DESIGN OF A FUZZY-PID CONTROLLER FOR A NANOSCALE X-Y PLATFORM

Xiuli Zheng1, Yi-Hua Fan2, Ching-En Chen2, Ya-Qi Lin2, Hung-Wen Liao2 and Sheng-Chung Hsieh11School of Auto and Mechanical Engineering, Zhejiang Industry and Trade Vocational College, Wenzhou City, China

2Department of Mechanical Engineering, Chung Yuan Christian University, 32023, Taiwan, R.O.C.E-mail: yihuafan@cycu.edu.tw

IMETI 2015 I5004_SCINo. 16-CSME-38, E.I.C. Accession 3924

ABSTRACTA fuzzy-PID controller design was proposed in this paper for a nanoscale platform positioning system.The target nanoscale X-Y platform is mounted on a pantograph mechanism and restricts the rotation bytwo small sliders; the device is driven by a traditional X-Y platform with common precision. The goal ofthis study is to drive the target platform’s movement in the region of 5 mm × 5 mm for the positioning,with repeated positioning accuracy error less than 200 nm by the traditional X-Y platform. Due to thedifferent PID parameters affecting platform positioning accuracy and system response for the two axes, thefuzzy-PID controller will train to fit the mechanism to promote the positioning precision and path controleffect. The simulation and experimental results indicated that the proposed method is feasible for nano-scalemicro-platform positioning.

Keywords: fuzzy-PID controller; pantograph mechanism; nano-scale X-Y platform.

CONCEPTION D’UN RÉGULATEUR PID (À LOGIQUE FLOUE) POUR UNE PLATEFORMEX-Y NANOMÉTRIQUE

RÉSUMÉUne conception d’un régulateur PID (à logique floue) est proposée dans le présent article pour un système depositionnement de plateforme nanométrique. La plateforme X-Y ciblée est montée sur un mécanisme de typepantographe et est restreint par la rotation de deux petits glisseurs. L’appareil est entraîné par une plateformetraditionnelle X-Y avec une commune précision. Le but visé dans cette recherche est l’entraînement dumouvement de la plateforme dans une région de positionnement de 5 mm × 5 mm, en ayant un taux d’erreurde précision dans le positionnement répété de moins de 200 nm de la plateforme traditionnelle X-Y. Àcause des paramètres PID (à logique floue) affectant la précision du positionnement de la plateforme et laréponse du système pour les deux axes, le régulateur PID (à logique floue) sera guidé pour s’adapter aumécanisme pour favoriser la précision du positionnement et l’effet de contrôle de trajectoire. Les résultatsde la simulation expérimentale indiquent que la méthode préposée est une solution envisageable pour lepositionnement d’une micro-plateforme nanométrique.

Mots-clés : régulateur PID (à logique floue); mécanisme de type pantographe; plateforme nanométriqueX-Y.

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1. INTRODUCTION

As industrial products become increasingly smaller, the demands for high aspect ratios and superior surfaceshave been rapidly increasing in industries such as: aerospace, automotive, biomedical, optical, military andmicro-electronics packaging, etc. Therefore, developing a micro- or even a nano-level machine to satisfythe requirements for fast, direct, and mass manufacturing of miniaturized functional products from metals,polymers, composites, or ceramics has become increasingly important. The high-precision 2-axial platformis an important part of the high-precision machines; thus, many researchers have focused on this topic. Themethods proposed focus on the improvements of the precision of ball screws, motors and control methods.For example, the most precise platforms use two single axis robots which are driven by the motor and formthe X-Y platforms; thus, there have been some studies [1, 2] on the topics of how to drive the two robotsto achieve the micro/mesh size positioning and decrease the positioning errors. There have also been manystudies [3–5] on the topics of different plate structures design and control for precision machines. No matterwhat methods they used, a control algorithm is also needed to achieve the goal of precision positioning[6, 7]. However, the relevant literature indicates that micro-components are very expensive; thus, someresearchers promote the precision 2-axial platforms incorporating a mechanical structure [8]. A new typeof CNC machine tool with a toggle mechanism to obtain the characteristics of low-cost and fine-resolutionhas been developed in the article. The shortcoming is that the proposed machine needs a particular drivenmethod to drive the platform and to achieve the desired positioning accuracy.

Therefore, we proposed a pantograph-based 2-axial micro platform. The 2-axial micro platform in thispaper is driven by a tenfold pantograph mechanism, and the pantograph mechanism is controlled by atraditional X-Y table. The benefits are that the X-Y table does not require high-precision and through themechanism design, the target platform can achieve micro- or nano-scale precision. In addition, the controland driving systems are well developed in the traditional numerical control machining machines. We candrive the micro-platform using the controller of a traditional X-Y table and transfer the motion by thepantograph mechanism to form a precision 2-axial platform.

In recent years, fuzzy logic controllers have already been successfully used to find the parameters for PIDcontrollers; these papers focus on improving and achieving better system performance for PID controllersin industrial processes [9–11]. The fuzzy control is often viewed as a form of nonlinear PID control becauseit provides a nonlinear input/output mapping. Hence, the majority of fuzzy control applications belong tothe class of fuzzy PID-type controllers. The fuzzy PID-type controllers process the potential to improve andachieve better system performance over conventional PID controllers. Considering the manufacturing andassembly errors, the micro-platform will result in some unknown positioning errors. Thus a fuzzy PID-typecontroller with parameters self-tuning method is used to control the micro-platform in this paper to enhancethe positioning accuracy and reduce the influence of manufacturing and assembly errors. Theoretical andsimulation results showed that the method proposed herein is feasible for development of a micro-machiningdevice which can achieve nano-level precision.

