control system Engineering 3

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The Open University of Sri Lanka

Diploma in Technology - Level 04

Academic Year 2013/14

MEX4243 - CONTROL SYSTEMS ENGINEERING - TMA 1

(1) Answer all questions.(2) Write your registration number clearly on your answer script.

(3) Send your answer scripts under registered cover to the address given below or put it into the

assignment box available at the Department of Mechanical Engineering (Block 17), Nawala.

THE COURSE CO-ORDINATOR - MEX4243DEPARTMENT OF MECHANICAL ENGINEERING

THE OPEN UNIVERSITY OF SRI LANKA

P.O. BOX 21, NAWALA

NUGEGODA.

(4) Last date of submission 17thJanuary, 2014

(5) No late submissionswill be accepted.

Q1. (a) How do you differentiate between open loop control and closed loop

control?(b) Draw the component block diagram of each of the following control systems.

Human eye control system

The student teacher learning process

Speed control system of a dc motor

Identify the following components in each block diagram.

1. Process 5. Controlled output

2. Actuator 6. Actuator output

3. Sensor 7. Sensor output4. Reference input,

(c) Identify a two-input feedback control system that you encounter in your everyday

environment. Draw a block diagram for each system and identify the components

mentioned in problem (b).

Q2

(a) Write the dynamic equations which describe the system performance for the system given in

Figure (1) and obtain the transfer function 2X (s) / F(s). Consider both masses slide on a

frictionless surface and k=1N/m.

f(t)m

1

1 kgm

2

1 kg

x1

x2

k=1N/m

Frictionless surface

Figure 1


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(b) (i) Write the dynamic equations describing the circuit in Figure (2) and represent them in

the form of a differential equation of ).(2 tv

(ii) Obtain the transfer function, ( ) )(12 sVsV

(iii) If the input, ( )tv1 is a unit step, solve the differential equation for )(2 tv using Laplace

transform methods for the parameter values and initial conditions Vtv 1)( 02 = ,

.0)( 02 =tv

&

(iv) Obtain the final value of the out put voltage for the unit step input.

Fig. (2)

Q3. Figure 3 shows the block diagram of a control system, where R(s) is the reference signal and

C(s) is the output. Find the transfer function C(s)/ R(s) of the system by

(a)simplifying the block diagram.

(b)Applying the Masons gain formula.

Show all the steps in (a) and (b) clearly.

Figure 3

+ +

--

L

v2 (t)

C

v1(t)

1H2

R


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Q3.

Consider the control system in the figure 4 .

Figure 4

Select your system by substituting values for a and b of G(s) from your registration number.

Take the value of the first digitof your registration number asband take the value of the last

digitasa.

(a) Obtain the characteristic equation and calculate the following when unit step inputis applied to the system.

(i) Damping Frequency

(ii) Damping Ratio(iii) Settling Time(iv) Rise Time(v) Percent Overshoot

(b) Using part (a) state the nature of the response (damped, undamped . etc.) of

your system.

(c) Use MATLAB to plot the unit step response of the above system and verify the

answers in (a) and (b) above.

(d) Use MATLAB to show how your system responds when a unit ramp input is

applied.

Note: For all MATLAB/ Other programs you have to attach both scripts (code) and plots.

bass

bsG

++

=2

)(

R(s) C(s)

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control system Engineering 3