Engineering Manual o.. - HVAC.Amickracing

CONTROL FUNDAMENTALSPROPORTIONAL-INTEGRAL-DERIVATIVE (PID)CONTROLProportional-integral-derivative (PID) control adds thederivative function to PI control. The derivative functionopposes any change and is proportional to the rate of change.The more quickly the control point changes, the more correctiveaction the derivative function provides.If the control point moves away from the setpoint, the derivativefunction outputs a corrective action to bring the control point backmore quickly than through integral action alone. If the controlpoint moves toward the setpoint, the derivative function reducesthe corrective action to slow down the approach to setpoint, whichreduces the possibility of overshoot.The rate time setting determines the effect of derivative action.The proper setting depends on the time constants of the systembeing controlled.The derivative portion of PID control is expressed in thefollowing formula. Note that only a change in the magnitudeof the deviation can affect the output signal.Where:VKT DKT DdE/dtV = KT D= output signal= proportionality constant (gain)= rate time (time interval by which thederivative advances the effect ofproportional action)= rate gain constant= derivative of the deviation with respect totime (error signal rate of change)The complete mathematical expression for PID controlbecomes:KdEV = KE + ∫Edt + KT D dt+ MWhere:VKET 1K/T 1dtT DKT DdE/dtMT 1dEdtProportional Integral Derivative= output signal= proportionality constant (gain)= deviation (control point - setpoint)= reset time= reset gain= differential of time (increment in time)= rate time (time interval by which thederivative advances the effect ofproportional action)= rate gain constant= derivative of the deviation with respect totime (error signal rate of change)= value of the output when the deviationis zeroThe graphs in Figures 38, 39, and 40 show the effects of allthree modes on the controlled variable at system start-up. Withproportional control (Fig. 38), the output is a function of thedeviation of the controlled variable from the setpoint. As thecontrol point stabilizes, offset occurs. With the addition ofintegral control (Fig. 39), the control point returns to setpointover a period of time with some degree of overshoot. Thesignificant difference is the elimination of offset after the systemhas stabilized. Figure 40 shows that adding the derivativeelement reduces overshoot and decreases response time.SETPOINTSETPOINTSETPOINTCONTROLPOINTOFFSETT1 T2 T3 T4 T5 T6TIMEC2099Fig. 38. Proportional Control.CONTROLPOINTOFFSETT1 T2 T3 T4 T5 T6TIMEC2100Fig. 39. Proportional-Integral Control.OFFSETT1 T2 T3 T4 T5 T6TIMEC2501Fig. 40. Proportional-Integral-Derivative Control.ENHANCED PROPORTIONAL-INTEGRAL-DERIVATIVE (EPID) CONTROLThe startup overshoot, or undershoot in some applications,noted in Figures 38, 39, and 40 is attributable to the very largeerror often present at system startup. Microprocessor-based PIDstartup performance may be greatly enhanced by exterior errormanagement appendages available with enhanced proportionalintegral-derivative(EPID) control. Two basic EPID functionsare start value and error ramp time.ENGINEERING MANUAL OF AUTOMATIC CONTROL25