A Micro-Force-Tracking System Based on PVDF Static Micro-Force Sensor and Fuzzy-PID Control Method

This article is intended to design a static micro-force sensor with a simple structure employing the polymer material PVDF (polyvinylidene fluoride) film as its sensing element, and will carry out some micro-force tracking tests. During the tracking tests, this paper employs a Fuzzy-PID control method and an ordinary PD control method to control the system, and will also analyze the results of them.

Sensor's Inverse Model Controller and Its Calibration. The inverse model is shown in Eq.5, and the inverse controller can be designed as Eq.6 according to our previous work [6][7][8], here, R 2 , R 3 and B are all included in the proportional factor K, therefore the design parameters are only related to the R 1 and C 1 , and one can change the factor K as he/she needs in the experiments.
During the calibration of the PVDF sensor, R 2 =10KΩ, R 3 =100KΩ, K=10, and the filter is one 50HZ low-pass filter, the parameters of PVDF film are as follows: W=0.0123m, L=0.02971m, H=60µm, C p =0.2×10 -9 F. The devices of calibration are shown in Fig.3, one can get the relationship between the output signal (V) and the input signal (µN) illustrated in the Fig.4 when the xyz-positioning table carries the PVDF sensor to push the fixed GS-10 sensor. The linearity error of the static sensor is about 6%, and its resolution can reach µN level.

Design of Fuzzy PID Control Method
Reasons for Employing Fuzzy-PID Control. The accuracy of force-tracking is usually affected by the variable factors such as input signals, complex contact environment and also the circumstantial noise. In order to get high precision, a proper control method is required. Adaptive control is available in most conditions, it identifies the parameters of the complicated environment continuously, however, the accurate parameters depend on precise measurement of the inputs and outputs of the controlled plant, it is hard to do this when it comes to micro-scale objects and this method needs additional devices. Though a computer can not do this well, experienced people can

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Mechatronics and Information Technology make proper decisions to manage it. By employing these people's ideas, one can develop a Fuzzy-PID controller due to the very circumstance, this algorithm needs less equipments and it works effectively.

Fuzzy-PID Controller Design.
In this paper, a Fuzzy-PID controller is designed as a two-input and two-output one due to the fact that the XYZ-positioning table worked here is a mechanical integration system. Here the two inputs are the error of the force-tracking and its change ratio separately, the outputs are ∆K p and ∆K d which vary according to the fuzzy reasoning tables, so the In digital form, its range can be expressed as ∆K p , ∆K d , e ={ -6, -4, -2, 0, 2, 4, 6 }and e c ={ -6, -3, 0, 3, 6 }. K e and K c can be decided due to the actual error and its change ratio, so does ∆K p , ∆K d . The algorithm of updating K p and K d is shown in Fig.6.  Table. When the system detects a big tracking error and the error is still becoming bigger, the phenomenon means the actuator is responding slowly, and K p is in charge of adjusting the property of response speed, so K p should be set a big enough value, however, K d is in charge of regulating the fluctuating nature, if wants to increase the speed of response, K d must be set a smaller one, so the fuzzy rule can be expressed as if e equals to NB and e c equals to NB then the output ∆K p should be PB, and the output ∆K d should be NB. One can get 5×7=35 rules totally, and the fuzzy rule Table.I. and Table.II. consist of all these rules.

Establishment of the Membership Function.
The performance characteristics of this system are that when the actual tracking-force is far from the desired force, the ∆K p and ∆K d values could change largely and they are relatively free in this case to regulate the system to respond faster, so the membership showed in Fig.7.(c), (d) is wider separately. While the actual tracking-force is approaching the desired force, it needs to avoid the excessive overshoot, therefore it is requested the membership function to be narrow in order to adjust this system precisely, as shown in Fig.7.(c) , (d), so the outputs in this article make use of the non-uniform distribution membership functions. The values of the output of ∆K p and ∆K d can be changed by the parameters K1 and K2, which are in the controller, according to the experiments' requirements. Simulation of the Force-tracking System. In this paper, the fuzzy method is designed in the Fuzzy logic tool of MATLAB, the parameters Ke ,Kc, K1, K2 are set 10, 5, 8 and 0.5 separately, and the original valve of K p and K d are set as 120 and 20 according to the actual error and the outputs. The whole system of simulation is shown in Fig.8. and the simulation result is shown in Fig.9 which confirms that the Fuzzy-PID method has a better property of inputs-tracking. And the practical controller is carried out in LABVIEW system.

Experimental System Set-up and the Force-Tracking Test
Experimental Set-up. The experimental system, as shown in Fig.10, 11, is mainly consisted of one XYZ-positioning table (positioning accuracy is up-to 0.125µm), one PIC MCU circuit with designed driving programs in it, one desktop PC with WINXP OS as a host computer and the corresponding control panel developed in the VC6.0, and the LABVIEW DAQ card ( PCI6221 16-bit A/D converter ) to acquire the signal F e generated by the PVDF sensor. Process of the Test and its Results. During the experiment, R 2 =10KΩ, R 3 =100KΩ, K=10, and 50HZ low-pass filter, the parameters of PVDF film are the same as mentioned above. The PVDF sensor will move with the XYZ-positioning table controlled by the host computer and the sensor's tip will compact with a fixed soft ball, and then it will generate the actual force signal F e which will follow the given designed force signal F d . In this paper two sets of test are carried out, one uses the ordinary PD control method and the other employs the Fuzzy-PID control method, and the original parameters K p , K d are set as 120 and 20 separately. Fig. 10.The force-tracking control panel Fig. 11.The force-tracking system set-up

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Let the system follow a desired saw signal and the test results are shown in Fig.12.(a), (b), the maximum force is 480µN. The tracking results illustrate that Fuzzy-PD control method is better than the ordinary PD method in this micro-force-tracking system.

Summary
In this paper, based on the inverse-model control method, a static PVDF micro-force sensor has been developed and it possesses good properties such as high linearity, resolution and simple structure. Then a Fuzzy-PID controller has been designed and closed-loop control test has been carried out, it confirms that this force-tracking system is feasible in micro-force control fields. The next step we will carry out some cell-injection tests using this method and system.