ICE401: PROCESS INSTRUMENTATION
AND CONTROL
Class 32
Performance criteria for tuning controllers
Dr. S. Meenatchisundaram
Email: [email protected]
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
Introduction:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
• The controller design problem is associated with three logical
questions in series:
1. What type of feedback controller should be used to control a
given process - P, PI, PID?
2. How do we select the best values for the adjustable
parameters of a feedback controllers - Kc, TI , TD ?
3. What performance criterion should be used for the selection
and tuning of the controller?
Introduction:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
There are variety of performance criteria we should use, such as:
• Keep the maximum deviation error as small as possible.
• Achieve short settling time.
• Minimize the integral of the errors until the process has settled
to its desired set point and so on.
• The following two performance criteria are widely used:
1. Simple performance criteria
2. Time – Integral performance criteria
Simple performance criteria:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
• The simple performance criteria is based on some characteristic
features of the closed-loop response of a system.
Time-integral performance criteria:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
• The three popular performance indices are:
� Integral of the Square Error (ISE):
� Integral of the Absolute value of the Square Error (IAE):
� Integral of the time – weighted Absolute Error (ITAE):
2
0
( )ISE e t dt
∞
= ∫
0
( )IAE e t dt
∞
= ∫
0
( )ITAE t e t dt
∞
= ∫
Time-integral performance criteria:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
• Now, select the type of the controller and the values of its
adjusted parameters in such a way as to minimize the ISE,IAE or
ITAE of the system’s response.
• The selection of any one criteria depends on the characteristics of
the system we want to control.
• The following are some general guidelines:
1. If we want to strongly suppress large errors, ISE is better than IAE because
the errors are squared and thus contribute more to the value of the integral.
2. For the suppression of small errors, IAE is better than ISE because when
we square small numbers(smaller than one) they become even smaller.
3. To suppress errors that persist for long times, the ITAE criterion will tune
the controllers better because the presence of large ‘t’ amplifies the effect
of even small errors in the value of the integral.
Time-integral performance criteria:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
• Figure in the next slide shows the shape of the expected closed-
loop responses.
• While tuning using ISE, IAE or ITAE performance criteria, the
following two points needs to be remembered:
1. Different criteria lead to different controller designs.
2. For the same time integral criterion, different input changes
lead to different designs.
Time-integral performance criteria:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
Time-integral performance criteria:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
• The following steps should be kept in mind while selecting a
feedback controller:
1. Define an appropriate performance criterion(e.g. ISE, IAE,
or ITAE).
2. Compute the value of the performance criterion using a P, or
PI, or PID controller with the best settings for the adjusted
parameters Kc ,TI , TD.
3. Select that controller which gives the best value for the
performance criterion.
General prediction for selection:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
General prediction for selection:
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
Top Related