Sketching the root locus
We can see that the root locus can be plotted by locating the points in the s-plane for
which the angles add up to an odd multiple of
180o. We can now construct rules for sketching a root locus, plotting any point of interest
if r
The take home part of the second midterm is:
Deasign dynamic compensator for
(s + 5)
G(s) = -
s(s^2 + s + 10)
such that the closed loop system has overshot
no more than 15%, settling time no more than
5s, and ess \leq 0.1 for the unit ramp inpiut.
The
Analysis of the Continuous Linear System
Through the design in project 1, the plant with the servo system was calculated as
12.88
. Figure 1 shows the frequency response of this system.
s + 6.5s 3 + 20.7 s 2
4
Figure 1
Due to the required response time of
A1
Appendix A
Design of Continuous-Time System
Transfer Function and Kp/Kv Derivation:
KpAm
AmKp
AmKp
Tm
= Tm * s + AmKv + 1 =
=
2
AmKp
AmKv + 1 AmKp
d
Tm * s + ( AmKv + 1) * s + AmKp
1+
s 2 + s(
)+
Tm * s + AmKv + 1
Tm
Tm
n =
2
AmKp
Tm
AND 2 n = 4.8 ~ 8
Page: 1
Project 1
EE 4002
Alicia Corbett
Michael Dantin
Scott Hammatt
Patrick Quebedeaux
Introduction
The first logical step in designing a feedback controller for the ball and beam
system is to analyze the DC motor, the part of the system that causes the
Page: 1
Project 1
EE 4002
Alicia Corbett
Michael Dantin
Scott Hammatt
Patrick Quebedeaux
Introduction
The first logical step in designing a feedback controller for the ball and beam
system is to analyze the DC motor, the part of the system that causes the
J ohnnyLara
EE4002
DesignProject2:
DigitalControlofthe
BallBeamSystem
M ay3,2004
Introduction
The purpose of this project is to gain experience and knowledge of the
performance of an uncompensated system and how it reflects our design if the system is
un
Page: 1
Karrie Hugghins
Patrick Quebedeaux
Matthew Bull
EE 4580
Report 1 of Design Project 1
September 12, 2003
Executive Summary
The first logical step in designing a feedback controller for the ball and beam system
is to analyze the DC motor, the part o
Page: 1
Project 1
EE 4002
Alicia Corbett
Michael Dantin
Scott Hammatt
Patrick Quebedeaux
Introduction
The first logical step in designing a feedback controller for the ball and beam
system is to analyze the DC motor, the part of the system that causes the
J ohnnyLara
EE4002
DesignProject2:
DigitalControlofthe
BallBeamSystem
M ay3,2004
Introduction
The purpose of this project is to gain experience and knowledge of the
performance of an uncompensated system and how it reflects our design if the system is
un
Page: 1
EE-4580 CONTROL DESIGN
PROJECT 2- BALL AND BEAM SYSTEM
JASON MCALLISTER
438-49-4726
11-17-04
Page: 2
Project Summary
Our goal is to design two compensators: one for the actuator which is a D.C. Motor
(inner-loop), and the other is for the ball and
Jason McAllister
November 29, 2004
UNCOMPENSATED SYSTEM
Step Response
1.4
1.2
System: Closed Loop: r to y
I/O: r to y
Settling Time (sec): 9.96
1
System: Closed Loop: r to y
I/O: r to y
Peak amplitude: 1
Overshoot (%): 0.314
At time (sec): 10.9
Amplitude
Rening the root locus sketch
We have covered the rules for a rapid sketch
of the root locus. For full use of the sketch we
need to calculate the points of interest of the
sketch, point on the real axis where the root
locus enters or leaves the complex pla
Angles of departure and arrival
Looking at the open loop poles and zeros
below, the root locus starts at the poles and
ends at zeros but at what angles?
j
Taking a point () close to a complex pole.
Assuming this point lies on the root locus, the
angles
Designing via root locus
We have seen how a root locus graphically
displays stability information, in addition root
locus can also display the transient response of
a system.
j
closed loop pole
open loop pole
A and B represent the actual and desired tran
Improving transient response
Again, we will study two techniques, placing
a pure dierentiator in the forward path, and
placing a zero and more distant pole.
Ideal derivative compensation (PD)
The transient response of a system can be selected by choosing
Types of electrical noises
(i) Johnson Noise
Johnson noise occurs in any device that dissipates power, such as resistor,
hence it is very common. Principle of equipartition of energy states: For a
system in thermal equilibrium with its surroundings : The
Signals
Signal a transmitted effect conveying a message
A essential characteristic of a signal is that of change, since it must be
capable of carrying information.
The change must be partly unpredictable.
It is also necessary to discuss the sinusoidal or
EE4580 Test Fall 2004
Suppose that the plant model is given by
G(s) =
10(s + 1)(s + 10)
.
s(s2 + s + 25)
1. Sketch straightline approximation for magnitude Bode plot.
2. Find errors at corner frequencies, and make corrections with dashed line.
3. Repeat 1
Modeling of Inverted Pendulum
We consider line movement for simplication. This example has
applications to the launch of rocket or missiles. We will demonstrate the use of Lagrange mechanics in modeling.
vy
v
m
vz
L
u(t)
M
y
Step 1: Total kinetic energy
Iterative Design Algorithm
We consider an iterative design method:
(a) Design zy , z , and Ky > 0, such that the three zeros of
(s) = 0 are in the right locations.
z
5.67
zy
5.67
(b) Design Kgy and pg such that the roots of
(s) = (s + pg )denp(s) + 3.2