Quantization problems and DCS advantages

Problems associated with quantization

Quantization rounds each sampled value to one of $2^n$ levels of an n-bit A/D converter. The step size is $Q = FSR/2^n$.

1. Quantization error: the difference between true and quantized value, between $-Q/2$ and $+Q/2$ with rounding.
2. Quantization noise: the error acts like random noise with variance $Q^2/12$, lowering signal-to-noise ratio.
3. Loss of resolution: changes smaller than one step are not seen (dead zone).
4. Limit cycles: small sustained oscillations in closed loop due to the nonlinear staircase.
5. Steady-state error of up to one quantization step.
6. Round-off of coefficients and arithmetic in a short-word-length controller.

Example: a 4-bit ADC with 0 to 16 V has $Q = 1$ V; 6.4 V and 6.3 V both read 6 V, with error up to 0.5 V. An 8-bit ADC reduces $Q$ to 62.5 mV.

How it can be improved

• Use an ADC and processor with more bits (SNR improves about 6 dB per bit).
• Scale the signal to the full ADC range.
• Use rounding rather than truncation.
• Oversample and filter/average the readings.
• Add dither to break limit cycles.
• Use longer word length or floating point in the control algorithm.

Advantages of digital control system over analog

• Flexible: control law changed by reprogramming, not rewiring.
• Accurate and drift-free: no change with temperature or ageing of components.
• Better noise immunity of digital signals.
• Complex/adaptive/nonlinear control is easy to implement in software.
• One computer serves many loops (time sharing), so cost per loop is low.
• Easy data storage, display, alarms and networking.
• Smaller, cheaper, more reliable hardware.