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4-4 PID Control Concepts Models 2510 and 2510-AT User’s Manual

Proportional-derivative (PD) control

The stability and overshoot problems that occur when a proportional controller is used at

high gain can be minimized by adding a term proportional to the time-derivative of the

error signal as follows:

Here, K

is the derivative gain.

Proportional-integral-derivative (PID) control

Although PD control deals well with the overshoot and ringing problems associated with

proportional control, it does not cure the problem with steady-state error. However, it is

possible to eliminate this error while using relatively low proportional gain by adding an

integral term to the control function as follows:

Here, K

, the integral gain parameter, is sometimes known as the controller reset level.

This form of function is known as proportional-integral-differential, or PID control for

which the Model 2510 is optimized. The effect of the integral term is to change the TEC

power until the time-averaged value of the temperature error is zero. Figure 4-3 shows the

result of adding the integral term to the control function.

To summarize:

•K

, the proportional constant, controls the loop gain.

•K

, the integral constant, offsets errors.

•K

, the derivative constant, affects the damping rate.

–()K

–()×+×=

–()K

–()

∫

×+× td+×=

Keithley 2510 User Manual

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