# PID Controller : Ziegler-Nichols Tuning Method

Consider the following system shown in Fig.2 (attached file) in which a PID controller is used to control the system.

The PID controller has the transfer function Gc(s) = Kp(1 + 1/Tis + Tds)

Design a PID controller for this system using Ziegler-Nichols tuning method for determination of Kp, Ti and Td. Then obtain a unit-step response curve and check to see if the designed system exhibits approximately 25% maximum overshoot. If the maximum overshoot is excessive (40% or more), make a fine tuning (most suitable tuning) and reduce the amount of the maximum overshoot to approximately 25% or less.

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• PID Controller.doc
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PID Controller and Ziegler-Nichols Tuning Method are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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Ubolthip Sethakaset, PhD (IP)

Rating 5.0/5

Active since 2004

BEng, Kasetsart University
MEng, Kasetsart University
PhD , University of Victoria

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Extracted Content from Question Files:

• PID Controller.doc

Consider the following system shown in Fig.2 in which a PID controller is used to
control the system.

R(s) + C(s)
+ Gc(s) 1
s ( s + 1)( s + 5)
__

PID controller

Fig.2
The PID controller has the transfer function

 
1
Gc(s)= Kp 1 +
 T s + Td s 

 
i

Design a PID controller for this system using Ziegler-Nichols tuning method for
determination of Kp, Ti and Td . Then obtain a unit-step response curve and check to see
if the designed system exhibits approximately 25% maximum overshoot. If the maximum
overshoot is excessive(40% or more), make a fine tuning (most suitable tuning) and
reduce the amount of the maximum overshoot to approximately 25% or less.