Advanced Controller Design and Implementation of a Sensorized ...

Proceedings of the 2004 IEEE International Conference on Robotics & Automation New Orleans, LA • April 2004

Advanced Controller Design and Implementation of a Sensorized Microgripper for Micromanipulation Jungyul Park*, Sangmin Kim*, Deok-Ho Kim*, Byungkyu Kim*‡,SangJoo Kwon**, Jong-Oh Park* and Kyo-Il Lee*** * ** Microsystem Research Center Korea Institute of Industrial Technology Korea Institute of Science and 35-3 HongChonRi, IbJangMyun, Technology ChonAnsi, ChungNam 330-32, Korea P.O.BOX 131, Cheongryang, Seoul, 130- [email protected] 650, Korea,

{sortpark, ksm, kim-dh,bkim, jop}@kist.re.kr

*** School of Mechanical and Aerospace Engineering Seoul National University San 56-1, Shinlim-dong, Kwanak-gu, Seoul, 151-742, Korea, [email protected]

‡ The author to whom all correspondence should be addressed Abstract— This paper presents the design, and control of a sensorized microgripper using VCM(voice coil motor). In order to increase the sensitivity of the sensorized microgripper, shape design and determination of sensor position are performed using finite element analysis. Micro EDM (Electric Discharge Machine) and wire cutting technique are employed to fabricate the microgripper. Empirical model of the microgripper is achieved to analyze the performance and to control the position and gripping force. By using this identification model, both the perfect tracking controller (PTC) for the position control, and the adaptive zero-phase error tracking controller (ZPETC) for the force control are implemented. The effectiveness of the proposed model-based control method is verified by both simulation and experimental studies. Simulation and experimental results show that the proposed control method can be effectively applied to improve the motion tracking performance. Especially, in case of force control to grip and manipulate soft materials such as biomaterials and tissues, the proposed controller can be very useful to prevent the invasion of the target material by excessive force. Keywords-Microgripper; Strain gauge ZPETC; Force control; Micromanipulation

I.

sensors;

Adaptive

INTRODUCTION

Recently, the microscale sensing and/or manipulation have become a challenging issue in microassembly of hybrid microsystems and biomanipulation. Especially, a feedbacksensor based manipulation is necessary to realize efficient and reliable handling of micro objects under uncertain environment [1], [2]. As a component of the micromanipulation system, a microgripper plays a very important role in manipulating a micro object. There are different kinds of microgripper according to the fabrication method, actuators and sensors which is attached at microgrippers. For example, microgrippers are fabricated by silicon surface micromachining [3], the laser micromachining [9], and the Electro-Discharge Machining (EDM) [4], [7]. Electrostatic actuators [3], piezoactuators [5], [7], vacuum actuators [6], and

0-7803-8232-3/04/$17.00 ©2004 IEEE

Lorentz force-type actuators such as voice-coil motors [9] are used in generating micro gripper’s motion. Concerning the sensorization of microgrippers, several microgrippers integrated with a piezoresistive force sensor [8] or a semiconductor strain-guage sensor [4], [7] have been reported. The needs of sensorized microgrippers are greatly increasing in assembling and testing microsystem components for high precision and reliability [10], [11], [12] and/or measuring the mechanical properties of biological cells and tissues [13]. The fundamental requirements of the microgripper for microassembly systems are the large force to weight ratio, the high precise actuation, and the feedbacksensing capability. For achieving high precision gripping performance, not only a reliable actuating mechanism but also an effective control method which considers the dynamics of the microgripper is earnestly required. In spite of increasing needs, there are few researches on the applications of advanced control method and its implementation for motion control of microgrippers except the references as [7] and [14]. However, these studies did not consider the system dynamics in controlling the motion of microgripper [7], and implemented the simple PI controller [14] which can not effectively compensate for the phase error in tracking the reference signal. Moreover, in case the gripping object is changed, a control parameter tuning process should be followed in the previous researches. In this paper, we present the identified model and modelbased adaptive control of a sensorized microgripper using VCM. This paper describes 1) shape design of the sensorized microgripper and determination of attaching positions of strain gauge sensors in the microgripper, which are based on FE analysis, 2) fabrication using micro EDM and wire cutting technique, 3) empirical modeling using system identification technique to analyze the performance and to control position and force of the microgripper, 4) design, implementation and validation of the proposed control method for the microgripper, which consist of the perfect tracking controller for the position control and the adaptive zero-phase error tracking controller

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for the force control[15-17]. The proposed controllers are successfully applied to real-time tracking control of the microgripper and overcome the mentioned above problems of the controllers which were implemented in the previous work[7] [14].

