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