ABSTRACT
In 1943 J. G. Ziegler and N. B. Nichols suggested a technique for tuning the parameters of a PID controller. Their method was based on testing the plant in a closed loop with the PID controller in the proportional mode. The proportional gain was increased until the loop started to oscillate and then the value of gain and oscillation frequency was measured. The actual phase shift varies with harmonic content of input signal in a complex manner, because the phase shift depends on the amplitudes and phases of the individual input components. From an engineering viewpoint one can judge accuracy of describing function (DF) results by estimating the distortion in the input to the nonlinearity. Experience indicates that the percentage accuracy of the DF method in predicting the fundamental amplitude and frequency of the limit cycle is less than the percentage distortion in the fedback signal. The limit-cycle amplitude predicted by the DF is an approximation to the fundamental harmonic.
