Controller operating in automatic mode but with the integral and derivative terms temporarily shut off. The controller gain is increased until even the slightest error causes a sustained sinusoidal oscillation in the process variable as shown in the "Ziegler-Nichols closed-loop test" graphic.
        The smallest controller gain that can cause such an oscillation is called the ultimate gainPU. The period of those sinusoidal oscillations is called the ultimate periodTU. The appropriate tuning parameters are computed from these two values according to the Ziegler-Nichols tuning rules:
        P=0.6·P u
        T I="0".5·T u
        T D="0".125·T u

        Forcing the closed loop system into sustained oscillations with a proportional-only controller reveals the process's ultimate gain PU and ultimate period TU. UnfortunatelyCONTROL ENGINEERING China版权所有, doing so can also cause dramatic and sometimes dangerous swings in the control effort and the process variable

        Caveats
        But even the Ziegler-Nichols methods aren't so straightforward in actual practice. Different PID controllers use different versions of the PID formula控制工程网版权所有, and each must be tuned according to a different set of tuning rules. The rules also change when:
        •The controller is not equipped with integral and/or derivative terms;
        •The process itself is inherently oscillatory;
        •The process behaves as if it contains its own integral term (as with level control); and/or
        •The process deadtime is very small or significantly larger than the process t