Question

Consider two control systems with the following transfer functions

System 1: \(G\left( s \right) = \frac{1}{{3s + 1}}\) 

System 2: \(G\left( s \right) = \frac{1}{{s + 1}}\) 

Which of the following is true?

1. Bandwidth of System 1 is greater than bandwidth of System 2
2. Bandwidth of System 2 is greater than bandwidth of System 1
3. Bandwidth of both the systems are same
4. Both the systems have infinite bandwidth

Answer 1

Correct Answer - Option 2 : Bandwidth of System 2 is greater than bandwidth of System 1

Concept:

LTI system in time constant form is defined as:

\(C\left( s \right) = \frac{{K\left( {1 + s{\tau _1}} \right)\left( {1 + s{\tau _2}} \right) \cdots }}{{{s^n}\left( {1 + s{\tau _a}} \right)\left( {1 + s{\tau _b}} \right) \cdots }}\)

τ₁, τ₂ ⋯ and τ_a, τ_b ⋯ are time constants.

Bandwidth

For the first order systems bandwidth is defined as the reciprocal of the time constant.

\(BW = \frac {1}{\tau}\)

NOTE: Bandwidth in control systems represents the Speed of the system.

Calculation:

Given functions are

\(G\left( s \right) = \frac{1}{{3s + 1}}\) and \(G\left( s \right) = \frac{1}{{s + 1}}\)

Comparing with the standard forms we get time constants as:

τ₁ = 3 sec and τ₂ = 1 sec

BW₁ = 1/3 Hz

BW₂ = 1/1 Hz

BW₂ > BW₁

Hence statement 2 is correct.