In a cascade control system, the closed loop transfer function of the inner loop may be assumed to have a single time-constant T1 . Similarly, the closed loop transfer

Q. In a cascade control system, the closed loop transfer function of the inner loop may be assumed to have a single time-constant T₁ . Similarly, the closed loop transfer function of the outer loop may be assumed to have a single time-constant T₂. The desired relationship between T₁ and T₂ in a well-designed control system is

(A) T₁ is much less than T₂

(B) T₁ is equal to _T2

(C) T₁ is much greater than T₂

(D) T₁ is independent of T₂

Ans: T₁ is much less than T₂

Sol:

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.

⇒ T₂ > 3_T1

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