Hi Irfan.
I notice your comment here, “.. but in 10V zener fluctuates only a bit from 11.88 to 11.96” so if we look at that result, then the voltage drop across the transistor and LED is 1.88 volts isn’t it? That’s the voltage with R4 at a zero value or close as make no difference.
As we are aiming at getting a cut-off at 13.6 volts than we need to arrive at a value for the zener/resistor combination of 11.72 volts.
As we have found that making R4 a 5K variable and that gives just over 1 volt adjustment, we could then make up the right voltage drop from a 10 volt zener by adding two diodes (1N4001,.. anything silicon really) in series. Each diode has a forward voltage drop of 0.6 volts (actually between 0.6 and 0.7 but always give as the ‘worst case’) and that would then make the effective zener+diodes a value of 11.2 volts, the 5K can then be used to trim the extra 0.7 volts and you should be in business.
In every case such as these where circuits don’t work quite as expected, it is neccessary to take a step back and look at what causes the error, then tweak the smallest number of component values till it does work. Adding series diodes to a zener reference is quite common practice because it gets expensive for equipment manufacturers to specify odd values which are not produced in such large numbers.
I would also add the 100nF capacitor from the junction of the diodes and R4 to 0 volts to be certain you will not get random variations due to noise. Zener diodes are electronically very noisy devices as they approach the point where they start to operate.
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