.IndustrialControlSystems.Controllers.AutoTuning.ATPIrelayNCdigital

Information

Description

Proportional + Integral controller with AutoTuning, Automatic, Tracking mode and bias signal.
The control law is defined as

              1+sTi 
  CS(s) = Kp ------- (SP(s) - PV(S))
               sTi

Scheme

Name	Description	Conditional?
SP	Set Point	NO
PV	Process Variable	NO
CS	Control Signal	NO
TR	Track Reference signal	YES (useTS)
TS	Track Switch signal	YES (useTS)
Bias	Biasing signal	YES (useBIAS)
ATreq	AutoTuning request	YES (useAT)

The controller can have various operating conditions:

Automatic,
Auto Tuning,
and Tracking

In the Automatic mode, the control output is computed with the proportional+integral control law, while in the tracking mode
it is defined by the input TR.

Auto Tuning

This section presents the Modelica realisations of the fully digital of the considered autotuning methodology. The block inputs are the set point (SP) and the process variable (PV), plus a boolean one, a pulse on which initiates the autotuning procedure; the output is clearly the control signal (CS). The initial values for K and Ti, as well as the required phase margin pm, are provided as parameters. The autotuning procedure is composed of the following steps:

start with the controller in PI mode;
when the AT pulse is received,

initialise the relay plus integrator control,
connect it to the process,
and wait for a permanent oscillation;

when a permanent oscillation is detected, compute its frequency (wox), and by means of the following equation determine the corresponding process frequency response magnitude (the phase is -90 degrees);
```
  Pox    := pi^2*(rPVmax-rPVmin)/8/(rCSmax-rCSmin)
  
```

apply equations

  TI     := tan(pm/180*pi)/wox
  K      := tan(pm/180*pi)/(Pox*sqrt(1+(tan(pm/180*pi))^2))

to tune the regulator, and finally switch back to PI mode.

It is worth noticing that any industrial realisation would be more articulated than those illustrated in the following. For example, some logic would need introducing to abort the procedure in the case of unexpected and/or possibly harmful system behaviours, a confirmation should be requested to the operator in order to accept or decline the proposed parameters prior to updating the PI, and so forth. Such features are however omitted here since they are lengthy to discuss in the necessary detail, and substantially inessential for the purpose of this work.

References

For more information please refers to the following paper:

Efficient hybrid simulation of autotuning PI controllers
Alberto Leva, Marco Bonvini
8th Modelica Conference, Dresden, Germany
march 20-22, 2011

Revisions

Industrial Control Systems (v 1.0.0) : April-May 2012