Analog-to-digital converters: sliding mode observer as a pulse modulator

Sliding mode observers (SMO) and principles of digital delta (Δ) and sigma (Σ) modulation in implementations of feedback processing systems under the discrete-time control with a zero-order-hold are analyzed. An equivalency is established between the structures of Δ - and Σ -modulators on one hand and the sliding mode observers configured as a "signal estimator" and a "disturbance estimator". The perceived similarity is utilized in combining the properties of a control system and a communication system in one on an example of a PD-controller with Σ Δ -modulation. A common problem of excessive chattering in SMO or the "hunting" of the estimate about the signal in Δ -modulator is addressed. Another setback, which is the slope overload problem, is addressed using the adaptive gain and a SMO with higher order sliding modes. In addition, a new type of pulse modulator, the second differential pulse code modulator, is proposed