ask 7 Examine the P, I, and D parameters on the dynamic responses of the transfer functions in question 3. see below for the answer from question 3
ask 7 Examine the P, I, and D parameters on the dynamic responses of the transfer functions in question 3. see below for the answer from question 3
Chapter40: Push-button Synchronizing
Section: Chapter Questions
Problem 5SQ
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Task 7
- Examine the P, I, and D parameters on the dynamic responses of the transfer functions in question 3.
see below for the answer from question 3
Transcribed Image Text:Step 4: Calculating range of Kp,Kd and Ki for stable system
=> By Routh stability criteria:
The system will be stable if "There is NO-sign change of first coloum of Routh-Array"
=> The system will be stable if:
> 0
(38-Kd+Kp)
6
=> 38-Kd+Kp > 0
=> Kp-Kd> 38
Also:
(38-Kd+Kp)
6
=>
=>
-(4-Kp) + 6Ki
(38-Kd+Kp)
6
(38-Kd+Kp)
-(4-Kp) +6Ki> 0
6
=>
> (38-Kd-Kp) (4-Kp) +36 Ki> 0
Also:
-Ki>O
=> Ki<0
We Take Marginal Stability condition:
=> Kp-Kd> 38
and (38-Kd-Kp)(4-Kp) +36Ki > 0
But Ki<0
Ki> (Kp-4) (38-Kd+Kp)
> 0
=>
> (Kp-4) (38-Kd+Kp) < 0
=> KP-40
=> Kp> 4
We Know
Kp-Kd> 38
=> 4-Kd> 38
=> Kd<-34
Solution
Finally We have calculated unit step stability criteria using Routh method for above system
System will be Stable if:
Kp> 4
Kd< - 34
Ki<0
![To analyze the stability of the system using the Routh-Hurwitz method, we need to determine the
characteristic equation. The characteristic equation is obtained by setting the denominator of the
closed-loop transfer function T(s) equal to zero:
=>
> Charachetristics equation CE will be:
1
=> CE = [1-{-
(s³ +6s²+7s+4)
After simlifies the expression we get:
CE=s4 +6s³+(7- Kd)s² + (4-Kp)s - Ki
Ki
x[Kp+^ + Kd x s]}] = 0
S](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac58b9ad-fa5b-484f-b886-8310827fb48f%2F6ce9b7e8-55e1-4bc1-9282-eb21a0cbcb28%2Foxx0ozp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:To analyze the stability of the system using the Routh-Hurwitz method, we need to determine the
characteristic equation. The characteristic equation is obtained by setting the denominator of the
closed-loop transfer function T(s) equal to zero:
=>
> Charachetristics equation CE will be:
1
=> CE = [1-{-
(s³ +6s²+7s+4)
After simlifies the expression we get:
CE=s4 +6s³+(7- Kd)s² + (4-Kp)s - Ki
Ki
x[Kp+^ + Kd x s]}] = 0
S
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