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
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.