I am very much confused finding the time constant and DC gain for the below step response. The idea is to find PI gains for speed control and I am following this tutorial online Tutorial Link
Below is the open loop step response when a 10 V is applied across the DC motor. The battery is of 26 V, which means that a PWM duty cycle of 38% or 0.38 (10/26). The X-axis is time(seconds) and the y-axis is Gear box output shaft RPM. Initially it stayed at 100 RPM and then it fell down to 50RPM.
As explained in the tutorial link provided above,I am trying to find a first order transfer function between PWM Duty cycle and the output shaft angular velocity. What should be my DC gain ? Currently i am applying only 0.38(38%) duty does the time constant change if applied 1 (100 %) duty cycle ?
I am new to this topic let me know if any further information is needed.