(Solved): 8. Use mason's gain formula to find the transfer function of the given signal flow xraph: a) 1(e ...

8. Use mason's gain formula to find the transfer function of the given signal flow xraph: a) $$\frac{abd}{1?(\mathrm{ec})}$$ b) $$\frac{\text{ abdes }}{1?(\text{ bctef }+\text{ bcef }}$$ c) $$\frac{abd}{1?(bc+af)+bcof}$$ d) $$\frac{\text{ adedef }}{1?(be+ef)+bcof}$$ Choose the correct answer 1. Given the matrix $$\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ ?6& ?11& ?6\end{array}\right]$$ the Eigen value are a) $$1,2,3$$ b) 1 c) $$?1,?2,?3$$ d) 0 2. Stability of a system implies that: a) Small changes in the system imput does not result in large change in system output b) Small changes in the system parameters does not result in large change in system output c) Small changes in the initial conditions does not result in large change in system output d) All of the above mentioned 3. A linear time invariant system is stable if : a) System in excited by the bounded input, the output is also bounded b) In the absence of input output tends zeto c) Both a and b d) System is excited by the bounded input, the output is not bounded 8. Use mason's gain formula to find the transfer function of the given signal flow graph: a) $$\frac{\text{ ald }}{1?(\mathrm{ec})}$$ b) $$\frac{\text{ abeeg }}{1?(\text{ br }+ef+b+bcof}$$ c) $$\frac{adi}{1?(bc+ef)+hcef}$$ d) $$\frac{\text{ adedof }}{1?(bc+rf)+bcof}$$ Question 1 1. Which among the following is a unique model of a system? a) Transfer function b) State variable c) Block diagram d) Signal flow graphs 2. The minimum number of states require to describe the two degree differential equation: a) 1 b) 2 c) 3 d) 4 3. Which of the following transfer function will have the greatest maximum overshoot? a) b) c) d) 4. Find the type and order of the system given below: a) 2,3 b) 2,2 c) 3,3 d) None of the mentioned 4. Find the type and order of the system given below: a) 2,3 b) 2,2 c) 3,3 d) None of the mentioned 5. Find the initial and final values of the following function: $$F(s)=\frac{12(S+1)}{S(S+2{)}^2(S+3)}$$ a) $$1,?$$ b) $$0,?$$ c) $$?,1$$ d) 0,1 6. Consider a system with transfer function $$\mathrm{G}(\mathrm{s})=\frac{\mathrm{S}+6}{{\mathrm{KS}}^2+\mathrm{S}+6}$$ its damping ratio will be $$0.5$$ when the values of $$K$$ is: a) $$2/6$$ b) 3 c) $$1/6$$ d) 6 7. The output in response to a unit step input for a particular continuous control system is $$c(t)=1?{\mathrm{e}}^4$$, What is the delay time Td? a) $$0.36$$ b) $$0.18$$ c) $$0.693$$ d) $$0.289$$ 8. Which of the following quantities give a measure of the transient characteristics of a control system, when subjected to unit step excitation. 1. Maximum overshoot 2. Maximum undershoot 3. Overall gain 4. Delay time 5. Rise time 6. Fall time a) 1,3 and 5 b) 2,4 and 5 c) 2,4 and 6 d) 1,4 and 5 9. Consider the unity feedback system with open loop transfer function $$=KK/s(s+1)(s+2)$$ the minimum value of the steady state error to a ramp input $$r(t)=6tu(t)$$ a) 1 b) 2 c) 3 d) 4 10. A unity feedback system with an open loop transfer function $$G(s)=$$ $$\frac{K(S+1)}{S^3+a{S}^2+2S+1}$$ What values of ' $$K$$ ' and 'a' should be chosen so that the system Oscillates? a) $$K=2$$, a $$=1$$ b) $$K=2,a=0.75$$ c) $$K=4,a=1$$ d) $$K=4,a=0.75$$ Fill the answers in the table