AKGEC/IQAC/QP/01
AJAY KUMAR GARG ENGINEERING COLLEGE GHAZIABAD
TUTORIAL SHEET - 1
Department: ECE Course: B. Tech (ECE)
Semester: VI Subject: KEC-602, CS
OBE Remarks:
Q. No. 1 2 3 4 5 6 7
CO No. CO1 CO1 CO1 CO1 CO1 CO1 CO1
Blooms L6 L5 L3 L6 L4 L5 L6
Level*
*Bloom’s Level: L1: Remember, L2: Understand, L3: Apply, L4: Analyze, L5: Evaluate, L6: Create
Submission Date ________________
1. Obtain the closed loop transfer function of the control system shown in figure below by block
diagram reduction technique. Also verify the result by signal flow graph method.
2. Evaluate the closed loop transfer function for the system represented by block diagram given below
when the input R is (i) at station A (ii) at station B.
3. Find the closed loop transfer function of the system given below using mason’s gain formula.
AKGEC/IQAC/QP/01
4. Represent the following set of equations by a signal flow graph and determining the overall gain
relating x5 and x1 using Mason’s gain formula.
x2 ax1 fx2
x3 bx2 ex4
x4 cx3 hx5
x5 dx4 gx2
5. Determine the overall gain of given signal flow graph using Mason’s gain formula.
6. Write the differential equations describing the dynamics of the system shown in fig. below and find
the ration X2(s)/F(s).
7. Write the differential equations describing the dynamics of the system shown in figure below. Also
obtain the analogous electrical circuit based on force-current (f-i) analogy.
AKGEC/IQAC/QP/01
Prepared By:
Dr. Sulekha Saxena
Asso. Prof., ECE
AKGEC/IQAC/QP/01
AJAY KUMAR GARG ENGINEERING COLLEGE GHAZIABAD
TUTORIAL SHEET 2
Department: ECE Course: B. Tech (ECE)
Semester: VI Subject: KEC-602, CS
Q. No. 1 2 3 4 5 6 7 8 9
CO NO. CO2 CO2 CO2 CO2 CO2 CO2 CO2 CO2 CO2
Blooms L5 L6 L5 L3 L3 L5 L5 L6 L6
Level*
*Bloom’s Level: L1: Remember, L2: Understand, L3: Apply, L4: Analyze, L5: Evaluate, L6: Create
Submission Date ________________
1. Obtain a state model of the system described by the transfer function
Y ( s) 5
3
U ( s ) s 6s 7
2. Construct signal flow graph and state model for a system whose transfer function is
Y ( s ) 6 s 3 4 s 2 3s 10
U ( s ) s 3 8s 2 4 s 20
3. For the given transfer function obtain the state model.
y(s) K
G ( s) 3
u ( s ) s a3 s 2 a2 s a1
4. Apply cascade decomposing method to obtain state space representation of the transfer
function given below-
s 2 6s 8
G( s)
( s 3)( s 2 2s 5)
5. Consider the network shown in figure below and write the state variable in matrix form.
6. Obtain the state model for the given transfer function using block diagram representation-
y( s) K (C2 s C1 )
G( s) 3
u ( s) s a3 s 2 a2 s a1
AKGEC/IQAC/QP/01
7. For the following state equation, determine the transfer function Y(s)/ U(s).
0 3 0
x(t ) x(t ) u (t )
2 3 3
y (t ) 1 0 x(t ) u (t )
8. Obtain the state model for the system described by the given transfer function
y( s) 20(4s 2)
G( s) 3
u ( s ) s 5s 2 8s 2
9. Obtain the state equations for the field controlled D.C motor shown in figure below-
Prepared By:
Dr. Sulekha Saxena
Asso. Prof., ECE
AKGEC/IQAC/QP/01
AJAY KUMAR GARG ENGINEERING COLLEGE GHAZIABAD
TUTORIAL SHEET 3
Department: ECE Course: B. Tech (ECE)
Semester: VI Subject: KEC-602, CS
Q. No. 1 2 3 4 5 6 7 8 9
CO NO. CO3 CO3 CO3 CO3 CO3 CO3 CO3 CO3 CO3
Blooms L5 L5 L6 L3 L4 L4 L5 L5 L6
Level*
*Bloom’s Level: L1: Remember, L2: Understand, L3: Apply, L4: Analyze, L5: Evaluate, L6: Create
Submission Date ________________
C ( s) 25
1. A second order system is given by 2 Find its rise time, peak overshoot and
R( s) s 6s 25
settling time if subjected to unit step input. Also calculate expression for its output response.
2. The open loop transfer function of a unity feedback system is given by,
K
G( s) K , 0
s( s 1)
With a given value of K, the peak overshoot was found to be 80%. It is proposed to reduce the peak
overshoot to 20% by decreasing the gain. Find the new value of K in terms of the old value.
3. Obtain an expression for a unit step time response of a control system whose transfer function is
given by
C ( s) 0.168
3
R( s) s 1.5s 0.5s 0.168
2
4. For a control system shown in figure below. Find the values of K1and K2 so that Mp=25% and
Tp=4sec. Assume unit step input.
