SYSTEM ENGINEERING

SYSTEM ENGINEERING
SEM-V, 2011-12
B.TECH EXAMINATION
UTTARAKHAND TECHNICAL UNIVERSITY

Time: 3 hours

Total Marks: 100

Attempt any four parts:

1. What is open loop and closed loop system? Giveadvantages and disadvantages of closed loop control system.
2. Explain force-voltage analogy with relevant diagram andequations.
3. Draw f-i analog system of Fig. 1.

   

   Figure. 1

4. Determine the transfer function C/R from the system shown in Fig. 2, using block diagram reduction technique.

   

   Figure . 2

5. Represent the following set of equation by a signal flow graph and determine the overall gain relating x and x using Mason's gain formula.
   x = ax₁ + fx₂          x = bx₂ + ex₄
   x = cx₃ + hx₅         x = dx₄ + gx₂
6. For the following mechanical system shown in Fig. 3.
   (a) Draw free body diagram
   (b) Write the system dynamic equations
   (c) Draw electrical analogous circuit

   

   Figure.3

Attempt any four parts:

1. Derive expression for time response of second order control system for unit step input.
2. When a second order control system is subjected to a unit step input, the values of ξ= 0.5 and ω_n = 6 rad/sec. Determine the rise time, and peak overshoot
3. For the system shown in Fig.4. Determine K_p and e_ss for unit step input.

   

   Figure.4

4. What are dynamic error coefficients?
5. Classify the various types of controllers; also discuss in brief PID control action.
6. A unity feedback system is characterized by an open loop transfer function.
   
   Determine the gain K so that the system will have a damping ration of 0.5. For this value of K determine settling time and peak time for a unit step input.

Attempt any two parts:

1. Explain sampler, sampling process, sampling theorem and zero-order-hold-circuit used in sampled data control system.
2. Explain any five properties of z-transformation and solve the difference equation c(k+2)+3c(k+1)+2c(k)=u)k; c(0)=1 and c(k)=0 for k<-1.
3. Determine the pulse transfer function and stability for the system shown in fig.5, for
   (a) T = 0.5 sec
   (b) T = 1.0 sec

   

   Figure.5

   What conclusion is obtained from the results of (a) and (b)?

Attempt any two parts:

1. How Diagonalization is done in discrete control system? Write down model matrix and diagonal matrix for the system having coefficients matrix.
   
2. Write down properties of state transition matrix. Obtain the time response of the system given below.
   x = ax
   Where given x(0) = [1  1]^T And 
3. Check the controllability and observability of a system having following coefficient matrices.
   

Attempt any two parts:

1. What is purpose of linearization? Describe the linearization process of a non-linear state model.
2. How stability of non linear system is checked by Liapunov's stability criteria? Consider a non linear system is described by the equation
   x₁ = x₂
   x₂ = - x₂ – x₁³
   Check the stability of the system by Liapunov's method.
3. Construct a Liapunov's function for the following system using variable gradient method and examine stability of the following system
   x₁ = -x₁ - 2x₁² x₂
   x₂ = -x₂