blockLimPID

P, PI, PD, and PID controller with limited output, anti-windup compensation and setpoint weighting

Extends from Modelica.Blocks.Interfaces.SVcontrol (Single-Variable continuous controller).

Information

PID controller in the standard form

y = k ( e(t) + 1 ⁄ T_i ∫ e(s) ds + T_d de(t)⁄dt ),

where y is the control signal, e(t) = u_s - u_m is the control error, with u_s being the set point and u_m being the measured quantity, k is the gain, T_i is the time constant of the integral term and T_d is the time constant of the derivative term.

Note that the units of k are the inverse of the units of the control error, while the units of T_i and T_d are seconds.

For detailed treatment of integrator anti-windup, set-point weights and output limitation, see Modelica.Blocks.Continuous.LimPID.

Options

This controller can be configured as follows.

P, PI, PD, or PID action

Through the parameter controllerType, the controller can be configured as P, PI, PD or PID controller. The default configuration is PI.

Direct or reverse acting

Through the parameter reverseActing, the controller can be configured to be reverse or direct acting. The above standard form is reverse acting, which is the default configuration. For a reverse acting controller, for a constant set point, an increase in measurement signal u_m decreases the control output signal y (Montgomery and McDowall, 2008). Thus,

for a heating coil with a two-way valve, leave reverseActing = true, but
for a cooling coil with a two-way valve, set reverseActing = false.

Reset of the controller output

The controller can be configured to enable an input port that allows resetting the controller output. The controller output can be reset as follows:

If reset = Buildings.Types.Reset.Disabled, which is the default, then the controller output is never reset.
If reset = Buildings.Types.Reset.Parameter, then a boolean input signal trigger is enabled. Whenever the value of this input changes from false to true, the controller output is reset by setting y to the value of the parameter y_reset.
If reset = Buildings.Types.Reset.Input, then a boolean input signal trigger and a real input signal y_reset_in are enabled. Whenever the value of trigger changes from false to true, the controller output is reset by setting the value of y to y_reset_in.

Note that this controller implements an integrator anti-windup. Therefore, for most applications, keeping the default setting of reset = Buildings.Types.Reset.Disabled is sufficient. However, if the controller is used in conjuction with equipment that is being switched on, better control performance may be achieved by resetting the controller output when the equipment is switched on. This is in particular the case in situations where the equipment control input should continuously increase as the equipment is switched on, such as a light dimmer that may slowly increase the luminance, or a variable speed drive of a motor that should continuously increase the speed.

References

R. Montgomery and R. McDowall (2008). "Fundamentals of HVAC Control Systems." American Society of Heating Refrigerating and Air-Conditioning Engineers Inc. Atlanta, GA.

Parameters

Type	Name	Default	Description
Modelica.Blocks.Types.SimpleController	controllerType	Modelica.Blocks.Types.SimpleController.PI	Type of controller
Real	k	1	Gain of controller
Modelica.Units.SI.Time	Ti	0.5	Time constant of Integrator block
Modelica.Units.SI.Time	Td	0.1	Time constant of Derivative block
Real	yMax	1	Upper limit of output
Real	yMin	0	Lower limit of output
Real	wp	1	Set-point weight for Proportional block (0..1)
Real	wd	0	Set-point weight for Derivative block (0..1)
Real	Ni	0.9	Ni*Ti is time constant of anti-windup compensation
Real	Nd	10	The higher Nd, the more ideal the derivative block
Boolean	reverseActing	true	Set to true for reverse acting, or false for direct acting control action
Initialization
Modelica.Blocks.Types.Init	initType	Modelica.Blocks.Types.Init.InitialState	Type of initialization (1: no init, 2: steady state, 3: initial state, 4: initial output)
Real	xi_start	0	Initial or guess value value for integrator output (= integrator state)
Real	xd_start	0	Initial or guess value for state of derivative block
Real	y_start	0	Initial value of output
Advanced
Boolean	strict	true	= true, if strict limits with noEvent(..)
Integrator reset
Buildings.Types.Reset	reset	Buildings.Types.Reset.Disabled	Type of controller output reset
Real	y_reset	xi_start	Value to which the controller output is reset if the boolean trigger has a rising edge, used if reset == Buildings.Types.Reset.Parameter

Connectors

Type	Name	Description
RealInput	u_s (from SVcontrol)	Connector of setpoint input signal
RealInput	u_m (from SVcontrol)	Connector of measurement input signal
RealOutput	y (from SVcontrol)	Connector of actuator output signal
Modelica.Blocks.Interfaces.BooleanInput	trigger	Resets the controller output when trigger becomes true
Modelica.Blocks.Interfaces.RealInput	y_reset_in	Input signal for state to which integrator is reset, enabled if reset = Buildings.Types.Reset.Input

Components

Type	Name	Default	Description
Real	controlError	u_s - u_m	Control error (set point - measurement)
Modelica.Blocks.Math.Add	addP		Adder for P gain
Modelica.Blocks.Math.Add	addD		Adder for D gain
Modelica.Blocks.Math.Gain	P		Proportional term
Utilities.Math.IntegratorWithReset	I		Integral term
Modelica.Blocks.Continuous.Derivative	D		Derivative term
Modelica.Blocks.Math.Add3	addPID		Adder for the gains

Name	Description
Limiterprotected	Limit the range of a signal

Revisions

June 1, 2020, by Michael Wetter:
Corrected wrong convention of reverse and direct action.
Changed default configuration from PID to PI.
This is for issue 1365.
March 9, 2020, by Michael Wetter:
Corrected wrong unit declaration for parameter k.
This is for issue 1316.
October 19, 2019, by Filip Jorissen:
Disabled homotopy to ensure bounded outputs by copying the implementation from MSL 3.2.3 and by hardcoding the implementation for homotopyType=NoHomotopy. See issue 1221.
September 29, 2016, by Michael Wetter:
Refactored model.
August 25, 2016, by Michael Wetter:
Removed parameter limitsAtInit because it was only propagated to the instance limiter, but this block no longer makes use of this parameter. This is a non-backward compatible change.
Revised implemenentation, added comments, made some parameter in the instances final.
July 18, 2016, by Philipp Mehrfeld:
Added integrator reset. This is for issue 494.
March 15, 2016, by Michael Wetter:
Changed the default value to strict=true in order to avoid events when the controller saturates. This is for issue 433.
February 24, 2010, by Michael Wetter:
First implementation.