Hybrid delta modulator: stability analysis using sliding mode theory

Abstract

The present study proposes a new dynamic two-level quantizer, called as hybrid delta modulator ( $\Delta _{H} $-M), which combines the features of both delta-modulator and delta-sigma modulator. In the transient state, the $\Delta _{H} $-M exhibits the dynamical behaviour of delta modulator (Δ-M) while in steady state, its behaviour is similar to delta-sigma modulator ( $\Delta \Sigma $-M). This study investigates about various dynamics of the proposed $\Delta _{H} $-M in both continuous and discrete-time domains. The stability conditions of $\Delta _{H} $-M are derived using the theory of sliding and quasi-sliding mode. The theoretical results are validated through extensive simulations. Abbreviations: Δ-M: delta modulator; $\Delta _{H} $-M: hybrid delta modulator; $\Delta \Sigma $-M: delta sigma modulator; ADC: analogue to digital converter; CT: continuous-time; DAC: digital to analogue converter; DT: discrete-time; NCS: networked control system; QSM: quasi-sliding model; QSMD: quasi-sliding mode domain; SS: steady state; TP: transient process

Keywords

• $\Delta \Sigma $-modulation
• Δ-modulation
• sliding mode
• quasi-sliding mode
• quantized control
• single-bit