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
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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,