3 the microgripper are 15.5 × 5.22 × 0.5 mm . The initial gap of the gripping hand is about 100 um, adjustable according to the size and shape of manipulated objects. The maximum size of the object that the gripper can handle is up to 300 um. 1

1 NODAL SOLUTION

II.

NODAL SOLUTION

DEC 2 2002 01:51:16

STEP=1 SUB =1 TIME=1 EPTOEQV (AVG) DMX =.412E-05 SMX =.310E-06

DESIGN AND FABRICATION

DEC 2 2002 01:45:05

STEP=1 SUB =1 TIME=1 EPTOEQV (AVG) DMX =.126E-03 SMX =.928E-06

MN

MN

MX MX

A. FE Analysis Before the microgripper system was fabricated, FE analysis for geometry design was carried out to increase the sensitvity of the position and force sensor. Since it is not easy to control the displacement in the micro scale by conventional mechanism such as gears and link structures, we use the elastic flexure hinge mechanism to mechanically amplify the small displacement of the microgripper. Therefore, in the geometry design, it is very critical in determining the shape and position of hinge as well as global shape of microgripper. The left side of Fig.1 describes variation of strain when the external force (the driving force by VCM and repulsive force due to contact between the microgripper tip and the target object) is applied, and the right side illustrates variation of displacement when the driving force is applied according to various geometry designs. That is, the left side of Fig.1 corresponds to the configuration of gripping an object, and the right side corresponds to the configuration that the tip of the microgripper is opened. In the case of gripping an object, we assume that the tip of microgripper is fixed and the microgipper is pulled by constant force. When the tip of the microgripper is opened, the microgripper is just assumed to be pushed by constant force. The FE analysis result in Fig. 1 shows that the shape design in the last case ((e), (f)) is preferred considering that its maximum strain is the largest among various design, in case of gripping the object, and maximum strain, when the tip of microgripper is opened, is similar to other design. Our microgripper was fabricated according to results of FE analysis, and position/force sensors are attached at the maximum strain point shown in Fig.1. B. Fabrication Process Fig. 2 is a photograph of the developed microgripper which consists of VCM actuators, and two strain gauge sensors. By adopting the VCM as a driving mechanism, which is usually used for hard disk drives and optical disk drives, the microgripper can be controlled linearly, and also it can be realized with compact structure. The VCM generates linear force proportional to the applied current. And it is operated according to the principle of Lorentz force which is generated by the current-carrying conductor in a static magnetic field. In the VCM, the conductor and the moving coil are precisely aligned among four rectangular neodymium iron boron magnets which provide a high gap field. On the other hand, the wire cutting method is used to fabricate the microgripper. The saw shaped structure is obtained through micro EDM. This shape is advantageous to minimize the sticking force between the gripper and the target object. The symmetrical configuration is adopted to obtain accurate and repeatable measurements of force and position. The overall dimensions of

