Q1(a)
................................by KVL ................(1)
From the given transfer function
...................multiplying numerator and denominator by 1/LC
(b)
that is
...........(2)
......................(3)
on re arranging equation 1
.......................(4)
....................(5)
substituting the values of L ,C R
........(6)
............(7)
from equation 6 and 7
and output voltage Vo is voltage across capacitor
hence part b is verified
(c) substituting the values of L and c in transfer function we get
therefore poles are at S=-2,-3
from the state space representation
system matrix A is given by
eigen values are found by
determinant of
on solving
S(S+3)+(2/3)*3=0
s^2+3S+2=0
therefore S=-2,-1 are the eigen values from thesytem matrix which matches with the poles of the tranfer function
(d)
state transmission matrix is given by
L^-1{[SI-A]^-1}
[SI-A]^-1=(1/(S+2)(S+3))[ S+3 2/3
-3 S ]
taking the laplace inverse
State transmission matrix=[ S+3/(S+1)*(S+2) (2/3)/(S+1)*(S+2)
-3/(S+1)*(S+2) S/(S+1)*(S+2) ]
=[2e^-t -0.5e^-2t -(2/3)e^-t+(2/3)e^-2t
-3e^-t+3e^-2t e^-t+2e^-2t ]
there fore alpha=-0.5 , beta=-2 and gama=2/3
Question 1 a) Consider the electrical circuit in Figure 1. Determine the state space representation of the circuit where the output is voltage across the capacitor. (6 marks) b) From result obtained in (a), predict the transfer function. (4 marks) [10 MARKS] 192 192 192 m V:(t) 1 H 1F volt) Figure 1
a) Consider the electrical circuit in Figure 1. Determine the state space representation of the circuit where the output is voltage across the capacitor. (6 marks) b) From result obtained in (a), predict the transfer function. (4 marks) [10 MARKS] 1 Ω 192 112 W vi(t) 1 H elle 1 H Illl 1 F volt) Figure 1
the circuit is figure 1 a) Consider the electrical circuit in Figure 1. Determine the state space representation of the circuit where the output is voltage across the capacitor. (6 marks) b) From result obtained in (a), predict the transfer function. (4 marks) [10 MARKS] 112 112 192 M + + vi(t) 1 H llll 1 H elle 1F HE vo(t)
2. For the circuit shown in Figure 2: (a) (5 points) Calculate the transfer function H(s)-Volo)/V(o). (b) (5 points) Find vo(t) due to a unit step input using the residue method. (e) (5 points) Find vo(t) due to a unit ramp input using the residue method. (d) (10 points) If v(t) 5/5 cos(2t-33.43499) V, find the steady-state expression for volt). R2 R1 2Ω 2Ω L 2H Volt) С 0.5F
2. In the circuit shown in Figure 2, let C=0.5 F L=1H, R-312. Find the voltage vo(t) for t>0 L volt) Figure 2 2. In the circuit shown in Figure 2, let C=0.5 F L=1H, R-312. Find the voltage vo(t) for t>0 L volt) Figure 2
question 3 Question 1 a) Consider the electrical circuit in Figure 1. Determine the state space representation of the circuit where the output is voltage across the capacitor. (6 marks) b) From result obtained in (a), predict the transfer function. (4 marks) [10 MARKS] 192 192 122 w 1H lell 1H llll 1F vo(t) Figure 1
Question 1 a) Consider the electrical circuit in Figure 1. Determine the state space representation of the circuit where the output is voltage across the capacitor. (6 marks) b) From result obtained in (a), predict the transfer function. (4 marks) (10 MARKS] 122 112 112 M + + vi(t) 1 H llll 1 H elle 1F vo(t)
Question 1 a) Consider the electrical circuit in Figure 1. Determine the state space representation of the circuit where the output is voltage across the capacitor. (6 marks) b) From result obtained in (a), predict the transfer function. (4 marks) [10 MARKS] 192 192 112 M M w + + Vilt) 1 H sooo 1 H nooo 1F vo(t) Figure 1
Question #2 ( 25 points) C(s) a) Reduce the block diagram shown in Figure 1 to a single transfer function T(s) =R) using the append and connect commands in MATLAB. pts b) Using Simulink simulate the transfer obtained in a) for a step input. c) Obtain the state-space representation of T(s). [10 [5 pts [10 pts] C(s) Ris 50 s+I 2 Figure 1 -Irt Question #2 ( 25 points) C(s) a) Reduce the block diagram shown in Figure 1 to...
10.Represent the translational mechanical system shown in the Figure in state- space, where xX3(t) is the output IN- 11.Find the state equations and output equation for the phase-variable representation of the transfer function G(s) 2s+1/(s2+7s+ 9) 12. Convert the state and output equations shown to a transfer function. -1.5 2 u(t) X = X 4 0 Y [1.5 0.625]x 13. For each system shown, write the state equations and the output equation for the phase- variable representation 8s10 sh25 t26...