Component 407: Proportional-Integral Controller by HVACSIM+
General Description
This subroutine models an analog proportional-integral controller.
Proportional control alone can be modeled by setting the integral gain to zero.
A time constant is used to model the response time of the controller itself.
The feedback signal, generally representing a temperature, must be a control
variable, which can be obtained by passing a temperature through the Component
409 temperature sensor model.
Nomenclature
C - controller output (0 <= C <= 1)
Cf - feedback signal (controlled variable)
Cset - set point
Css - steady state controller output
E - error signal
I - integral portion of controller output
Ki - integral gain
Kp - proportional gain
Toll - time constant associated with controller response
Mathematical Description
The error signal is defined by
E = Cset - Cf
The integral portion of the output signal is given by
dI/dt = Ki*E
The output control signal is then determined:
dC/dt = (Css - C)/Toll
where
Css = Kp*E + I
This differential equation is solved by MODSIM, the main HVACSIM+ program,
unless the time constant, Toll, is less than one second, in which case it is
solved within the subroutine:
IF (Toll/DeltaT) < 0.05 OR | Css - C- | < 10^(-10) THEN
C = Css
ELSE
C = Css - (Css - C-)*exp(-DeltaT/Toll)
where C- is the value of C one time step ago.
Component 407 Configuration
Inputs Description
1 Cf - controlled variable
2 Cset - set point for controlled variable
3 I - integral portion of control signal (from first output)
4 C - output control signal (from second output)
Outputs Description
1 I - integral portion of control signal (0 <= I <= 1)
2 C - output control signal (0 <= C <= 1)
Parameters Description
1 Kp - proportional gain
2 Ki - integral gain
3 Toll - controller time constant
Reference:
1. HVACSIM+ Building Systems and Equipment Simulation Program Reference
Manual (NBSIR 84-2996)
Daniel R. Clark
United States Department of Commerce
National Institute of Standards and Technology
Gaithersburg, Maryland 20899-0001