Q3Control System
Question
Q.3. Find the order and type of the unity feedback system whose transfer function is given as :
Answer
The system is of order 7 (highest power of s in the denominator) and Type 4 (number of poles at the origin, from the s^4 factor).
For G(s) = 100(s+2)(s+10) / [s^4(s+10)(s^3+2s^2+5s+100)], the order is the degree of the characteristic equation's denominator polynomial: 4 (from s^4) + 1 (from s+10) + 3 (from the cubic) = 8, but one (s+10) factor is common to numerator and denominator, so after pole-zero cancellation the effective denominator degree is 4 + 3 = 7. Hence the order of the system is 7. The type of the system equals the number of poles located at the origin (s = 0), which is 4 (from the s^4 term). Therefore this is a Type-4, 7th-order system.