PI control of typical processes, with automatic tuning
Description
In this examples the typical processes (contained in model
TypicalTF )
are controlled with PI regulators with automatic tuning. The aim of this example is to show how the automatic
tuning algorithm works with varius processes. For each trasfer function taken into account have been compared the
parameter values before and after the tuning. Also the algorith parameters are listed too. It is possible to see
that they have different values, depending on the considered example (e.g. the slope must be adapted in order to
avoid big oscillations, the percentual tolerance have to be adapted if the period of the oscillation changes,...).
The example is made of three phases:
- Set point following with default parameters,
- Automatic tuning,
- Set point following with the tuned parameters.
Process Trasfer function
| Integrator |
Y(s) 1
---- = -----
U(s) 5s
|
Controller parameters
| Parameter | Before | After AT |
| Kp | 5 | 73.4625 |
| Ti | 1 | 0.273 |
Automatic Tuning algorithm parameters
| Parameter | Value |
| slope | 1 |
| PermOxPeriodPerc | 5 |
| pm | 65 |
| nOxMin | 3 |

Process Trasfer function
| Integrator + delay |
Y(s) 1 -1s
---- = ----- e
U(s) 5s
|
Controller parameters
| Parameter | Before | After AT |
| Kp | 5 | 1.067 |
| Ti | 30 | 26.54 |
Automatic Tuning algorithm parameters
| Parameter | Value |
| slope | 0.01 |
| PermOxPeriodPerc | 30 |
| pm | 70 |
| nOxMin | 3 |

Process Trasfer function
| First Order |
Y(s) 1
---- = --------
U(s) 1 + 5s
|
Controller parameters
| Parameter | Before | After AT |
| Kp | 5 | 71.5948 |
| Ti | 1 | 0.1365 |
Automatic Tuning algorithm parameters
| Parameter | Value |
| slope | 1 |
| PermOxPeriodPerc | 5 |
| pm | 65 |
| nOxMin | 3 |

Process Trasfer function
| First Order + delay |
Y(s) 1 -2s
---- = -------- e
U(s) 1 + 5s
|
Controller parameters
| Parameter | Before | After AT |
| Kp | 1 | 2.11 |
| Ti | 4 | 5.1879 |
Automatic Tuning algorithm parameters
| Parameter | Value |
| slope | 0.1 |
| PermOxPeriodPerc | 5 |
| pm | 65 |
| nOxMin | 3 |

Process Trasfer function
| Fast Slow |
Y(s) 1 + 5.8s
---- = --------------
U(s) (1 + 6s)(1+s)
|
Controller parameters
| Parameter | Before | After AT |
| Kp | 5 | 14.056 |
| Ti | 1 | 0.1365 |
Automatic Tuning algorithm parameters
| Parameter | Value |
| slope | 1 |
| PermOxPeriodPerc | 5 |
| pm | 65 |
| nOxMin | 3 |

Process Trasfer function
| Overshooting |
Y(s) 1 + 8s
---- = ---------------
U(s) (1 + 5s)(1+2s)
|
Controller parameters
| Parameter | Before | After AT |
| Kp | 5 | 17.3146 |
| Ti | 1 | 0.1365 |
Automatic Tuning algorithm parameters
| Parameter | Value |
| slope | 1 |
| PermOxPeriodPerc | 5 |
| pm | 65 |
| nOxMin | 3 |

Process Trasfer function
| Undershooting |
Y(s) 1 - 5.5s
---- = ---------------
U(s) (1 + 5s)(1+2s)
|
Controller parameters
| Parameter | Before | After AT |
| Kp | 0.1 | 7.69 |
| Ti | 1 | 0.692 |
Automatic Tuning algorithm parameters
| Parameter | Value |
| slope | 0.05 |
| PermOxPeriodPerc | 5 |
| pm | 45 |
| nOxMin | 3 |

Process Trasfer function
| Complex Poles |
Y(s) 1
---- = --------------------
U(s) 1 + 1.2 s + 0.025s
|
Controller parameters
| Parameter | Before | After AT |
| Kp | 1 | 0.548 |
| Ti | 5 | 4.3 |
Automatic Tuning algorithm parameters
| Parameter | Value |
| slope | 0.1 |
| PermOxPeriodPerc | 5 |
| pm | 65 |
| nOxMin | 3 |

- Industrial Control Systems (v 1.0.0) : April-May 2012
- List of revisions:
- 11 May 2012 (author: Marco Bonvini)
- Main Authors:
- Marco Bonvini; <bonvini@elet.polimi.it>
- Alberto Leva <leva@elet.polimi.it>
- Politecnico di Milano
- Dipartimento di Elettronica e Informazione
- Via Ponzio 34/5
- 20133 Milano - ITALIA -
- Copyright:
- Copyright © 2010-2012, Marco Bonvini and Alberto Leva.
- The IndustrialControlSystems package is free software; it can be redistributed and/or modified under the terms of the Modelica license.
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