2. MECHANISM OF MICRO-PLATFORM

A pantograph mechanism combined with a rotating joint was proposed to enhance the accuracy of a 2-DOFx-y platform with micrometer precision to achieve nano-level precision in the target platform for millingmachine tools. The photograph of the pantograph mechanism based micro X-Y platform system is shown inFig. 1a. It uses four links to form a parallelogram as shown in Fig. 1b. When the point P is moving, a similarbut reduced moving trajectory will appear at point E; however, the phenomenon is only satisfied at point E,whereas other points in the neighborhood of E will not move in a proportional relationship and will rotatearound E as E is driven by point P. Therefore, in order to make the platform move following the trajectory ofpoint E without rotating, an additional designed rotation joint in the target platform was required, as shown

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(a) Photograph of pantograph mechanism based micro-platform

(b) X-Y pantograph mechanism (c) Rotating joint at position E

Fig. 1. Sketch diagram of the micro X-Y platform.

in Fig. 1c. Thus, all points in the target platform will move the same as point E. The target platform can alsobe driven by point P in the same relationship of points E and P.

Figure 1b also shows the geometry of the micro x-y platform mechanisms. Point P is the control pointof a traditional x-y platform, and point E is the moving target point of a micro x-y platform. The positionrelationship of points E and P can be expressed as

XE =ECAB

XP (1)

and

YE =ECAB

YP, (2)

where XP and YP are the displacements of the force input point P of the traditional platform; XE and YE arethe displacements of the output point E of the target micro-platform, individually.

3. CONTROLLER DESIGN

Let us consider a controller structure that simply connects the PID-type fuzzy controllers together in parallel,as shown in Fig. 2. The performance of a PID controller is based on the choice of the KP, KI and KDparameters. Thus, a self-adjusting mechanism for tuning the parameters of the fuzzy-PID controller was

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Fig. 2. Structure of fuzzy self-adjusting PID controller.

Fig. 3. Membership functions.

Table 1. Rule base of KP.

proposed in this paper. The membership functions of KP, KI and KD are shown in Fig. 3. Tables 1–3are the rule bases for KP, KI and KD, respectively. The parameters KP, KI and KD of the self-tuningfuzzy-PID controller are adjusted based on the amount of deviation and the rate of deviation change inthe system. When the deviation is large, in order to increase response time, KP requires larger, but inorder to avoid differential saturation, KD should be decreased, and KI will usually adjust to zero to preventsaturation. When the offset is medium in size, the KP value should take a smaller to avoid to producing an

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Table 2. Rule base of KI.

Table 3. Rule base of KD.

Fig. 4. The simulation wave forms by using the fuzzy adjusted PID.

excessive overshoot and KI also needs to take a small value. When the deviation is small and close to the setvalue, should increase the gains of KP and KI to make the system has good stability and avoid oscillationphenomenon.

4. SIMULATION AND EXPERIMENTAL RESULTS

Figure 4 is the simulation results of the 1 mm step response, in which the system is controlled by theproposed fuzzy adjusted PID controller and a traditional PID controller. The simulation results showed thatthe proposed fuzzy PID controller has a rise time of 0.6 s, the settling time is about 2.3 s, with an error in

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Fig. 5. The parameter of KP, PI, PD are formed by using the fuzzy adjusted PID.

(a) Path of fuzzy PID controller and traditional PID

(b) Errors

Fig. 6. X-axis position in 0.5 mm without load.

800 nm and has an overshoot about 0.02 mm. The simulation result of traditional PID controller is plotedas the orginal curve. Its rise time is 1.6 s, the settling time is about 3.4 s. Figure 5 shows the variation ofthe gains of KP, KI and KD. The initial values of KP, KI and KD are set as 3, 0.35 and 0.01, respectively.Figures 6 and 7 show the experimental results without any load on the target platform by the fuzzy PIDcontroller and the traditional PID controller. The sample time of the system is 0.25 s. They show that the X

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(a) Path of fuzzy PID controller and traditional PID

(b) Errors

Fig. 7. Y-axis position in 0.5 mm without load.

(a) Path of fuzzy PID controller and traditional PID

(b) Errors

Fig. 8. X-axis position in 5 mm with 0.5 kg load.

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(a) Path of fuzzy PID controller and traditional PID

(b) Errors

Fig. 9. Y-axis position in 5 mm with 0.5 kg load.

and Y axes positioning errors of target platform are within 200 nm by the fuzzy PID controller and 800 nmby the traditional PID controller in 0.5 mm strokes.

Figures 8 and 9 show the experimental results with a 0.5 kg load put on the center of target platform.They show that although there is an influence of the mass, the X and Y axes positioning errors of the targetplatform can also be maintained in the region of 200 nm in 5 mm strokes.

5. CONCLUSIONS

The paper proposed a prototype of a nano-scale X-Y platform with a 10 zoom-out ratio pantograph mech-anism. The simulation and experimental results verify that the proposed system can successfully controlthe target platform within 200 nm positioning precision by the fuzzy adjusted PID controller. The data alsodemonstrate the feasibility of the mechanism design. The experimental results show that the system cansuccessfully upgrade the precision from the original 2 µm to the 200 nm level by the proposed mechanism,without complex control methods.

ACKNOWLEDGEMENT

This research was supported in part by the specific research field project of the Chung Yuan ChristianUniversity, Taiwan, under grant CYCU-98-CR-ME.

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