Key Point : A block diagram in which, forward path contains only one block, feedback path contains only one block, one summing point and one take off point represents simple or canonical form of a closed loop system.
This can be achieved by using block diagram reduction rules without disturbing output of the system. This form is very useful as its closed loop transfer function can be easily calculated by using standard result. This result is derived in this section.
The simple form can be shown as in the Fig. 1.
where, R(s)Laplace of reference input r(t)
C(s)Laplace of controlled output c(t)
E(s) →Laplace of error signal e(t)
B(s)Laplace of feedback signal b(t)
G(s)Equivalent forward path transfer function
H(s)→ Equivalent feedback path transfer function.
Key Point: G(s) and H(s) can be obtained by reducing complicated block diagram by using block diagram reduction rules.
1. Derivation of T.F. of Simple Closed Loop System
Referring to the Fig. 1, we can write following equations as,
Use + sign for negative feedback and Use - sign for positive feedback.
This can be represented as in the Fig. 2.
Key Point: This can be used as a standard result to eliminate such simple loops in a complicated system reduction procedure.