Previous Year Question
The transfer function of a phase lead controller is (1 + 3Ts) / (1 + Ts). What will be the maximum phase provided by this controller?
Correct answer: D
Explanation
For a lead network (1+aTs)/(1+Ts) with a=3, the maximum phase lead satisfies sinφm=(a−1)/(a+1)=2/4=0.5. Therefore φm=30°.
Formula
sinφm=(a−1)/(a+1); a=3 ⇒ φm=30°
Step-by-step solution
Correct Answer
D — 30°
Concept and Reasoning
For a lead network (1+aTs)/(1+Ts) with a=3, the maximum phase lead satisfies sinφm=(a−1)/(a+1)=2/4=0.5. Therefore φm=30°.
Calculation / Key Relation
sinφm=(a−1)/(a+1)
a=3 ⇒ φm=30°
Exam Takeaway
For lead compensation, a>1 and the maximum phase follows the sine relation.
Common Mistake
Do not take the coefficient ratio itself as an angle.
Common mistake
Do not take the coefficient ratio itself as an angle.
Exam tip
For lead compensation, a>1 and the maximum phase follows the sine relation.
Quick method
For lead compensation, a>1 and the maximum phase follows the sine relation.