Stability and Performance Analysis of Bit-Stream-Based Feedback Control Systems

Abstract

Bit stream (BS)-based feedback control systems often use a delta–sigma modulator ( $\Delta\Sigma$ -M) as a two-level dynamic quantizer to encode and decode feedback signals. The stability and performance of such systems are critically dependent on the selection of the quantizer step size. This paper derives the stability condition of a BS-based control system in terms of the quantizer step size using sliding mode analysis. It is proved that the quantized system is equivalent to the original system on the sliding manifold under ideal sliding. However, the presence of the quantizer in a $\Delta\Sigma$ -M introduces noise into the system that often degrades the performance of the overall system. This paper therefore determines the optimum quantizer gain, i.e., the upper and lower boundaries of the quantizer, which maintains the stability and reduces the quantization noise. BS-based proportional–integral–differential (BS-PID) controllers are designed using the proposed optimal dynamic quantizer and implemented using three different realizations. Simulation results show that the optimal quantizer significantly reduces the noise within the system bandwidth. The effectiveness of the BS-PID controller with the optimal quantizer is further demonstrated using the experimental prototype of a dc servomechanism by designing a BS-PID controller. The experimental results from a laboratory prototype illustrate that the BS-PID controller gives identical performance to a traditional PID controller and effectively controls the system while consuming less information rate (channel interfaces) and hardware resources.