Y

Y

Z

X

Z

X

Driving Force 0

.688E-07 .344E-07

.138E-06 .103E-06

.206E-06 .172E-06

.275E-06 .241E-06

Driving Force 0

.310E-06

(a) Maximum strain = 0.412e-5 1

.206E-06 .103E-06

.413E-06 .309E-06

.619E-06 .516E-06

.825E-06 .722E-06

.928E-06

(b) Maximum strain = 0.126e-3 1

NODAL SOLUTION

NODAL SOLUTION DEC 2 2002 02:14:19

STEP=1 SUB =1 TIME=1 EPTOEQV (AVG) DMX =.539E-05 SMX =.534E-06

DEC 2 2002 02:22:12

STEP=1 SUB =1 TIME=1 EPTOEQV (AVG) DMX =.124E-03 SMX =.102E-05

MN

MN

MX MX

Y Z

Y

X

Z

X

Driving Force

Driving Force 0

.119E-06 .594E-07

.237E-06 .178E-06

.356E-06 .297E-06

.475E-06 .415E-06

0 .534E-06

(c) Maximum strain = 0.539e-5 1

.227E-06 .113E-06

.453E-06 .340E-06

.680E-06 .567E-06

.907E-06 .794E-06

.102E-05

(d) Maximum strain = 0.124e-3 1

NODAL SOLUTION

NODAL SOLUTION DEC 2 2002 02:03:12

STEP=1 SUB =1 TIME=1 EPTOEQV (AVG) DMX =.709E-05 SMX =.350E-06

MN

DEC 2 2002 01:59:20

STEP=1 SUB =1 TIME=1 EPTOEQV (AVG) DMX =.122E-03 SMX =.103E-05

MN

MX MX

Y Z

Y X

Z

Driving Force

Force sensor 0

.779E-07 .389E-07

.156E-06 .117E-06

.234E-06 .195E-06

.311E-06 .273E-06

X

0 .350E-06

(e) Maximum strain = 0.709e-5

Driving Force

Position sensor .228E-06 .114E-06

.456E-06 .342E-06

.683E-06 .570E-06

.911E-06 .797E-06

.103E-05

(f) Maximum strain = 0.122e-3

Figure 1. Variation of strain and displacement according to various designs Position Sensor

Voice Coil Motor

Micro Gripping Hand

Force Sensor

Figure 2. Photograph for the microgripper actuated by voice coil motors.

C. Sensor Calibration Sensor calibration for two strain gauges (model: KYOWA KSN-2-120-E5-11) is essential to determine the reference of force and displacement of the microgripper. As seen in Fig. 3(a), the displacement of the microgripper tip according to the force variation is measured using the laser displacement sensor (model: KEYENCE LK3100). Simultaneously, the

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signal of strain gauge is monitored to obtain the relationship between the strain and the displacement of the microgripper tip. Calibration result shows good linearity although it has some hysteresis as shown in Fig. 3(c). The other strain gauge for detecting the force is attached at the position which is determined by the FE analysis and measures deformation at the hinge of the microgripper. This strain gauge sensor was calibrated by operating the microgripper tip against the load cell (Transducer techniques GSO10), as shown in Fig. 3(b). The output signal from the load cell ranges from 3 to 23mN approximately. The lines in Fig. 3(c) and Fig. 3(d) were obtained using the moving average method. After calibration, the output signals from two strain gauges are used as position and force signal in the microgripper.

(a)

order to obtain reasonable match between experiments and model predictions. A possible alternative is to capture the dynamics that is essential to the design of controller for target system and to obtain a low-order control oriented empirical model. In this section, two empirical models for position/force control are obtained based on the system identification technique [18]. The experimental data to identify the two empirical models for position/force control is obtained by means of excitation of sinusoidal signals whose amplitudes are 0.1V and frequency from 0.1 to 10Hz. The bandwidth from 0.1 to 10Hz is selected because motions in standard micromanipulation tasks are quite slow [14]. In case of the system identification for the force model, a 230um optical fiber is selected as the gripping object. In case of the system identification for the position control, the microgripper is operated freely. The output signals from the position/force sensor are acquired with 10 msec sampling time. After proper filtering, MATLAB System Identification Toolbox [19] is used to process the data and to obtain an ARX (autoregressive with exogenous input) model. The ARX models for open-loop position and force control system of the microgripper are obtained respectively as follows: Position model:

Gp (z) =

(b)

0.01148−0.03162z−1 + 0.0288z−2 −0.008662z−3 1− 2.993z−1 + 2.987z−2 −0.9935z−3

(1)

poles : 0.9994 + 0.0017i, 0.9994 - 0.0017i, 0.9947 zeros : 0.9995 + 0.0017i, 0.9995 - 0.0017i, 0.7552 Force model:

Gf (z) =

0.0006493 − 0.001245 z−1 1 − 1.14 z−1 + 0.2967 z−2

(2)

poles : 0.7387, 0.4016 (c)

zeros : 1.9174, 0

(d)

Figure 3. Sensor calibration for strain gauges: (a) Experimental setup for the position sensor calibration. (b) Experimental setup for the force sensor calibration. (c) Results of the position sensor calibration. (d) Results of the force sensor calibration.

