Quantization Noise and Limit Cycling in Digital Closed-Loop Systems

The practical and reliable application of direct digital control in industrial systems is a long way from the study of sampling control in modern control literature. Numerous mechanical failures of hydraulic tubes, seals, and mechanical connections have demonstrated that these systems are easily fatigued by ``jitter'' or the type of noise that can arise in digital systems due to quantization of signals. Yet the transition from analog to microprocessor-based control implies a sampled control with inherent noise due to finite word length and finite sampling period. Even if the sampling frequency does not cause instability, it can fatigue the system with limit cycles. This paper investigates the effects of quantization and establishes bounds on limit cycles in digital closed-loop systems by examining a typical proportional plus integral type of controller found in process control. The work is based on the technique used by Long and Trick [1] to establish bounds on limit cycles in digital filters.