Which is your problem? The question is not clear.

Do you have problem with finding where to point it, or making it point to the desired position?

If the sun comes close to zenith, the array should really be able to point there, the installation is incorrect if it can't. Ideally, one axis of the mechanics should be parallel to the earth axis, and that one would just have to go constant speed while the sun is up and the other one would just have to adjust elevation once per day.

If there are limitations prohibiting following the sun to zenith (or any other point on the desired trajectory), you need to find the actual working limits, otherwise you will hit the end stops, possibly damaging things, or at least loose more time than necessary trying to track along forbidden trajectories. With the limits, you should be able to construct trajectories, that will work for every day. The date and time completely determines where to point. Without these limits, the control might end up in a dead end state (local error minimum with no path to the global minimum).

Finding the rig limits are crucial.

 the problem is that I don't know the start angle or the end angle of the zenith. the tracker slope on mast should varies from 0 to 90 but it isn't. there is a slope between the tracker table and the mast on the steep position and also on the fleet position. I should know that slope to put it in the program. how to measure this slope?

The usual way to get accurate sensor calibration is manual measurement of a few positions in manual mode and making a conversion table or correcting function.

The mechanics can also include non-linear components, so if the slope is not constant, more points will be needed.

could you give example for sensors?

In the first link is a nice write-up of the different types of sensors for tracking the rig. To get more robust positioning, you can try to also track the sun, but knowing where the rig is, is important for safety and it is definitely needed for manual operation. The sensor requiring minimal hardware would probably be a single turn encoder with quadrature output, such as described in the second link.

http://blog.pepperl-fuchs.us/blog/bid/253098/5-Ways-to-Track-Your-Solar-Tracker

http://www.arduinoos.com/2010/06/rotary-encoders/

You can make the sensor using phototransistors, 4 is enough, one for each cardinal direction. You need to isolate light from the transisrtors installing them in an angled position or installing a dividing cross between them.

The idea is that you get the same amount of signal only when you point directly to the sun, otherwise you get an unbalanced measurement.

From that point is easy to implement a PID loop and make your panels track sun easily.

This is an old problem. I supervised a group of students who designed and executed the project with closed loop control using microcontroller. Is your system a feedback control one? how many degrees of freedom do you have? Your source of error could be one of the followings if the system is feedback control tracking system:

1- Uncalibrated sensors.

2- Sensors not positioned accurately in a balanced distribution.

3- You are implementing open-loop control based on time.

4-The system controller is not PID, if you are using on-off control steady state error is very likely.

5- The controller integrator action is absent or not well tuned, or the PID is not well tuned.

6- If you are doing feedback control, you don't need gear ratio, or any knowledge about the Zenith or Azimuth or elevation. Regardless of how you put the system it should accurately track the sun.

The first step is to understand what kind of control you are implementing.

Best wishes! 

I am doing both of controllers ( open loop with time calculations and closed loop with  sun  sensors) but first I want to control it precisely with time calculations. so I need to know the starting  and stop angle of the mechanical structure. I repeat I don't want to depend on the sun sensors completely.

Hi!

If your problem is to determine the right elevation angle, you must to take into account this angle depend on your latitude,  besides date and time, and consequently the table of values should be changed for every day. A easy tool on line to determine the elevation angle is the elevation versus azimuth chart, you can obtain in the URL: http://www.sunearthtools.com/dp/tools/pos_sun.php?lang=en

You must to enter your geographic coordinates at “search” textbox, or the name of your place at “name” textbox and the charts polar and cartesian are automatically generated. And in the section “Annual sun path” you can download a excel or csv type file with the elevation and azimouth angles for each day of the year in steps of 5, 10, 15, 20, 30 or 60 minutes.

On the other hand you don’t need to try following the sun for elevation angles less than five degree.

Thank you for your help, but I am working with concentrated PV which requires 0.1 degree precision. and this URL 

is not precise. there is error 6 degrees compared to my calculation which is closer to the precise angle

http://www.sunearthtools.com/dp/tools/pos_sun.php

Please, allow me an observation:

I have not checked the accuracy of algorithm used in SunEarthTools.com to obtain Sun position but in the section Sun position equation it says:

The calculation of the position of the sun is based on equations from Astronomical Algorithms, by J.J. Michalsky.

Accuracy of 0.01 deg, the observed values may vary from calculations because they depend by: atmospheric composition, temperature, pressure and other conditions.

It’s very rare the diference in 6 degree that you point in your answer above.