1. Improved Track Algorithm of the Four-quadrant Position-sensing Detector Hau-Ming Huang 1, Bing-Yuh Lu 1,2,*, Ming-Li Tung 1, Mei Wang 1, Yigh-Pyng Lin 1, Jyi-Lai Shen 1, Chi Wang 1, Jen-Ming Hsiao 1 1 Tungnan University, Taipei, Taiwan 2 National Formosa University, Taiwan

2. Introduction: Traditional Approach of Four- quadrant Position-sensing Detector Iterations:

3. Introduction

4. Introduction: Improved Equations where C2=0.3 Beta=1.2

5. Introduction: Improved Position Errors

6. Methods Simplify the questions

7. Methods Modify the shape difference of the circle and the square

8. Methods Add the buffer in the algorithm x_dis[n+1]=(x_dis[n]-x’)*[1-2*(|x’|+k x* x’ 2 )] y_dis[n+1]=(y_dis[n]-y’)*[1-2*(|y’|+k y* y’ 2 )] where k x =1+0.5*x’ k y =1+0.5*y’

9. Results: The statistics of Monte Carlo simulation for average times and standard deviation of movements (where k d =[k x,k y ])

10. Method: Implementation of p The value p is a ratio which is implemented with cascaded resistors in the principle of voltage division, or the floating point operation in microcontrollers. In a low-cost microcontroller, such as the INTEL 8051 Series, the algorithm of division is complex.

11. Method: Implementation of p Ideally the values of the two cascaded resistors R 1 and R 2 should be: That is:

12. Results: cascaded resistors We can improve the stability of p by taking R 1 =330kΩ, and R 2 =82kΩ to meet the requirements of frequently employed resistors in industry. That is, p=0.7853 with related error of 0.0074%.

13. Results: digital computation p=3/4

14. Results: digital computation p=3.14/4

15. Discussion: Frequency response Traditional: H x (s)=1 H y (s)=1 RMN: anti-vibration of the PSD

16. Discussion: Cost analysis of cascaded resistors The optimal combinations of the cascaded resistors are: (1) in full surface mount device (SMD) board, the R 1 =330kΩ 1%, and R 2 =82kΩ 5% (2) in non-full SMD board, R 1 =330kΩ 1% (SMD), and R 2 =82kΩ 5% (carbon film) From the perspectives on stability, precision, and cost.

17. Conclusion The RMN algorithm: Improves performance in speed, but requires few components in analog circuit design. Feasible to use the RMN algorithm in practical applications. Global warming: Sun tracker for solar cell

18. Acknowledgements “The investigation of smart solar light tracker controller”, the Institute of Nuclear Energy Research, Atomic Energy Council, Taiwan

19. Appreciate!