Class 20 effect of kp, ki & kd and pid control mode

ICE401: PROCESS INSTRUMENTATION
AND CONTROL
Class 20
Effect of Kp, Ki & Kd and PID Control Mode
Dr. S. Meenatchisundaram
Email: meenasundar@gmail.com
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Jan – May 2015

Function of the Proportional Term:
• The plot below illustrates the variation in process variable
for a set point response.
• The error used in the proportional calculation is shown on
the plot:
• At time t = 25 min, e(25) = 60–56 = 4, at time t = 40 min,
e(40) = 60–62 = –2

Function of the Proportional Term:
• Computing and plot e(t) at each point in time t

Function of the Integral Term:
• The integral sum of error is computed as the shaded areas
between the SP and PV traces as

• Since it is controller error that drives the calculation, we
get a direct view the situation from a controller error plot
as shown below

• At time t = 60 min on the plots, the integral sum is 135 –
34 = 101. The response is largely settled out at t = 90 min,
and the integral sum is then 135 – 34 + 7 = 108.
• The response is largely complete at time t = 90 min, yet
the integral sum of all error is not zero.
• In this example, the integral sum has a final or residual
value of 108.
• It is this residual value that enables integral action of the
PI controller to eliminate offset.

Effects of Kp, Ki and Kd:
• Effects of Kp:

• Effects of Ki:

• Effects of Kd:

Three-Mode Controller (PID):
• One of the most powerful but complex controller mode
operations combines the proportional, integral, and
derivative modes.
• This system can be used for virtually any process
condition. The analytic expression is
• This mode eliminates the offset of the proportional mode
and still provides fast response.
0
( ) (0)
t
p
P P P I p P D I
de
p t K e K K e dt K K p
dt
= + + +∫

• For a three-mode controller with KP = 5, KI = 0.7 s-1, KD =
0.5 s and PI(0) = 20%, draw a plot of the controller output
for the error given in figure.
Solution:
• The error can be expressed in three time regions.
0 ≤ t ≤ 1 ep = t %
1 ≤ t ≤ 3 ep = 1 %
3 ≤ t ep = -0.5t +2.5 %

Case 1: 0 ≤ t ≤ 1 ep = t %
Case 2: 1 ≤ t ≤ 3 ep = 1 %
1
1
0
5 3.5 2.5 20pde
p t t dt
dt
= + + +∫
1 5 1.75 2.5 20p t= + + +
( )2 3.5 1 26.75p t= − +
2 p
1
5 3.5 e 2.5 21.75
t
p
p
de
p e dt
dt
= + + +∫

Case 3: 3 ≤ t ≤ 5 ep = -0.5t +2.5 %
( )
2
3
0.5 4.5
5 0.5 2.5 3.5 2.5 7.5 28.75
2 2
t
p t t
 −
= − + + + + − + 
 
3 p
3
5 3.5 e 2.5 28.75
t
p
p
de
p e dt
dt
= + + +∫
2
3 0.875 6.25 21.625p t t= − + +

References:
• Process Control Instrumentation Technology, by Curtis D.
Johnson, Eighth Edition, Pearson Education Limited.

Class 20 effect of kp, ki & kd and pid control mode

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Class 20 effect of kp, ki & kd and pid control mode