III.

SYSTEM IDENTIFICATION

After the sensor calibration for two strain gauges, we used system identification techniques to design the model-based adaptive controller design for the microgripper. The developed microgripper consists of a microgripper body, a VCM driver, sensors, an analog amplifier and filters. The mathematical model of the microgripper can be obtained using physical based modeling for each component of the above. But it has some drawbacks when applied to the controller design considered in this paper: 1) The model order is too high; 2) The governing differential equations are too stiff to numerically solve in real-time; 3) There are numerous unknown parameters that need to be estimated or tuned in

From equations (1)-(2), the position model has the stable poles and zeros, that is, all poles and zeros are inside the unit circle in z-plane, but the force model has the unstable zero, that is non-minimum phase system. Unstable zero is problematic because it causes the phase and the gain errors in tracking. Generally, the flexible system are known to have unstable zero dynamics [21, 22]. Since the elastic flexure hinge mechanism is adopted, the microgripper system can have unstable zeros. The identified system model is evaluated through the percentage of the output variation which compares measured outputs with identified model outputs. The definition of the percentage of the output variation is given as, fit = 100 × (1 − norm( yid − ym ) / norm( ym − mean( ym ))) (3)

5027

where yid : identified model outputs, ym : measured outputs from the system.

A more detailed description about the percentage of the output variation can be founded in [19]. Fig. 4 and 5 show results of system identification for the microgripper. Fig. 4(a) and 5 (a) are the frequency response of the identified system and of the real system for the position/force in the microgripper respectively. Fig. 4(b) and 5(b) compares the time response from the identified model with experimental data. As a result, the position model for the microgripper is identified with its percentage output variation 85.30% and the force model with its percentage out variation 72.13%. 0.25

Voltage from position sensor [V]

r (t ) =

0.15 0.1 0.05

-0.15 -0.2 51

(a)

52 Time [sec]

53

54

(b)

Figure 4. Results of system identification for position of the microgripper: (a) Comparison of frequency response from the identified system with the real system (position). (b) Comparison of time response from identified model with experimental data (position). 0.2

-55 -60 10

0

10

1

Frequency [Hz] 200

Phase[deg]

Measured data Identified model

0.15

150 100

Voltage from force sensor [V]

Magnitude[dB]

Identified System Real System

0.1 0.05 0 -0.05 -0.1

Figure 6. Block diagram of feedforward controller for perfect tracking.

-0.15

50 0 10

0

10 Frequency [Hz]

(a)

1

-0.2 50

51

52 Time [sec]

53

54

(b)

Figure 5. Results of system identification for force of the microgripper: (a) Comparison of frequency response from the identified system with the real system (force). (b) Comparison of time response from identified model with experimental data (force).

IV.

(4)

operator, Ac ( z −1 ) is the denominator, and Bc ( z −1 ) is the numerator of the position feedback loop transfer function. This tracking controller provides y (t ) = yd (t ) (perfect tracking) as long as all the initial conditions are zero. As depicted in Fig. 6, the perfect tracking controller cancels all the closed loop poles and zeros so that the overall transfer function from yd (t ) to y (t ) is unity. To stabilize the feedback loop in Fig. 6, a PD type feedback controller can be selected.

-0.1

-40

Ac ( z −1 ) yd (t ) Bc ( z −1 )

where yd (t ) is the desired output, z −1 is one step delay

0 -0.05

-0.25 50

-50

A. Perfect tracking controller for the position control Since the empirical modeling for the position control system of the microgripper has no unstable poles and zeros, we consider a feedforward tracking controller which provides the reference input in the form,

Measured data Identfied model

0.2

-45

desired output. The ZEPTC cancels the poles and cancelable zeros of the closed loop system and compensates phase shifts induced by uncancelable zeros. This implies that the overall transfer function from the reference input to the plant output has zero phase shift characteristics at all frequencies [15].

