Control Systems: Week 06

Home

Sites

ABdA

Help

E-mail

WEEK 06: MODES OF CONTROL: PROPORTIONAL-DERIVATIVE

Sections: On-Off | Proportional | P-Integral | P-Derivative | P-I-D

Proportional Plus Derivative Mode of Control

Description. Popularly called the Rate Control. The final correcting device's position is determined by the magnitude of the error signal [proportional part] and the time rate of change of error [derivative part]. The Time Rate of Change of Error is the rate of how rapidly the error is changing. This mode of control is very seldom used in temperature control, but popular in industrial servocontrol systems.

Principle of Operation. The proportional part positions the valve in proportion to the magnitude of the error signal. The derivative part, consisting of a capacitance and a resistance but in reverse compared to the P-I mode.

If the error signal changes slowly, the position pot wiper will follow rather slowly, thus the capacitor at the derivative part can catch up and therefore it can charge. If the error signal changes rapidly, the position pot wiper will follow rapidly, thus the capacitor cannot catch up with charging.

Time Constant [TC]. The value of the derivative time constant is derived from the relationship of the capacitance and resistance, through the use of transient analysis. When the derivative time constant, Der.TC, is small, i.e., the resistance is also small, the integral part is less effective, thus the controller acts like a typical proportional mode of control. When the time constant is large, i.e., the resistance is large, the control is more effective, because the control will generate large overcorrection for rapid changes.

Rate Time [RT]. The Rate Time, RT, is the amount of time allowed for the measured value to change through the full controller range, F.C.R. It is also the amount of time to "look ahead" or "see the future". Thus, this mode of control is applied when "overcorrection" in the offset is necessary. Algebraically, the rate time is equal to the numerical value of the derivative time contant multiplied by a numerical constant, k.

Proportional-Integral P-I-D Mode