State the sampling theorem and its implication for digital control in mechatronics.

State the sampling theorem and its implication for digital control in mechatronics.

• A. Sampling frequency must be equal to the system clock; otherwise control fails.
• B. Sampling frequency must be at least twice the highest frequency content; to avoid aliasing, sample well above loop bandwidth.
• C. Sampling frequency is independent of the signal spectrum in digital control.
• D. Sampling should be minimized to reduce computation load.

Answer: (B)

Nyquist sampling theory says you must sample at least twice the highest frequency present in the signal to represent it without aliasing. In digital control, that means the sampling rate has to be high enough to capture the dynamics that matter for the controller—essentially up to the loop bandwidth and the plant’s fast dynamics. Sampling well above the loop bandwidth helps prevent aliasing, so the digital measurements and the resulting control action reflect the true system behavior. If the rate is too low, fast dynamics fold into lower frequencies, measurements become distorted, and the controller can misread the plant, potentially destabilizing the loop or degrading performance. So, choose a sampling rate at least twice the signal content and typically well above the loop bandwidth to ensure accurate sensing and stable control. The other notions—requiring the clock to match exactly, ignoring the signal spectrum, or minimizing sampling to reduce computation—do not provide the necessary fidelity for reliable digital control.

Nyquist sampling theory says you must sample at least twice the highest frequency present in the signal to represent it without aliasing. In digital control, that means the sampling rate has to be high enough to capture the dynamics that matter for the controller—essentially up to the loop bandwidth and the plant’s fast dynamics. Sampling well above the loop bandwidth helps prevent aliasing, so the digital measurements and the resulting control action reflect the true system behavior. If the rate is too low, fast dynamics fold into lower frequencies, measurements become distorted, and the controller can misread the plant, potentially destabilizing the loop or degrading performance. So, choose a sampling rate at least twice the signal content and typically well above the loop bandwidth to ensure accurate sensing and stable control. The other notions—requiring the clock to match exactly, ignoring the signal spectrum, or minimizing sampling to reduce computation—do not provide the necessary fidelity for reliable digital control.