CONTROL ENGINEERING

MEC522

Group Assignment

Lab Assignment

MUHAMAD IDHAM BIN KADIR

2009651992

SYED MOHD FARID BIN SYED MOHD FUZI

2009434552

MOHD HAZHAM BIN SOKAYAIL

2009490274

TERRY JOY NICHOLAS

2009674744

COLLINS EMANG LIAN

2009260656

EMD7M5A

EM220

FAKULTI KEJURUTERAAN MEKANIKAL

UITM

LECTURER : MR MOHD SAIFUL BAHARI BIN SHAARI

3 May 2012

Example 1.1

For the circuit of Figure 1.1, the initial conditions are iL (0) = 0, and Vc (0) = 0.5 V.

By using Kirchoff’s voltage law (KVL),

Substitution of (1.1) into (1.2) yields

Substituting the values of the circuit constants and rearranging we get:

Using the Laplace Transformation

By the voltage division* expression,

Using partial fraction expansion,† we let

and by substitution into (1.18)

Taking the Inverse Laplace transform‡ we find that

express the differential equation of Example 1.1 as

Use Simulink to draw a similar block diagram.

Block diagram

Output

Example 1.2

A fourth−order network is described by the differential equation

where y(t)is the output representing the voltage or current of the network, and u(t) is any input, and the initial conditions are y(0) = y'(0) = y''(0) = y'''(0) = 0.

a. We will express (1.27) as a set of state equationsb. It is known that the solution of the differential equation

subject to the initial conditions y(0) = y'(0) = y''(0) = y'''(0) = 0, has the solution

In our set of state equations, we will select appropriate values for the coefficients a3, a2, a1, and a0 so that the new set of the state equations will represent the differential equation of (1.28) and using Simulink, we will display the waveform of the output .

The differential equation of (1.28) is of fourth-order; therefore, we must define four state variables that will be used with the four first-order state equations.

We denote the state variables as x1, x2, x3 and , x4 and we relate them to the terms of thegiven differential equation as

We observe that

and in matrix form

In compact form, (1.32) is written as

Also, the output is

where

and since the output is defined as

By inspection the differential equation of (1.27) will be reduced to the differential equation of (1.28) if we let

and thus the differential equation of (1.28) can be expressed in state−space form as

where

Since the output is defined as

in matrix form it is expressed as

Use Simulink

Block diagram

Output

Example 3

Use Simulink

Block diagram

Exercise 1

The s−domain equivalent circuit is shown below.

and by substitution of the given circuit constants,

By the voltage division expression,

from which

Use Simulink

Block diagram

Command in MATLAB:

>> syms s

fd=ilaplace(1/(s^2+s+1))

fd = (2*3^(1/2)*sin((3^(1/2)*t)/2))/(3*exp(t/2))

>> t=0.1:0.01:15;...

td=2./3.*3.^(1./2).*exp(-1./2.*t).*sin(1./2.*3.^(1./2).*t);...

plot(t,td); grid

Output

Example 2.15

Pulse type: Time basedTime (t): Use simulation timeAmplitude: 0.25Period (secs): 2Pulse width (% of period): 50Phase delay (secs): 0

Block diagram

Output