Backlash in a velocity lag servomechanism

The frequency response method of analysis of servomechanisms has been extensively applied in the analysis and synthesis of linear systems, and several studies have shown that useful results can be obtained in certain nonlinear cases. The application of the sinusoidal frequency response method to nonlinear systems has been based on the assumption that the input to the nonlinear element is sinusoidal and that the behavior of the complete system can be satisfactorily represented by considering only its fundamental Fourier series component. Tustin and Goldfarb applied this method to the analysis of servomechanisms having backlash and non-viscous friction.1,2 Kochenburger has found good experimental agreement with the theoretical results of this method in several contactor servomechanisms.3 He has shown that this method serves as a useful guide in designing appropriate linear equalizing networks to improve their performance. These networks allow the system to remain stable for smaller dead zones and also give a higher range of frequency over which the contactor servomechanism's output reproduces its input with small error. He used this method to compute the over-all frequency response for various amplitudes of the sinusoidal input to the system and showed that it was possible to obtain well damped performance as evidenced by a low resonance peak. Johnson has shown how the gain phase angle transfer locus may be used to indicate the presence of sustained constant amplitude oscillation in a nonlinear system and has shown that nonlinear equalizing networks may be used to eliminate sustained oscillations and improve system performance.4 In this paper the amplitude and period of sustained oscillations computed by this method for a velocity lag servomechanism incorporating only one time constant (which will be referred to as the motor time constant) will be compared with an exact treatment of this problem given by Oldenbourg and Sartorius.5