Question

Generally, the bandwidth of a control system indicates ____ characteristic of the system.

• A. Linearity
• B. Causality
• C. Gain
• D. Noise-filtering

Hint:

Bandwidth is a measure of the range of frequencies a system can effectively process.
Wider bandwidth \(\implies\) faster response, ability to follow fast inputs, but potentially more noise passed.
Narrower bandwidth \(\implies\) slower response, but better filtering of high-frequency noise.
The relationship is often \(t_{rise} \approx 0.35 / BW\).

Answer 1

The Correct Option is D

The bandwidth of a control system is the range of frequencies over which the system responds effectively, typically defined by the frequency at which the magnitude of the frequency response drops by 3 dB (or to \(1/\sqrt{2}\) of its DC or midband value). What bandwidth indicates:
Speed of Response: A wider bandwidth generally corresponds to a faster system response (e.g., shorter rise time, settling time). The system can follow rapid changes in the input.
Ability to Track Signals: A system with a wider bandwidth can accurately track input signals containing higher frequency components.
Noise Filtering/Susceptibility:
A system with a \textit{limited bandwidth} will inherently filter out (attenuate) high-frequency noise components that lie outside its passband. This is a form of noise-filtering.
Conversely, a system with a very \textit{wide bandwidth} might be more susceptible to high-frequency noise as it will pass these components through. Let's consider the options: (a) Linearity: Bandwidth doesn't directly indicate linearity. A system can be linear with a narrow or wide bandwidth. (b) Causality: Bandwidth doesn't directly indicate causality. (c) Gain: Bandwidth is a range of frequencies, while gain is the amplification factor (which might be frequency-dependent). Midband gain is a specific value. (d) Noise-filtering: A system with a defined (and typically finite) bandwidth will act as a filter. If the bandwidth is relatively narrow, it will filter out high-frequency noise. If it's wide, it might pass more noise. The characteristic of having a bandwidth inherently implies some form of frequency selectivity, which relates to noise filtering. For instance, a low-pass system (which all practical control systems are to some extent) filters out high-frequency noise. Given the options, "Noise-filtering" is a characteristic significantly influenced by the system's bandwidth. A limited bandwidth implies the system filters out frequencies beyond that limit, which often includes noise. While speed of response is perhaps the most direct indicator, "noise-filtering" is also a valid characteristic related to bandwidth. If the system has a limited bandwidth, it will filter noise outside this band. \[ \boxed{\text{Noise-filtering}} \]