# What is the corresponding transfer function between r and y?

What is the corresponding transfer function between r and y??

I have tried $$\frac{( \frac{k_i}{s}+k_p+k_d\ s )\times P(s)}{1-(-1)(\frac{k_i}{s}+k_p+k_d\ s)\times P(s)}$$

• What have you worked out so far ? Please edit the steps you have already worked out into the question. Have you tried block diagram reduction methods ? Are you familiar with the feedback formula $\frac{G}{1+GH}$ ? Please edit all such details into the question.
– AJN
Jun 20, 2021 at 7:55
• i have tried( ki/s+kp+kds)*p(s)/1-(-1)(ki/s+kp+kds)*p(s) Jun 20, 2021 at 8:07
• Is the diagram drawn correctly ? Do the input lines to Kp and Kd come from the summing junction or the -1 block ? If it comes from the -1 block, it is somewhat suspicious. I think your answer is correct only if the input to the Kp and Kd are same as the input given to Ki. Otherwise, you can't add those terms. If I carefully look at the input lines to Kp and Kd, I can see that the lines are darker leading to the summing block. Hmmm.... suspicious....
– AJN
Jun 20, 2021 at 8:27
• Also, what are signs to the summing blocks ? are all positive ?
– AJN
Jun 20, 2021 at 8:28
• all positive ..i have the answer but i dont understand hem Gyr=bki/(1+bkd)s^2+(a+bkp)s+bki Jun 20, 2021 at 8:33

## 1 Answer

If Kp and Kd are fed from the -1 block, then you have two loops; an inner loop and an outer loop. Solve the inner loop (q to y) using the feedback formula. To solve the inner loop, imagine that the parts shown in pink colour in the diagram below, are not present in the diagram. Replace the result ($$\frac{Y(s)}{Q(s)}$$) back into the diagram.

Now solve the outer loop $$\frac{Y(s)}{R(s)}$$ using the result from the inner loop. Use the feedback formula for that also.

I have redrawn the diagram to clearly show the two loops. (Check the redrawn figure for correctness).

• thank you i got the correct answer .. i have a question .how did we become two (-1) blue and red ..??did we move pick off point ?? Jun 20, 2021 at 10:46
• If you are familiar with block diagram reduction methods; yes; the pick off point was shifted from output side of the -1 block to its input side. That results in two copies of the block.
– AJN
Jun 20, 2021 at 12:26
• thank you very much Jun 20, 2021 at 13:04