PID

Limited PID controller

Diagram

Information

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This element makes use of the →LimPID element in the Modelica Standard Library. The controller is a very flexible component which allows to model P, PI, PD, PID controllers as needed.

A PID controller continually calculates the error e(t) = u_desiredValue(t) - u_currentValuet(t) and then applies a correction based upon proportional (P), integral (I), and derivatice (D) terms as indicated in the standard form

y(t) = ...

The parameter k here denotes the total gain for the controller's output, i.e., the sum of the respective error terms. Ti can be thought of as the time span to correct the total accumulated error, while Td is the time to forecast the error into the future, i.e., the current rate of change for the error times Td.

Parameters (19)

controllerType	Value: SimpleController.PID Type: SimpleController Description: Type of controller
k	Value: 1 Type: GainType (1/s) Description: Gain of controller [GainType]
Ti	Value: 0.5 Type: Time (s) Description: Time constant of integrator (i.e., gain for integrator = 1/Ti)
Td	Value: 0.1 Type: Time (s) Description: Derivative gain (i.e., time span for error prediction)
yMax	Value: inf Type: Rate (1/s) Description: Upper limit of output
yMin	Value: -yMax Type: Rate (1/s) Description: Lower limit of output
wp	Value: 1 Type: Fraction Description: Set-point weight for Proportional block (0..1)
wd	Value: 0 Type: Fraction Description: Set-point weight for Derivative block (0..1)
Ni	Value: 0.9 Type: Dimensionless Description: Ni*Ti is time constant of anti-windup compensation
Nd	Value: 10 Type: Dimensionless Description: The higher Nd, the more ideal the derivative block
kFF	Value: 1 Type: Dimensionless Description: Gain of feed-forward input
initType	Value: Init.NoInit Type: Init Description: Type of initialization (1: no init, 2: steady state, 3: initial state, 4: initial output)
xi_start	Value: 0 Type: Unspecified Description: Initial or guess value for integrator output (= integrator state)
xd_start	Value: 0 Type: Unspecified Description: Initial or guess value for state of derivative block
y_start	Value: 0 Type: Rate (1/s) Description: Initial value of output
homotopyType	Value: LimiterHomotopy.Linear Type: LimiterHomotopy Description: Simplified model for homotopy-based initialization
hasFeedForward	Value: false Type: Boolean Description: Use feed-forward input?
strict	Value: false Type: Boolean Description: = true, if strict limits with noEvent(..)
limitsAtInit	Value: true Type: Boolean Description: Has no longer an effect and is only kept for backwards compatibility (the implementation uses now the homotopy operator)

Connectors (4)

	y	Type: RealOutput Description: Policy output signal
	u_desiredValue	Type: RealInput Description: The goal to meet (setpoint)
	u_currentValue	Type: RealInput Description: The measured state of the system under control
	u_feedForward	Type: RealInput Description: An optional feedforward input

Components (1)

	PID	Type: LimPID Description: P, PI, PD, and PID controller with limited output, anti-windup compensation, setpoint weighting and optional feed-forward

PID

Type: LimPID

Description: P, PI, PD, and PID controller with limited output, anti-windup compensation, setpoint weighting and optional feed-forward

Revisions

Updated type definitions and documentation in v2.0.0.

Class adapted as to be compliant with MSL 4.0.0 in v2.2.