Question

In a cascade control system, the closed loop transfer function of the inner loop may be assumed to have a single time-constant τ₁. Similarly, the closed loop transfer function of the outer loop may be assumed to have a single time-constant τ₂. The desired relationship between τ₁ and τ₂ in a well-designed control system is
1. τ₁ is much less than τ₂
2. τ₁ is equal to τ₂
3. τ₁ is much greater than τ₂
4. τ₁ is independent of τ₂

Answer 1

Correct Answer - Option 1 : τ₁ is much less than τ₂

In a cascade (or) master slave control system, then inner loop must be faster than outer loop. Inner loop acts as slave loop whereas outer loop acts as slave loop.

For proper control, inner loop should be at least 3 times faster than outer loop.

\(\Rightarrow {\tau _2} > 3{\tau _1}\)

Hence the time constant of inner loop is much lower than that of outer loop.