Following M-File is used to obtain results;
clc
clear all
close all
t=0:1:20;
dt=1;
qin=0.1;
qinnon=2.1;
y=zeros(20,1);
% Dimension of the array is defined for linear model
ynon=zeros(20,1); % Dimension of the array is defined for non-linear model
y(1)=0;

AE 383 SYSTEM DYNAMICS
Lecture Notes 3 (June 24th 2006)
Transfer Function Representation of Dynamic Systems
Transfer function of a system is defined as the ratio of the Laplace transform of the output to the
Laplace transform of the input, with zero initi

AE 383 SYSTEM DYNAMICS
Lecture Notes 2 (July 22nd 2006)
Laplace Transform
Transformations are frequently used to simplify an analytical problem. Taking logarithms, for
example, is a transformation that transforms the multiplication of two numbers into add

AE 383 SYSTEM DYNAMICS
A system is considered as an assemblage of components or elements .
Dynamics refers to situations which change with time.
System Dynamics:
i.
ii.
iii.
iv.
v.
vi.
Deals with entire operating machines and processes rather than isolate

AE 383 System Dynamics
HW#3
Due: Dec. 27, 2005
1.
Using Rouths stability test, examine the stability of the systems whose characteristic
equations are given below.
a. s 7 + 2.3s 6 + 4 s 5 + 5.6s 4 + 7 s 3 + 11s 2 + 18s + 12.3
b. s 5 + 2 s 4 + 20s 3 + 32 s

AE383 System Dynamics
HW#2
Due: November 24, 2005
1. Write the equations of the two-tank system depicted below. The restrictions at A, B, and C
are of same type and same diameter, The flow rate through the restrictions is proportional
square root law of t

AE 383 System Dynamics
Homework #1
Due: Oct. 20, 2005
1. Find the Laplace transformation of the following time functions:
t0
8 + cos(2t )
a. f (t ) =
7
t /2
0 t /5
t + cos(5t )
b. g (t ) = 2 / 5 + t / 5 t 4 / 5
0
t > 4 / 5
2. Solve the following o.d.e.s

AE383 HOMEWORK#5 SOLUTION
1- In Simulink we write the following diagram:
The outputs are as follows:
(> plot(tout',bir) command will help us to draw the figure)
Res pons e for z eta=0. 1
Res pons e for z et a=0. 3
1.8
1.4
1.6
1.2
1.4
1
1
Res pons e
Res po

AE383 System Dynamics
Homework #5
Due: December 27, 2004
100
. Using Simulink
s + 20 + 100
obtain the response of this system to step input for various values of the damping ratio,
( = 0.1, 0.3, 0.7, 1., 1.5) . Comment on your results. (Hint: Run simulati

AE 383 SYSTEM DYNAMICS
Lecture Notes 4 (June 27th 2006)
Step and Frequency Response of Ideal Elements
We want to know the dynamic response of these ideal elements. Dynamic response could refer
to response to any time-varying input, but two standard inputs

AE 383 SYSTEM DYNAMICS
Lecture Notes 4 (June 29th 2006)
Electrical Systems
Basic Elements:
Resistance elements
Capacitance elements
Inductance elements
Resistance of a linear resistor is R =
eR
i
(ohms law)
eR is the voltage across the resistor
i is the c

AE 383 System Dynamics
Summer 2005-2006
Instructor:
Office:
e-mail:
Dr. Volkan Nalbantolu
AE 202
vnalbant@mgeo.aselsan.com.tr
Course objectives:
The main objective of the course is to introduce methods for building mathematical models of engineering
syste

AE 383 System Dynamics
Fall 2004
Introduction to Simulink
Simulink is the extension of Matlab to program dynamic system simulations using blocks. The
approach is quite similar to the block diagram approach employed in automatic control systems
discipline.

AE 383 System Dynamics
Introduction to Matlab (v.2)
Fall 2004
Introduction to Matlab
Matlab executes the commands given at its command line identified by a double arrow. Some
basic commands of Matlab are given below.
> x = exp(-0.2696 *
.2)*sin(2*pi*0.3)/

AE 383 System Dynamics Lecture Notes 9 (July 22nd 2006)
Poles and the Stability of Linear Systems
Remember that the natural response of a dynamic system is given by the complementary
solution (the homogeneous solution) of the differential equation.
&
a& +

AE 383 System Dynamics Lecture Notes 8 (July 11th 2006)
FLUID SYSTEMS
Hydraulic systems use liquids (incompressibility) (free surface)
Pneumatic systems use gases (expands to fill its vessel)
Fluid systems involve pressure signals
Pressure = force per uni

AE 383 System Dynamics
Lecture Notes 7 (July 8th 2006)
Frequency Response (Sinusoidal Response) of 1st Order Systems
If we make our system input sinusoidal with amplitude qA and frequency rad /s, the system
equation becomes
dq0
+ q0 = Kq A sin t
dt
Rememb

AE 383 System Dynamics
Lecture Notes 6 (July 4th 2006)
First Order Systems
We will analyze certain combinations of the basic elements of mechanical and
electrical systems. We have found analogies between elements. We will also
encounter analogies between

AE 383 System Dynamics
Homework #4
Due: December 6, 2004
1. Linearize the following nonlinear ordinary differential equation around the
equilibrium defined by f (t ) = 1 : y + y + 27 y 3 = f (t ) .
2. Following nonlinear ordinary differential equation is

AE 383 System Dynamics Homework 3
Handed out: August 4, 2007
1.
Due: August 9 , 2007
A free vibration of the system shown in the Figure indicates that the amplitude of
vibration decreases to 25% of the value at t = t0 after four cycles of motion.
Determin

AE 383 SYSTEM DYNAMICS
Homework 2, Due July 26th 2007
1. Obtain the equivalent spring constant, keq, for the system shown in the figure below.
k2
k1
k3
2. Consider the system shown in the figure below. The bar A-A has no mass. The spring constant
k = 2000

AE 383 System Dynamics
Handed out: July 20, 2006
1.
Homework 5
Due: July 25, 2006
A free vibration of the system shown in the Figure indicates that the amplitude of
vibration decreases to 25% of the value at t = t0 after four cycles of motion.
Determine t

AE 383 System Dynamics
Homework 1
Handed out:
Due:
June 19th , 2006
June 27th , 2006
1) Perform the summation Z1 + Z2 = Z for the following complex numbers and check
your answers graphically
a)
Z1 = 4e( /4)j ;
b)
|Z1| = 28, Z1 = 45o ;
Z2 = 1.0 + j2.0
|Z2|