TRACKING CONTROLLER DESIGN

When a desired trajectory is given, the transfer function between the trajectory input and the actual plant output should be unity for perfect tracking. This may be achieved by canceling the poles and zeros of the closed-loop system. In this regards, the poles of the plant can be modified to the desired location by a feedback controller so that they can be cancelled easily. But the zeros of the plant are not influenced by the feedback control. They can be cancelled by a feedforward controller only. But, if the plant has the unstable zero, it should not be cancelled directly. And it causes the phase and the gain errors in tracking control. The ZPETC can solve this problem. The ZPETC is based on the inversion of the closed loop transfer function so that the product of the ZPETC and the closed loop transfer function comes close to unity for arbitrary

B. Adaptive ZPETC for the force control From equation (2), the force model of the microgripper has a unstable zero. Therefore, the force controller can not apply the perfect tracking controller unlike the position control. If only the feedback loop is applied, the unstable zero causes the tracking errors. Tracking errors in the force control can cause damage to the gripping object due to excessive force than the reference force. Also, if target object for gripping is changed or gripping force is changed due to aging of the system, the control parameters must be tuned for tracking the desired trajectory. In this study, we apply the adaptive ZPETC for the force control, which can solve the above problems [16, 17]. As shown in Fig. 7, the adaptive ZPETC includes three parts as follows: force feedback loop which is selected as proportional controller, the parameter estimation and the ZPETC with parameter adaptation. In this study, the ZPETC without parameter adaptation is designed as

5028

u (t ) =

Bc ( z ) Ac ( z −1 ) yd (t ) , [ Bc (1)]2

(5)

where Ac ( z −1 ) is the denominator of the force feedback loop transfer function, Bc ( z ) is obtained by replacing every

z −1 in Bc ( z −1 ) , that is the numerator of the force feedback loop transfer function, with z, and [ Bc (1) ] is a scaling factor which normalizes the low frequency gain of the overall transfer function from yd (t ) to y (t ) to unity. Since the standard micromanipulation tasks are quite slow, the ZPETC can show good tracking performance in the microgripper. Note that, in real implementation of the controller, Bc ( z −1 ) is recognized as unacceptable polynomial to avoid unstable pole-zero cancellation. Considering the ZPETC design as in equation (5), the phase of the overall transfer function from the reference input to the plant output can be zero and the magnitude can be unity in low frequency. 2

Then, the RLS algorithm with the forgetting factor λ (t ) is derived as

θ (t ) = θ (t − 1) +

Aˆc ( z −1 ) y (t ) = Bˆ c ( z −1 )u (t − 1) + e(t )

R (t − 1)ϕ n (t − 1) 1 + ϕ nT (t − 1) R(t − 1)ϕ n (t − 1)

(9)

⋅ ⎡⎣ yn (t ) − θ T (t − 1)ϕ n (t − 1) ⎤⎦ where

R (t ) =

For the adaptive ZPETC, the force feedback loop model, which is fixed in case of the ZPETC, is updated by the parameter estimation, which is a recursive least square algorithm (RLS). For a more detailed description on the stability and convergence during the estimation process, interested readers are referred [20]. The estimated system can be represented with the ARX model as:

e(t ) , n(t − 1) = max(1, ϕ (t − 1) 2 ) . n(t − 1)

en (t ) =

R (t − 1)ϕ n (t − 1)ϕ nT (t − 1) R(t − 1) ⎤ 1 ⎡ ⎢ R (t − 1) − ⎥ 1 + ϕ nT (t − 1) R (t − 1)ϕ n (t − 1) ⎦ λ (t ) ⎣

R (0) = R (0) > 0 ,

λ (t ) = 1 −

ϕ nT (t − 1) R(t − 1) R(t − 1)ϕ n (t − 1) 1 , tr ( R(0)) 1 + ϕ nT (t − 1) R(t − 1)ϕ n (t − 1)

