modelATPIrelayNCmixedMode

PI controller with Auto Tuning algorithm - mixed continuous/discrete time version -

Extends from IndustrialControlSystems.Controllers.Interfaces.Controller (Partial interface for a generic controller).

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.

Mixed Mode

When everything is digital, things are simple, and the only issue to care about is to correctly manage the regulator tracking while the relay is driving the control signal so as to achieve the required permanent oscillation. If conversely one wants to represent the controller as a continuous-time system, it is necessary to suitably coordinate it with the digital procedure. The solution adopted here can be summarised as follows. First, implement the controller in the desired form (here, for consistence with the digital case, an antiwindup PI was chosen) as differential and algebraic equations. Then, realise the autotuning procedure as a digital algorithm, including the control computation during that procedure, exactly as it was in the fully digital case. Finally, manage the autotuning request event by (a) setting a flag that selects the control output to be that coming from the equations or the algorithm, depending on the mode, and (b) initialising the algorithm output to the last equation output. Analogously, manage the autotuning termination by resetting the above flag, and reinitialising the equation-based controller state to match the last algorithm output. The only (small) disadvantage of such a solution is that the equation-based controller stays in place during the autotuning phase. However the resulting overhead is generally very limited, given the invariantly simple structure of the controller, while there is a gain in terms of simplicity with respect to possible alternative solutions attempting to avoid said overhead.

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

Parameters

Type	Name	Default	Description
Real	eps (from Controller)	1e-1	small time constant that represents the time for switching between auto and tracking mode
Boolean	useTS (from Controller)	false	=true, if TS and TR inputs are enabled
Boolean	useBIAS (from Controller)	false	=true, if BIAS input is enabled
Boolean	useAT (from Controller)	false	=true, if AutoTuning input is enabled
Boolean	useGS (from Controller)	false	=true, if GainScheduling inputs are enabled
Boolean	useSAT (from Controller)	false	=true, if Saturation outputs are enabled
Discretisation
Real	Ts (from Controller)	0	Sampling time (if <= 0 continuous time)
IndustrialControlSystems.LinearSystems.Discrete.Types.discrMethod	method (from Controller)	IndustrialControlSystems.LinearSystems.Discrete.Types.discrMethod.BE	Discretisation method
Saturation
Boolean	AntiWindup (from Controller)	false	Flag that enables the antiwindup feature
Real	CSmin (from Controller)	0	minimum value of the CS
Real	CSmax (from Controller)	1	maximum value of the CS
Initialisation
Real	CS_start (from Controller)	0	output initial value
Parameters
Real	Kp	5	Proportional gain (initial value)
Real	Ti	1	Integral time (initial value)
Auto Tuning Algorithm
Real	slope	1	Slope of the signal
Real	permOxPeriodPerc	5	allowed % difference between period measurements
Real	pm	45	Phase Margin required
Integer	nOxMin	3	minimum number of oscillations

Connectors

Type	Name	Description
Modelica.Blocks.Interfaces.RealInput	TR (from Controller)	Track Reference signal
Modelica.Blocks.Interfaces.BooleanInput	TS (from Controller)	Track Switch signal
Modelica.Blocks.Interfaces.RealInput	BIAS (from Controller)	Bias
Modelica.Blocks.Interfaces.RealInput	SP (from Controller)	Set Point signal
Modelica.Blocks.Interfaces.RealOutput	CS (from Controller)	Control signal
Modelica.Blocks.Interfaces.RealInput	PV (from Controller)	Process Variable signal
Modelica.Blocks.Interfaces.BooleanInput	ATreq (from Controller)	Auto Tuning request
Modelica.Blocks.Interfaces.BooleanOutput	satHI (from Controller)
Modelica.Blocks.Interfaces.BooleanOutput	satLOW (from Controller)

Components

Type	Name	Description
Real	bias (from Controller)	bias signal
Real	tr (from Controller)	track reference value
Boolean	ts (from Controller)	track reference signal
Boolean	at_req (from Controller)	auto tuning enabling signal
Boolean	satHigh (from Controller)	High saturation signal
Boolean	satLow (from Controller)	Low saturation signal
Integer	iMode
Real	K
Real	TI

Revisions

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