Improved Track Algorithm of the Four-quadrant Position-sensing

DetectorHau-Ming Huang1, Bing-Yuh Lu1,2,*, Ming-Li Tung1, Mei Wang1,

Yigh-Pyng Lin1, Jyi-Lai Shen1, Chi Wang1, Jen-Ming Hsiao1

1Tungnan University, Taipei, Taiwan2National Formosa University, Taiwan

Introduction: Traditional Approach of Four-quadrant Position-sensing Detector

DCBA

CBDAx

)()(

DCBA

DCBAy

)()(

Iterations:

Introduction

Introduction: Improved Equations

where C2=0.3 Beta=1.2

Introduction: Improved Position Errors

Methods

• Simplify the questions

Methods

• Modify the shape difference of the circle and the square

1111

)11()11('

DCBA

CBDApx

1111

)11()11('

DCBA

DCBApy

windowsquaredofPSDtheforp

windowcircularofPSDthefor p

14

Methods

• Add the buffer in the algorithm

x_dis[n+1]=(x_dis[n]-x’)*[1-2*(|x’|+kx*x’2)]

y_dis[n+1]=(y_dis[n]-y’)*[1-2*(|y’|+ky*y’2)]

wherekx=1+0.5*x’ky=1+0.5*y’

Results: The statistics of Monte Carlo simulation for average times and standard deviation of movements (where kd=[kx,ky])

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.

Method: Implementation of p

Ideally the values of the two cascaded resistors R1 and R2 should be:

That is:

Results: cascaded resistors

• We can improve the stability of p by taking R1=330kΩ, and R2=82kΩ to meet the requirements of frequently employed resistors in industry. That is, p=0.7853 with related error of 0.0074%.

Results: digital computation p=3/4

Results: digital computation p=3.14/4

Discussion: Frequency response

• Traditional:Hx(s)=1

Hy(s)=1

• RMN: anti-vibration of the PSD

Discussion: Cost analysis of cascaded resistors

• The optimal combinations of the cascaded resistors are: (1) in full surface mount device (SMD) board, the R1=330kΩ 1%, and R2=82kΩ 5%

(2) in non-full SMD board, R1=330kΩ 1% (SMD), and R2=82kΩ 5% (carbon film)

• From the perspectives on stability, precision, and cost.

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

Acknowledgements

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

Appreciate!