modelPID

Proportional + Integral + Derivative two degree of freedom controller

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

Information

Description

Proportional + Integral + Derivative with two degree of freedom controller with Automatic, Tracking mode and bias signal.
The control law is defined as

            [                      1                        sTd                      ]
  CS(s) = Kp[ (bSP(s) - PV(s)) + ----- (SP(s) - PV(S)) + -----------(cSP(s) - PV(s)) ]
            [                     sTi                     1 + sTd/N                  ]

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 (*)

(*) AutoTuning Not available here, please see the package
AutoTuning

The controller can have various operating conditions:

Automatic,
and Tracking

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

To note that in the tracking mode the output of the integral block is forced to follow the track reference

              1
  I(s) = ---------- TR(S)
           1+s*eps

where eps is a small time constant. Thanks to such a scheme, the integrator does not diverge while the tracking mode
is enabled.

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
Real	Tt	max(1e3eps, sqrt(TiTd))	Reset time for the integrator (it should be larger than Td and smaller than Ti)
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
Real	Ti	1	Integral time
Real	Td	1	Derivative time
Real	N	10	Derivative filter ratio
Real	b	1	Set point weighting for the proportional action
Real	c	1	Set point weighting for the derivative action

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
Real	Paction	proportional action
Real	Iaction	integral action
Real	Daction	derivative action
Real	Fder	filtered weigthed error
Real	satin	saturation input
Real	satDiff	difference between saturation input and output signals
Real	cs	Control Signal before the biasing

Revisions

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