Topic: Control Systems
The signal flow diagram for a certain feedback control system is shown in figure. Now consider the following set of equations for the nodes
1. $x_{2}=a_{1}x_{1}+a_{9}x_{3}$
2. $x_{3}=a_{2}x_{2}+a_{8}x_{4}$
3. $x_{4}=a_{3}x_{3}+a_{5}x_{2}$
4. $x_{5}=a_{4}x_{4}+a_{6}x_{2}$
Which of the following are correct?
- A. 1, 2 and 3
- B. 1, 3 and 4
- C. 2, 3 and 4
- D. 1, 2 and 4
Answer: D. 1, 2 and 4
Explanation: Based on the signal flow graph:
Node $x_2 = a_1 x_1 + a_9 x_3$ (Correct)
Node $x_3 = a_2 x_2 + a_8 x_4$ (Correct)
Node $x_4 = a_3 x_3 + a_5 x_2 + a_7 x_4$ (The given equation 3 misses the $a_7 x_4$ term, hence incorrect)
Node $x_5 = a_4 x_4 + a_6 x_2$ (Correct)
Thus, statements 1, 2, and 4 are correct.