A new adaptive identification method of critical loop gain for multi-input multi-output plants

A new identification method of the critical gain and the critical frequency is proposed. This method can be applied to a large industrial plant with many controllers, and the convergence of the identification procedure is guaranteed theoretically. This method is simple and is not sensitive to disturbances. It can be used for tuning the multiloop PID controllers by Ziegler-Nichols rule. Instead of using relay feedback, a saturation nonlinearity and a time-varying gain are inserted in the loop, and the gain is tuned by the difference signal between the input and the output of the saturation function so that a sinusoidal oscillation may continue