Question

The transfer function of a first-order controller is given as;

\({{G}_{C}}\left( s \right)=\frac{K\left( s+a \right)}{s+b}\)

Where K, a and b are positive real numbers. The condition for this controller to act as a phase lead compensator is
1. a < b
2. a > b
3. K < ab
4. K > ab

Answer 1

Correct Answer - Option 1 : a < b

Concept:

The general expression for a lead compensator is;

\(G\left( s \right)=\frac{\left( \alpha \right)\left( 1+Ts \right)}{\left( 1+\alpha Ts \right)}\)

And for a lead compensator α < 1

Analysis:

Given lead compensator expression is;

\({{G}_{c}}\left( s \right)=\frac{k\left( s+a \right)}{\left( s+b \right)}\)

On comparing it with the standard expression we get;

\(T=\frac{1}{a}~,~~\alpha T=\frac{1}{b}\)

\(\Rightarrow \frac{\alpha }{a}=\frac{1}{b}\Rightarrow \alpha =\frac{a}{b}\)

⇒ a < b

Hence option – 1 is correct.