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!
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