EE482 Fall 2014
HW#2
Problem 1 Do Problem P2.3, Dorf (12th ed.), page 142
Due: 9/9/2014
Problem 2
Do Problem P2.5, Dorf (12th ed.), page 142.
Problem 3
Do Problem P2.31, Dorf (12th ed.), page 147.
Problem 4
Do problem CP2.5, Dorf (12th ed.), page 157. Lab
LINEAR SYSTEMS (ENGR 6331/SYSM 6307/MECH 6300)
Design Application #3
Coupled Carts
Consider the problem of a pair of masses connected by a spring as shown below. Each cart
experiences an external force Fi in the positive zi direction as indicated. Due to
LINEAR SYSTEMS (MECH 6300/ENGR 6331/SYSM 6307)
Design Application Problem Set A:
State Variable Representations
1. Consider Design Application #2, the inverted pendulum on a cart. If the translational motion
is described by z, the Lagrangian function is
1
LINEAR SYSTEMS (ENGR 6331/SYSM 6307/MECH 6300)
Design Application #2
Inverted Pendulum on a Cart
Consider the classic problem of an inverted pendulum (bob on a mass-less rod) pivoted at its
base (frictionless hinge) which is mounted on a motorized cart. F
Second Order Systems
A system which has two poles is called the second order system
We consider a special class of second order systems in the form
1) Where are the locations of the poles and zeros of the system?
System Response Page 1
Case 1.
is the most
Introduction
Control system analysis and design focuses on
1. Stability
2. Performance
Transient Response, and steady state error
Steady State Error Page 1
Steady State Error
Definition:
Steady state error is the difference between the
input and the outp
Steady State Error with Disturbance
What is the steady state error?
Steady State Error Page 1
Example 4
For the system given below find the steady state error due to
the unit step disturbance.
Steady State Error Page 2
Steady State Error Page 3
Example
Poles, Zeros and System Response
A review of what we have seen so far and where we are going.
Consider the transfer function
What are the poles of the transfer function?
What are the zeros of the transfer function?
System Response Page 1
Example 1
Examp
Higher Order Systems
High order systems:
Higher order systems refer to the systems with additional
poles (more than two poles) or with zeros.
General rule:
For higher order systems, we cannot use those approaches
discussed so far for the first and second
Reduction of Multiple Systems
Motivation:
Consider the following system:
Given input and system's transfer function, we can easily find the
output. What is that?
How about the output of the following system?
Would it be as simple as the previous one?
Mechanical Components
Mechanical Components Page 1
Solving a Mechanical System
1) Assume a positive direction of motion
2) Draw a free-body diagram for each point of motion
3) Place on the body all forces that act on the body or caused by the motion
a) Fo
MATHEMATICAL DESCRIPTIONS OF SYSTEMS
invariant systems constitutes only a very small part of
we are able to give a complete
foundation for studying more
The class of lumped linear time
nonlinear and linear systems. For this small class of systems,
treatme
LINEAR SYSTEMS (ENGR 6331/SYSM 6307/MECH 6300)
Design Application #1
DC Motor with Load
A common application of control concepts is position control of an inertial load utilizing a
DC motor. In this problem we describe the dynamics of such a system to be
EE482 Fall 2014
HW#7
Problem 1 Do Problem E7.11 Dorf (12th ed.), page 527
Problem 2 Do Problem, P7.4 Dorf (12th ed.), page 530
Solution
Problem 3 Do Problem, P7.5 Dorf (12th ed.), page 530
Problem 4 Do Problem, AP7.2 Dorf (12th ed.), page 540
Problem 5 Do
EE482 Fall 2014
_
HW#5
Problem 1 Do Problem P5.1, Dorf (12th ed.), page 371.
_ Solution
Problem 2 Do Problem P5.5, Dorf (12th ed.), page 372
Problem 3 Do Problem CDP5.1, Dorf (12th ed.), page 379.
Problem 4 Do Problem CP5.8, Dorf (12th ed.), page 383.
Pro
EE482 Fall 2014
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HW#6
Problem 1 Do Problem P6.14, Dorf (12th ed.), page 433
Problem 2 Do Problem P6.18, Dorf (12th ed.), page 434
_ Solution
Problem 3 Do Problem P6.19, Dorf (12th ed.), page 434
Problem 4 Do Problem AP6.6, Dorf (12th ed.), page 436-437
P
EE482 Fall 2014
Problem 1
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HW#4
E4.10, Dorf (12th ed.), page 284-285
_
Solution
Problem 2 P4.1, Dorf (12th ed.), page 287
The tank level control block diagram is
Problem 3
a.
P4.6, Dorf (12th ed.), page 289
b.
c.
Therefore, if
Problem 4
CDP4.1, Dorf (12t
EE482 Fall 2014
_
HW#3 _
Problem 1
a. E3.17, Dorf (12th ed.), page 219
b. E3.18, Dorf (12th ed.), page 219
Solution
Problem 2
P3.2, Dorf (12th ed.), page 220.
The corresponding block diagram and signal flow graph are:
a.
b.
Problem 3
P3.30, Dorf (12th ed.
EE482 Fall 2014
HW#1
Due: 9/2/2014
Problem 1 Do Problem P1.4, Dorf (12th ed.), page 39.
The accurate control of a nuclear reactor is important for power system
generators. Assuming the number of neutrons present is proportional to
the power level, an ioni
DC Motor Transfer Functions
(Reference: Dorf and Bishop, Modern Control Systems, 9th Ed., Prentice-Hall, Inc. 2001)
The figure at the right represents a DC motor attached
to an inertial load. The voltages applied to the field and
armature sides of the mot
EE482 Fall 2014
HW#3
Problem 1
a. Do Problem E3.17, Dorf (12th ed.), page 219
b. Do Problem E3.18, Dorf (12th ed.), page 219
Due: 9/16/2014
Problem 2
Do Problem P3.2, Dorf (12th ed.), page 220.
Problem 3
Do Problem P3.30, Dorf (12th ed.), page 225-226
Pro
9/3/2014
Instructor
EE 482: Linear Control
Systems
Introduction
Class Instructor
Dr. Farooq Ahmad
Delta Tau Data systems, Inc.
Email: fahmad@csun.edu (USC email will be available in 2nd week)
Office Hours: EEB , Tue 5:45 6:25 PM
Class TA and Grader
Kira