rocedure each time the process variable passes the setpoint in either direction forces the process variable to oscillate out of sync with the Control effort but at the same frequency.
        Although the process variable's oscillations aren't strictly sinusoidalwww.cechina.cn, their period turns out to be a close approximation of the ultimate period that Ziegler and Nichols used for their tuning rules. And the amplitude of the process variable's oscillations relative to the amplitude of the control effort's oscillations approximates the process's ultimate gain when multiplied by 4/π. So once the ultimate period and ultimate gain have been determined控制工程网版权所有, tuning the loop becomes a simple matter of plugging those two values into the Ziegler-Nichols tuning rules.

        To identify the ultimate period TU and ultimate gain PU of the processCONTROL ENGINEERING China版权所有, the control engineer running the test temporarily disables the PID block and replaces it with an on/off relay that forces the process variable to oscillate. The engineer then measures TU directly from the square-wave control effort and computes the value of PU according to
        PU = (4 · b) / (Π · a)
        where a is the amplitude of the controller's square wave and b is the amplitude of the process variable's resulting oscillations. By fixing a at a relatively small valueCONTROL ENGINEERING China版权所有, the engineer can also limit the value of b and thereby prevent the wild swings that sometimes plague the original Ziegler-Nichols open-loop test.
        Advantages
        But unlike the original Ziegler-Nichols closed-loop test控制工程网版权所有, the relay test can be configured to limit the amplitude of the process variable's oscillations by fixing the amplitude of the control effort's oscillations at a user-defined value. This allows the controller to f