This document discusses controller tuning methods for process instrumentation and control. It describes the ultimate cycle method which involves gradually increasing proportional gain while providing disturbances to determine the critical gain and period. It also describes frequency response methods which use Bode plots and stability criteria regarding phase and gain margins. Tuning is demonstrated using these methods to ensure stability and acceptable quality of control as measured by factors like rise time and overshoot.

1. ICE401: PROCESS INSTRUMENTATION
AND CONTROL
Class 31
Controller Tuning and Quality of Control
Dr. S. Meenatchisundaram
Email: meenasundar@gmail.com
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015

2. Ultimate Cycle Method:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
• Reduce any integral and derivative actions to their minimum effect.
• Gradually begin to increase the proportional gain while providing
periodic small disturbances to the process.
• Note the critical gain Kc, at which the dynamic variable just begins
to exhibit steady cycling—that is, oscillations about the setpoint.
• Note the critical period Tc of these oscillations measured in minutes.
Mode Proportional
Gain
Integral Time
(Min)
Derivative
Time (Min)
P 0.5 Kc --- ---
P + I 0.45 Kc Tc / 1.2 ---
P + I + D 0.6 Kc Tc / 2 Tc / 8

3. Frequency Response Methods:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
• The frequency response method of process-controller tuning
involves use of Bode plots for the process and control loops.
• The method is based on an application of the Bode plot stability
criteria and the effects that proportional gain, integral time, and
derivative time have on the Bode plot.
• These rules for stability are as follows:
• Rule 1: A system is stable if the phase lag is more positive than
‒ 1800 at the frequency for which the gain is unity (one).
• Rule 2: A system is stable if the gain is less than one (unity) at
the frequency for which the phase lag is ‒ 1800 .

4. Frequency Response Methods:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015

5. Frequency Response Methods:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
• Suppose, if the gain is slightly less than 1 when the phase lag is
1800, the system is stable. But if the gain is slightly greater than 1 at
1800, the system is unstable.
• It would be well to design a system with a margin of safety from
such limits to allow for variation in components and other unknown
factors.
• This consideration leads to the revised stability criteria, or more
properly, a margin of safety provided to each condition.
• The exact terminology is in terms of a gain margin and phase
margin from the limiting values quoted.
• Although no standards exist, a common condition is

6. Frequency Response Methods:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
1. If the phase lag is less than 1400 at the unity gain frequency, the
system is stable. This, then, is a 400 phase margin from the limiting
value of 1800.
2. If the gain is 5 dB below unity (or a gain of about 0.56) when the
phase lag is 1800, the system is stable. This is a 5-dB gain margin.

7. Frequency Response Methods:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
1800 phase occurs at 0.3 rad/s
angular frequency where the gain
is 0.7, which is too high.
Thus, the 0.56 or less gain
margin is not satisfied, and the
controller gain will have to be
reduced slightly.

8. Quality of control:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
• The responses of a typical system to a step load change is shown in
figure to illustrate the function of the various modes of control.
• A load change for this system corresponds to a change in the inlet
concentration of reactant to tank 1.
• As process control engineers, we would be more interested in
controlling against this kind of disturbance than against a set point
change because the set point or desired product concentration is
likely to remain relatively fixed.
• In other words, this is a regulator problem and the curves of Figure
are those we would use to determine the quality of control.

9. Quality of control:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
• However, the step change in set point is frequently used to
test control systems despite the fact that the system will be
primarily subject to load changes during actual operation.

10. Quality of control:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
• Values of the various parameters determined for the responses of
Fig. are summarized in Table.

11. Quality of control:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
• It can be seen from Fig. and Table that addition of integral action
eliminates offset at the expense of a more oscillatory response.
• When derivative action is also included, the response is much faster
(lower rise time) and much less oscillatory (lower response time).
• The large overshoots realized in all three cases are characteristic of
systems with relatively large time delays.

12. 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