0 < λ (t ) ≤ 1 , tr ( R (0)) = trace( R(0)) . Therefore, the final form for the adaptive ZPETC is given as follows:

(6)

u (t ) =

where

Bˆc ( z ) Aˆc ( z −1 ) yd (t ) . [ Bˆ (1)]2

(10)

c

Aˆc ( z −1 ) = 1 + a1 z −1 + a2 z −2 + L + an z − n

: estimated denominator of the force feedback loop,

yd(t)

Bˆ c ( z −1 ) = b0 + b1 z −1 + b2 z −2 + bm z − m

ZPETC

u(t)

: estimated numerator of the force feedback loop,

Feedback Controller

Microgripper

Parameter Estimation

y (t ), u (t ) : output and input signal, e(t ) : white Gaussian noise.

Figure 7. Block diagram of adaptive ZPETC tracking control system

If equation (6) can be rewritten as the regressor form: y (t ) = θ T ϕ (t − 1) + e(t )

(7)

where

V.

IMPLEMENTATION AND RESULTS

A. Experimental System Setup

θ = [a1 , a2 ,L , an , b0 , b1 , b2 ,L , bm ] , T

ϕ (t ) = [− y (t − 1), − y (t − 2), L , − y (t − n), u (t − 1), u (t − 2), L , u (t − m − 1)]T

.

Now, define the normalized regressor form as yn (t ) = θ T ϕ n (t − 1) + en (t )

(8)

where yn (t ) =

,

T

y (t ) ϕ (t − 1) , ϕ n (t − 1) = , n(t − 1) n(t − 1)

Figure 8. Hardware layout of the microgripper system.

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The hardware layout of the microgripper system is shown in Fig. 8. The voltage signal, that is control input signal, is generated using dSPACE 1103 with 10 msec sampling time. The voltage signal is converted to the current signal through the VCM driver. The VCM of the microgripper is actuated by this current signal. And the position/force signals from two strain gauges, which are the outputs of the microgripper, are amplified through the bridge circuit. These outputs are obtained through dSPACE 1103. B. Results and Discussions First, the perfect tracking controller for the position control is implemented. It is based on the empirical modeling in equation (1) for the position. Fig. 9 shows the performance comparison of perfect tracking controller with PID controller. Simulation and experiment results show that the performance of the perfect tracking controller is better than the performance of PID controller. When the perfect tracking controller is implemented to the microgripper, it is possible to decrease the fluctuation of the signal and settling time comparing the PID controller. Second, the adaptive ZPETC for the force control is implemented. The proportional gain K p ,which makes the force feedback loop internally stable, is chosen as

K p = 100 .

(11) 0.025 Presented control PID control Referece signal

Position signal from sensor [V]

0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 0

1

2

3

4

Presented control PID control

0.02 Error of position signal from sensor [V]

0.5

5

0.015 0.01 0.005 0 -0.005 -0.01 -0.015 -0.02 -0.025 0

1

Time [sec]

2 3 Time [sec]

4

Therefore, if the empirical model for the force control (equation(2)) is perfect, the transfer function for the force feedback loop can be derived as G fc =

0.06097 − 0.116909 z −1 . 1 − 1.1874 z −1 + 0.2786 z −2

In the simulation study, the above transfer function is estimated by RLS algorithm as equation (9). Fig. 10 illustrates the simulation results for parameters estimations when the adaptive ZPETC is applied. At first, the initial value of the parameters, that are the coefficients of the numerator and denominator of the force feedback loop, is different from the real value. But time is going, the estimated parameters are well converged to the real value in 1 sec. These results verified the stability, adaptation and convergence of the proposed control method. That is, although the system parameter is changed, the proposed control method may make the output signal follow the reference input. Therefore, using the proposed control method, the gripping force can be controlled despite the change of the target object and variation of the actuating force due to aging of the system. As shown in Fig. 11, the simulation and experiment results show a good agreement, and these results verify that the performance of the adaptive ZPETC is further superior to PID controller. It is shown that the adaptive ZPETC can follow the desired trajectory with no phase shift. But, the phase error of PID controller is nearly a half cycle of the desired signal. This phase errors of PID controller can be very critical, in case of gripping and manipulating soft materials, such as biomaterials and tissues, and optical fiber which can be easily brittle. Due to the phase error, if the force sensor signal is delayed, the operator will command the more excessive force input than reference signal. Also, since microgrippers can be used as a measurement system for the mechanical characteristics of micro objects, this phase error causes the failure in the analysis.

