This document discusses integral and derivative control modes in process instrumentation and control. It provides examples of calculating integral gain and designing an op-amp integral controller. It also explains the equations for theoretical and practical derivative control circuits and guidelines for derivative mode design, including setting a maximum frequency and capacitor value based on that frequency. The document is for an Instrumentation and Control course taught by Dr. S. Meenatchisundaram at MIT Manipal from August to November 2015.

1. ICE401: PROCESS INSTRUMENTATION
AND CONTROL
Class 25
Integral, Derivative Electronic Controllers
Dr. S. Meenatchisundaram
Email: meenasundar@gmail.com
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015

2. Integral Control Mode:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
• Suppose we have an input range of 6 V, an output range of 5 V, and
KI = 3.0%/(% ‒ min).
• Integral gain is often given in minutes because industrial processes
are slow, compared to a time of seconds.
• This gain is often expressed as integration time, TI, which is just the
inverse of the gain, so TI = 0.33 min or 19.8 sec.
• We must first convert the time units to seconds. Therefore
• An error of 1% for 1 s is found from
(0.01)(6 V)(1 s) = 0.06 V ‒ s
3% 0.05%1min
% min 60sec % s
    =
− −   

3. Integral Control Mode:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
• Furthermore, KI percent of the output (using the seconds
expression for gain) is
(0.0005)(5 V) = 0.0025V
• Therefore, the integral gain in terms of voltage must be
GI=(0.0025V)/(0.06V‒s)=0.0417s-1
• The values of R and C can be selected from this.

4. Integral Control Mode:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
Try:
An integral control system will have a measurement range of 0.4 to 2.0
V and an output range of 0 to 6.8 V. Design an op amp integral
controller to implement a gain of KI = 4.0%/(% ‒ min). Specify the
values of GI, R1 and C.
Solution:
We must first convert the time units to seconds. Therefore
KI percent of the output (using the seconds expression for gain) is
(0.000667)(6.8V) = 0.00454 V
4% 0.0667%1min
% min 60sec % s
    =
− −   

5. Integral Control Mode:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
• An error of 1% for 1 s is found from
(0.01)(1.6 V)(1 s) = 0.016 V ‒ s
• Therefore, the integral gain in terms of voltage must be
GI=(0.00454V)/(0.016V‒s)=0.283s-1
• Since, GI = 1/RC,
• RC = 3.524. By selecting C = 100µF, then R = 35.3K .

6. Derivative Control Mode:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
( ) p
D
de
p t K
dt
=
e
out
dV
V RC
dt
= −
• For a theoretical derivative op-amp circuit,

7. Derivative Control Mode:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
• For a practical derivative op-amp circuit,
• From the above equation, the output depends upon the derivative of
the input voltage, but there is now an extra term involving the
derivative of the output voltage.
• Essentially, we have a first-order differential equation relating input
and output voltage.
• For very high frequencies the impedance of the capacitor becomes
very small and can be neglected.
• Then the circuit becomes just an inverting amplifier with a gain is
‒ (R2/R1).
1 2
out e
out
dV dV
V R C R C
dt dt
+ = −

8. Derivative Control Mode:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
• At low frequency the impedance of the capacitor will be large so R1
can be neglected. Then, the response of can be given as,
• The circuit exhibits a derivative response provided the following
inequality is satisfied, i.e, 2 π f R1 C << 1.
• The following derivative mode design guidelines can be followed:
1. Estimate the maximum frequency at which the physical system
can respond, fmax.
2. Set 2πfmaxR1 C =0.1 and solve for R1. (C is found from the
mode derivative gain requirement.)
e
out
dV
V RC
dt
= −

9. References:
• Process Control Instrumentation Technology, by Curtis D.
Johnson, Eighth Edition, Pearson Education Limited.
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015