Sensitivity
Sensitivity is the degree to which changes in system
parameters affect system transfer function (or
performance).
Therefore, the sensitivity of transfer function T to
changes in paramete
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 l
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 p
Week6 - Stability of Control Systems
A stable system should exhibit a bounded output if the corresponding input
is bounded.
The stability of a feedback system is directly related to the location of
EE 482
Parameter design by the Root Locus
Parameter design
This method of parameter
design uses the root locus
approach to select the values
of the parameters.
Example 7.6: A welding head
for an auto
EE302 Controls Masons Gain Rule for Block Diagrams
DePiero
Masons Gain Rule is a technique for finding an overall transfer function. It is helpful
when trying to simplify complex systems. The purpose
EE482
Midterm Exam
October 24, 2013
Dr. Safonov
3:30-4:45 PM
CLOSED BOOK
No computers, calculators, phones or other electronic devices allowed
One 8 1 11 sheet of notes allowed (2-sided)
2
Have yo
EE 482
Root Locus Method - Steps
Step 1: Root locus construction procedure
a. Write the characteristic equation
1+F(s)=0 as 1+KP(s)=0
b. Find the m zeros zi and n poles pj of P(s)
Locate the poles an
EE 482: Mathematical
Models
Figure 2.2 (a) Spring-mass-damper system. (b) Free-body diagram.
2nd order systems
d2y
dy
m 2 b ky r t
dt
dt
RLC: Electric Circuits
Figure shows an RLC-circuit, as it
occu
EE482
Ch 3: State Variable Models
RLC Circuit Analysis: State Variables
1. For the above RLC circuit, the rate of change of
capacitor voltage is represented as
ic C
dv c
u ( t ) i L Eq. (1)
dt
2. Sim
Week5
EE482
The Performance of Feedback Control Systems
1. The time-domain performance specifications.
2. Use key input signals to test the response of the control system.
3. The correlation between t
EE482
Ch 4: Feedback Control System Analysis
1.
2.
3.
4.
Error Signals Analysis
Sensitivity Analysis
Transient Response
Steady State Analysis
Closed Loop Control System
A closed-loop system uses a mea
9/3/2014
Instructor
EE 482: Linear Control
Systems
Introduction
Class Instructor
Dr. Farooq Ahmad
Delta Tau Data systems, Inc.
Email: [email protected] (USC email will be available in 2nd week)
Office
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 D
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.
Pro
EE482 Fall 2014
_
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
Prob
EE482 Fall 2014
Problem 1
_
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.), p
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 (fric
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
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
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
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.
Stead
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 tr
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 thos
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 followin
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 fo
2nd Order Systems - Changing Parameters
Case 1:
Constant n
Variable d
Case 2:
Constant d
Variable n
Case 3:
Constant
Variable n
System Response Page 1
Case 4:
Constant n
Variable
System Response Pag
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
Example 3
Consider the following cruise control system. Determine the
type of the controller k(s) such that the desired speed can be
achieved without any steady state error.
Steady State Error Page 1
EE 482 Linear Control Systems
Instructor: Fariba Ariaei
Homework Set 4 - Solutions
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9