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


Bit stream (BS)-based feedback management systems often use a delta–sigma modulator ( $DeltaSigma$-M) as a 2-level dynamic quantizer to encode and decode feedback signals. The steadiness and performance of such systems are critically passionate about the selection of the quantizer step size. This paper derives the steadiness condition of a BS-primarily based control system in terms of the quantizer step size using sliding mode analysis. It's proved that the quantized system is appreciate the initial system on the sliding manifold under ideal sliding. But, the presence of the quantizer in an exceedingly $DeltaSigma$-M introduces noise into the system that often degrades the performance of the general system. This paper therefore determines the optimum quantizer gain, i.e., the higher and lower boundaries of the quantizer, that maintains the stability and reduces the quantization noise. BS-based mostly proportional–integral–differential (BS-PID) controllers are designed using the proposed optimal dynamic quantizer and implemented using 3 completely different realizations. Simulation results show that the optimal quantizer significantly reduces the noise at intervals the system bandwidth. The effectiveness of the BS-PID controller with the optimal quantizer is additional 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 offers identical performance to a traditional PID controller and effectively controls the system while consuming less information rate (channel interfaces) and hardware resources.

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