I am studying in one of the best engineering University of the world and our Professor wasn't able to deliver the concept as you did. I really appreciate your work kindly keep clearing our confusions.
good video. one question about canonical form though, at the end you say it would be incorrect to take the gain from the transfer function of 1/(0.5s + 0.5), but isn't the canonical form 1/s+a rather than 1/s+1 suggesting that you would need to look at another term to find the canonical form
In the video the canonical form is given as K/(tau*s+1) ... so for the transfer function 1/(0.5s+0.5) some students think the DC gain is K = 1 and the time constant is tau = 0.5. This is incorrect. In reality, you need to divide the numerator and denominator by 0.5 to get it into the canonical form, 2/(s+1). Therefore, the true DC gain is K = 2 and the true time constant is tau = 1.
Hello sir, i have watched maximum all of your videos, i was wondering that can you upload a video regarding "how to convert non linear equation to linear equation."
I am not sure what you mean with your question, but you can use the initial slope of a first-order step response to estimate the time constant. If you look at the figure shown around 23 minutes, it shows that the initial slope equals 1/time constant (if you extend the line, it crosses the steady-state value at time t = time constant). Alternatively, I tend to look at the time it takes to reach 63.2% of the total change since I think it is less sensitive to error.
If the steady-state output of the system is 5 V for a 2-V step, then the DC gain of the system is indeed 2.5. That, however, doesn't necessarily mean the controller constant K is 2.5.