5

-0.1

0.07

(a)

(12)

(b)

Estimated parameter Real parameter

0.068

Estimated parameter Real parameter

-0.105

0.066 -0.11

0.064

Position signal from sensor [V]

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b1

b0

PTC PID

0.5 Error of position signal from sensor [V]

PTC PID Reference

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-0.12 -0.125

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0

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1

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Estimated parameter Real parameter

0.006

-1.1

0.004

-1.15 -1.2

Figure 9. Performance comparison of perfect tracking controller with PID controller: (a) Tracking performance between PTC and PID controller (simulation). (b) Comparison of error of position signals (simulation). (c) Tracking performance between PTC and PID controller (experiment). (d) Comparison of error of position signals (experiment).

0

-1.25

-0.002

-1.3

-0.004

-1.35

-0.006

-1.4

-0.008

-1.45

-0.01 0

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a1

b2

(d)

Estimated parameter Real parameter

-1.05

0.002

(c)

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1

system identification technique. Through system identification of the microgripper, the empirical models for the position/force control are achieved. Based on the empirical models, the perfect tracking controllers for the position control and adaptive ZPETC for the force control are designed and implemented. The proposed controllers are verified through simulation and experimental study. All simulation and experimental results have proven the excellent performance and feasibility of the proposed controller comparing with the conventional PID. Especially, in case of griping and manipulating soft materials such as biomaterials and tissues, the proposed controller can be very useful to prevent the invasion of the target material by excessive force. Also, since many microgrippers have flexure structure, the proposed control method can be applied to other microgripper system.

0.4 Estimated parameter Real parameter

0.35 0.3

a2

0.25 0.2 0.15 0.1 0.05 0 0

0.2

0.4 0.6 Time [sec]

0.8

1

Figure 10. Parameters estimations when adaptive ZPETC is applied.

a1 and a2 are the coefficients of the denominator and b0 , b1 and b2 are the coefficients of the numerator in the force feedback loop transfer function. These paramters are from equation(12).

Reference PID control Adaptive ZPETC

0.1 0.05 0 -0.05 -0.1

ACKNOWLEDGEMENTS

0.2 0.15 0.1

This research, under the contract project code MS-02-32401, has been supported by the Intelligent Microsystem Center(IMC: http://www.microsystem.re.kr), which carries out one of the 21st century's Frontier R & D Projects sponsored by the Korea Ministry of Science & Technology.

0.05 0 -0.05 -0.1 -0.15 -0.2 -0.25

-0.15 0

PID control Adaptive ZPETC

0.25 Error of force signal from sensor [V]

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REFERENCES

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Reference PID control Adaptive ZPETC

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Figure 11. Performance comparison of force tacking performance between adaptive ZPETC and PID controller: (a)Tracking performance between adaptive ZPETC and PID controller (simulation). (b)Comparison of error of force signals (simulation). (c)Tracking performance between adaptive ZPETC and PID controller (experiment). (d)Comparison of error of force signals (experiment).

VI.

CONCLUSIONS

In this study, the design, fabrication, and advance control for a sensorized microgripper have been presented. To increase the sensitivity of the sensorized microgripper, the geometry design and the attachment point of position/force sensors are considered through the FE analysis. Based on these results, the sensorized microgripper was fabricated using the Micro EDM and wire cutting technique. For precise gripping and manipulation, we have implemented advanced model-based control method for the microgripper, which has been overlooked by previous researchers. We have proposed the respective proper controllers for the position/force control, which can be implemented with real-time in practice. These controllers consider the dynamics of the microgripper using

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