Stability Analysis of incremental Servos

The stability of sampled-data incremental servos is examined by both Lyapunov's second method and describing functions. The application of Lyapunov's second method leads to conditions that are sufficient to ensure that, under arbitrary initial conditions, the system will eventually reach equilibrium with the error within the threshold and with zero error derivatives. A describing function is evaluated for the combination of an on-off nonlinearity With threshold, a sampler, and an integration. By using the describing function, low-frequency oscillations can be predicted easily. A method for determining transient response by using z transforms expanded in power series is included in Appendix II.