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When Tuning the PID Controller, the D Gain Has a Different Sign from the I Gain

When you design a controller using PID Tuner, the resulting derivative gain, D, can have a different sign from the integral gain I. PID Tuner always returns a stable controller, even if one or more gains are negative.

For example, the following expression gives the PID controller transfer function in Ideal form:

c=P(1+Is+DssN+1)=P(1+DN)s2+(I+N)s+INs(s+N)

For a stable controller, all three numerator coefficients require positive values. Because N is positive, IN > 0 requires that I is also positive. However, the only restriction on D is (1 + DN) > 0. Therefore, as long as DN > –1, a negative D still yields a stable PID controller.

Similar reasoning applies for any controller type and for the Parallel controller form. For more information about controller transfer functions, see the PID controller block reference pages.

See Also

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