DESIGN OF A FUZZY-PID CONTROLLER FOR A NANOSCALE X-Y PLATFORM CONCEPTION D UN RÉGULATEUR PID (À LOGIQUE FLOUE) POUR UNE PLATEFORME X-Y NANOMÉTRIQUE

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1 DESIGN OF A FUZZY-PID CONTROLLER FOR A NANOSCALE X-Y PLATFORM Xiuli Zheng 1, Yi-Hua Fan 2, Ching-En Chen 2, Ya-Qi Lin 2, Hung-Wen Liao 2 and Sheng-Chung Hsieh 1 1 School of Auto and Mechanical Engineering, Zhejiang Industry and Trade Vocational College, Wenzhou City, China 2 Department of Mechanical Engineering, Chung Yuan Christian University, 32023, Taiwan, R.O.C. yihuafan@cycu.edu.tw IMETI 2015 I5004_SCI No. 16-CSME-38, E.I.C. Accession 3924 ABSTRACT A 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 by two small sliders; the device is driven by a traditional X-Y platform with common precision. The goal of this 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 the different PID parameters affecting platform positioning accuracy and system response for the two axes, the fuzzy-pid controller will train to fit the mechanism to promote the positioning precision and path control effect. The simulation and experimental results indicated that the proposed method is feasible for nano-scale micro-platform positioning. Keywords: fuzzy-pid controller; pantograph mechanism; nano-scale X-Y platform. CONCEPTION D UN RÉGULATEUR PID (À LOGIQUE FLOUE) POUR UNE PLATEFORME X-Y NANOMÉTRIQUE RÉSUMÉ Une conception d un régulateur PID (à logique floue) est proposée dans le présent article pour un système de positionnement de plateforme nanométrique. La plateforme X-Y ciblée est montée sur un mécanisme de type pantographe et est restreint par la rotation de deux petits glisseurs. L appareil est entraîné par une plateforme traditionnelle X-Y avec une commune précision. Le but visé dans cette recherche est l entraînement du mouvement de la plateforme dans une région de positionnement de 5 mm 5 mm, en ayant un taux d erreur de précision dans le positionnement répété de moins de 200 nm de la plateforme traditionnelle X-Y. À cause des paramètres PID (à logique floue) affectant la précision du positionnement de la plateforme et la réponse du système pour les deux axes, le régulateur PID (à logique floue) sera guidé pour s adapter au mécanisme pour favoriser la précision du positionnement et l effet de contrôle de trajectoire. Les résultats de la simulation expérimentale indiquent que la méthode préposée est une solution envisageable pour le positionnement d une micro-plateforme nanométrique. Mots-clés : régulateur PID (à logique floue); mécanisme de type pantographe; plateforme nanométrique X-Y. Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 5,

2 1. INTRODUCTION As industrial products become increasingly smaller, the demands for high aspect ratios and superior surfaces have been rapidly increasing in industries such as: aerospace, automotive, biomedical, optical, military and micro-electronics packaging, etc. Therefore, developing a micro- or even a nano-level machine to satisfy the 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 platform is an important part of the high-precision machines; thus, many researchers have focused on this topic. The methods 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 form the X-Y platforms; thus, there have been some studies [1, 2] on the topics of how to drive the two robots to achieve the micro/mesh size positioning and decrease the positioning errors. There have also been many studies [3 5] on the topics of different plate structures design and control for precision machines. No matter what 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, some researchers promote the precision 2-axial platforms incorporating a mechanical structure [8]. A new type of CNC machine tool with a toggle mechanism to obtain the characteristics of low-cost and fine-resolution has been developed in the article. The shortcoming is that the proposed machine needs a particular driven method 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 this paper is driven by a tenfold pantograph mechanism, and the pantograph mechanism is controlled by a traditional X-Y table. The benefits are that the X-Y table does not require high-precision and through the mechanism design, the target platform can achieve micro- or nano-scale precision. In addition, the control and driving systems are well developed in the traditional numerical control machining machines. We can drive the micro-platform using the controller of a traditional X-Y table and transfer the motion by the pantograph mechanism to form a precision 2-axial platform. In recent years, fuzzy logic controllers have already been successfully used to find the parameters for PID controllers; these papers focus on improving and achieving better system performance for PID controllers in industrial processes [9 11]. The fuzzy control is often viewed as a form of nonlinear PID control because it provides a nonlinear input/output mapping. Hence, the majority of fuzzy control applications belong to the class of fuzzy PID-type controllers. The fuzzy PID-type controllers process the potential to improve and achieve better system performance over conventional PID controllers. Considering the manufacturing and assembly errors, the micro-platform will result in some unknown positioning errors. Thus a fuzzy PID-type controller with parameters self-tuning method is used to control the micro-platform in this paper to enhance the positioning accuracy and reduce the influence of manufacturing and assembly errors. Theoretical and simulation results showed that the method proposed herein is feasible for development of a micro-machining device 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-DOF x-y platform with micrometer precision to achieve nano-level precision in the target platform for milling machine tools. The photograph of the pantograph mechanism based micro X-Y platform system is shown in Fig. 1a. It uses four links to form a parallelogram as shown in Fig. 1b. When the point P is moving, a similar but 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 rotate around E as E is driven by point P. Therefore, in order to make the platform move following the trajectory of point E without rotating, an additional designed rotation joint in the target platform was required, as shown 716 Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 5, 2016

3 (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 also be 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 point of a traditional x-y platform, and point E is the moving target point of a micro x-y platform. The position relationship of points E and P can be expressed as and X E = EC AB X P (1) Y E = EC AB Y P, (2) where X P and Y P are the displacements of the force input point P of the traditional platform; X E and Y E are the 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 KD parameters. Thus, a self-adjusting mechanism for tuning the parameters of the fuzzy-pid controller was Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 5,

4 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 3 are the rule bases for KP, KI and KD, respectively. The parameters KP, KI and KD of the self-tuning fuzzy-pid controller are adjusted based on the amount of deviation and the rate of deviation change in the system. When the deviation is large, in order to increase response time, KP requires larger, but in order to avoid differential saturation, KD should be decreased, and KI will usually adjust to zero to prevent saturation. When the offset is medium in size, the KP value should take a smaller to avoid to producing an 718 Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 5, 2016

5 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 set value, should increase the gains of KP and KI to make the system has good stability and avoid oscillation phenomenon. 4. SIMULATION AND EXPERIMENTAL RESULTS Figure 4 is the simulation results of the 1 mm step response, in which the system is controlled by the proposed fuzzy adjusted PID controller and a traditional PID controller. The simulation results showed that the proposed fuzzy PID controller has a rise time of 0.6 s, the settling time is about 2.3 s, with an error in Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 5,

6 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 ploted as the orginal curve. Its rise time is 1.6 s, the settling time is about 3.4 s. Figure 5 shows the variation of the 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 PID controller and the traditional PID controller. The sample time of the system is 0.25 s. They show that the X 720 Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 5, 2016

7 (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. Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 5,

8 (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 nm by 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 target platform 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 mechanism. The simulation and experimental results verify that the proposed system can successfully control the target platform within 200 nm positioning precision by the fuzzy adjusted PID controller. The data also demonstrate the feasibility of the mechanism design. The experimental results show that the system can successfully 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 Christian University, Taiwan, under grant CYCU-98-CR-ME. 722 Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 5, 2016

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