Instantaneous speed and disturbance torque observer using nonlinearity cancellation of shaft encoder

In this paper, the theoretical analysis, simulations and practical results of a new speed and disturbance torque observer are proposed. The analysis of the nonlinearity introduced by the encoder quantization allows improving the behaviour of the filter in all the speed range. A Kalman filter type observer has been developed. The main novelty is that the state estimate observational update takes place at the quantized position signal discontinuities. Unlike the usually, applied Kalman filter, the measurement noise covariance is variable. In this observer, it is a function of the shaft speed because the selection of the sampling instant results in a reduction of the output noise covariance. The observer adapts its gain depending on the state variables. The optimal gain calculation results in an observer bandwidth increase. Another advantage of this observer is that the self-sustained. oscillations are suppressed, obtaining asymptotic stability.