acceleration values of the vibration signals after stopping are calculated. It is observed that the residual vibration is sensitive to the deceleration time. The RMS values are lowest if the inverse of the deceleration time equals to the first natural frequency. It is highest if the inverse of the deceleration time equals to the half of the first natural frequency. It is observed that simulation and experimental results are in good agreement.
Conference Paper
Input shaping control is an interesting topic in control viewpoint. Recently, input shaping control has many methodologies as ZV, ZVD, ZVDD, EI, UM ... which are developed and published by many researchers on the world. The parameters, which are most important to build an input shaping controller are natural frequency and damping ratio. Actually, these parameters are not easy to determine in actual, in general. The error of natural frequency and damping ratio will be significantly affected to residual vibration in input shaping controller. This paper estimates the effect of natural frequency error to residual vibration of flexible beam in three input shaper ZV, ZVD, and ZVDD. The results will be shown clearly using mathematical form and experiments.
Conference Paper
Mechatrolink-III is a real-time Ethernet protocol designed to achieve high performance with short cycle time. The Mechatrolink-III protocol includes five communication phases: synchronization, cyclic communication, retry communication, C1 master message communication, and C2 master message communication. These communication phases directly affect the cycle time of Mechatrolink-III. This paper analyzes the real-time performance of the Mechatrolink-III protocol according to cycle time on line and tree topologies. Moreover, we measure parameters that influence these communication phases in our system, and construct a formula to calculate the cycle time based on those parameters.
This article presents an unsophisticated method for tuning the amplitudes and time locations of a three-impulse sequence input shaper. The method helps to solve the insufficient constraint equations directly. A wide range of shapers can be obtained using the proposed method, including Zero Vibration (ZV), Zero Vibration Derivative (ZVD) and Extra Insensitive (EI) or Specified Insensitive (SI) shapers. The impulse amplitudes can be produced without additional derivative constraints or an initial penalty of residual vibration. It is also shown that a more robust input shaper can be obtained using the new algorithm. Experimental results from a step motor are used to support the numerical solutions.
Active vibration suppression of flexible manipulators is important in many engineering applications, such as robot manipulators and high-speed flexible mechanisms. The demand for a short settling time and low energy consumption of vibration suppression requires consideration of optimal control. Under a wide range of operating conditions, however, the fixed optimal parameters determined for a control algorithm might not produce the best performance. Therefore, to enhance performance, this paper suggests a lookup table control method for a flexible manipulator. This method can tune itself to the optimal parameters on the basis of initial maximum responses to the controlled system. In this study, a multi-objective genetic algorithm is used to search for optimal parameters with regard to positive position feedback to the control algorithm. In turn, with the optimal parameters, the multi-objective functions of the settling time and energy consumption during the vibration control of a flexible manipulator can be minimized. The simulation and experimental results both indicate that the energy consumption can be reduced significantly if the settling time is slightly increased. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society
Precision positioning machines are required to run with higher speed and higher accuracy. The high running speed can cause strong excitations on the machine structure, which results in severe structure vibration and long settling time. This paper presents a low-vibration motion profile generation method to reduce the residual vibration. The acceleration profile is designed by using a level-shifted sinusoidal waveform to have an s-shape in order to control its change rate. Simulation and experimental studies showed that in comparison with conventional trapezoidal profile and s-curve profile, the residual vibration by using the proposed motion profile can be reduced significantly.
Conference Paper
Traditional design can not choose appropriate CPU, peripherals and I/O module for different slave station of MECHATROLINK-III bus. Aimed at these issues, this paper proposes a slave station solution based on SOPC technology. To make I/O device as an example, a MECHATROLINK-III bus slave station is designed using SOPC, NIOS soft core and FPGA technologies. Data link layer peripherals, I/O module and CPU are customized and implemented in this slave station. The operation mode of this slave station can be changed by software method instead of hardware. The interrupting module is constructed using IP component technology to enable the interrupt handler. Finally the slave station driver of MECHATROLINK-III bus is transplanted to this I/O device to achieve Master/Slave communication based on MECHATROLINK-III protocol. The experiment results show that the proposed solution can enhance reusability and flexibility of the slave station.