5. A certain unity feedback system is described by the following transfer function-
K
G( s)
s ( s 30)( s 50)
2
Determine the state error coefficients and also determine the value of K to limit the steady state
error to 20 units due to input r (t ) 1 10t 20t 2 .
6. Determine the sensitivity of the overall transfer function for the system shown in figure below with
respect to change in parameter (a) K (b) H
AKGEC/IQAC/QP/01
7. The figure below shows mechanical system and its response when 20N of force is applied to the
system. Calculate the value of M and B.
8. Find Kp, Kv, Ka and steady state error for a system with open loop transfer function as
10( s 2)( s 3)
G( s) H ( s)
s( s 1)( s 5)( s 4)
Where the input is r (t ) 3 t t
2
9. A unity feedback system has,
K (s )
G( s)
(s )2
It is to be designed to meet following specifications: Steady state error for a unit step input=0.1,
damping ratio=0.5, natural frequency of oscillations=3.163. Find K, α and β.
Prepared By:
Dr. Sulekha Saxena
Asso. Prof., ECE
AKGEC/IQAC/QP/01
AKGEC/IQAC/QP/01
AJAY KUMAR GARG ENGINEERING COLLEGE, GHAZIABAD
DEPARTMENT OF ELECTRONICS & COMMUNICATION
TUTORIAL SHEET 4
Department: ECE Course: B. Tech (ECE)
Semester: VI Subject: KEC-602, CS
Q. No. 1 2 3 4 5 6 7 8
CO NO. CO4 CO4 CO4 CO4 CO4 CO4 CO4 CO4
Blooms L5 L3 L3 L4 L5 L4 L5 L6
Level*
*Bloom’s Level: L1: Remember, L2: Understand, L3: Apply, L4: Analyze, L5: Evaluate, L6: Create
Submission Date ________________
1. The closed loop transfer function of a system is given by
C ( s) 50
R( s) s(1 sT )(1 .5s) 50
Using, Routh stability criterion find the value of T such that the system is driven on to the verge of
instability and the resulting frequency of oscillation.
2. A unity feedback control system is characterized
K ( s 13)
by the open loop transfer function G ( s) Using the routh hurwitz criterion.
s( s 3)( s 7)
(i) Calculate the range of values of K for the system to be stable.
(ii) What is the marginal value of K for stability? Determine the frequency of oscillations if any.
(iii) Check if K=1, all the roots of the characteristic equation of the above system have the
damping factor greater than 0.5.
3. Determine using Routh Hurwitz criterion if the largest time constant is less than, greater than or
equal to 1 sec for s3+4s2+6s+4=0.
4. Using Routh Hurwitz criterion determine the stability of following system: A type 1 system with
velocity error constant of 10 sec-1 and poles at s= -3 and s= -6.
Ke s
5. A feedback control system has an open loop transfer function G ( s) H ( s) . Determine the
s ( s 2 s 1)
2
value of K for the closed loop stability.
6. Determine the ranges of K such that the characteristics equation has roots more negative than
s 1 . s 3 3( K 1) s 2 (7 K 5) s 4 K 7 0
7. Determine using Routh Hurwitz criterion if the largest time constant is less than, greater than or
equal to 1 sec for s3+4s2+6s+4=0.
AKGEC/IQAC/QP/01
K
8. A unity feedback control system has an open loop transfer function G( s) , draw the root
s( s 4)
locus.
Prepared By:
Dr. Sulekha Saxena
Asso. Prof., ECE
AKGEC/IQAC/QP/01
AJAY KUMAR GARG ENGINEERING COLLEGE, GHAZIABAD
DEPARTMENT OF ELECTRONICS & COMMUNICATION
TUTORIAL SHEET – V
Department: ECE Course: B. Tech (ECE)
Semester: VI Subject: KEC-602, CS
Q. No. 1 2 3 4 5
CO NO. CO5 CO5 CO5 CO5 CO5
Blooms Level* L6 L3 L3 L6 L5
*Bloom’s Level: L1: Remember, L2: Understand, L3: Apply, L4: Analyze, L5: Evaluate, L6: Create
Submission Date ________________
(1 0.5s)
1. Sketch the nyquist plot for the system with G( s) H (s)
s (1 0.1s)(1 0.02s)
2
Comment on stability and find the value of gain margin.
2. Explain the steps for drawing the bode plots. Draw the bode plot for the transfer function
50
G( s)
s(1 0.25s)(1 0.1s)
From the graph determine gain crossover frequency, phase crossover frequency, G.M and P.M and
stability of the system.
3. Discuss Nyquist Stability criterion. Sketch the Nyquist plot for the system with
10( s 3)
G( s) H ( s)
s( s 1)
Comment on the closed loop stability of the system. Also find the gain margin in dB.
4. Explain the steps for drawing the bode plots. Draw the bode plot for the transfer function
20
G( s)
s(1 0.1s)
K
5. A unity feedback system has G ( s) when subjected to unit step input shows 25% peak
s(1 Ts)
overshoot while it shows resonant frequency 8 rad/sec in frequency domain. Calculate K and T.
Prepared By:
Dr. Sulekha Saxena
Asso. Prof., ECE
