Frequency Domain Design
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173
Prof. R.T. MCloskey, UCLA
Stability Margins
The sensitivity function S = 1/(1 + P C) was developed in the context of robust command tracking and disturbance
rejection. We noted the following (holds

The Fourier Transform
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Prof. R.T. MCloskey, UCLA
Background
The Fourier transform generalizes Fourier series to functions which are not periodic but still defined on the interval
(, ). The Fourier analysis of periodic func

Revisiting the Frequency Response Function
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Prof. R.T. MCloskey, UCLA
General perspective of a systems frequency response
The idea behind the frequency response function for a linear system is simple: a sinusoidal input ev

Fourier Series
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Prof. R.T. MCloskey, UCLA
Periodic functions and Fourier Series
Background
Fourier series are named after Joseph Fourier, a 18th century French mathematician who studied problems in
heat transfer and mechan

Control Systems Introduction
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Prof. R.T. MCloskey, UCLA
Feedback can manage" uncertainty: Motivating Examples
Uncertainty from:
imprecisely known plant"
imprecisely known operating environment
both examples motivate the

MAE172 - Control Systems Design Lab
Spring 2016
Lab #1
Lab Rules
No food or drinks in the lab
Stop the experiment before shutting down ControlDesk
Unplug the circuit box
Lab Objectives
In this lab you will analyze the spectral characteristics of variou

MAE172 Control Systems Design Lab
Prof. R.T. MCloskey, Mechanical and Aerospace Engineering, UCLA
C
R
Cn
Rn
Z
t
set of complex numbers
set of real numbers
set of vectors with n complex-valued elements
set of vectors with n real-valued elements
set of inte

Frequency Domain Performance Characterization
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124
Prof. R.T. MCloskey, UCLA
Closed-loop Performance Measures
Feedback controllers are designed for the following objectives
provide disturbance rejection
provide robust comman

State-Space Models
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210
Prof. R.T. MCloskey, UCLA
Introduction to State-Space Models
Instead of nth order ordinary differential equations, systems can be represented by state-space equations. For
finite-dimensional, linear, ti

Frequency Domain Stability Analysis
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137
Prof. R.T. MCloskey, UCLA
Connection between transfer function and state-space stability analysis
This section builds up the necessary tools to derive a simple test for the stability of

MAE172 - Control Systems Design Lab
Spring 2016
Lab #2
Lab Rules
No food or drinks in the lab
Stop the experiment before shutting down ControlDesk
Unplug the circuit box
Lab Objectives
The lab objectives are to perform a test on the resonator circuit w

MAE172 Control Systems Design Lab
Prof. R.T. MCloskey, Mechanical and Aerospace Engineering, UCLA
C
R
Cn
Rn
Z
t
set of complex numbers
set of real numbers
set of vectors with n complex-valued elements
set of vectors with n real-valued elements
set of inte

MAE172 Control Systems Design Lab
Prof. R.T. MCloskey, Mechanical and Aerospace Engineering, UCLA
C
R
Cn
Rn
Z
t
set of complex numbers
set of real numbers
set of vectors with n complex-valued elements
set of vectors with n real-valued elements
set of inte

MAE172 - Control Systems Design Lab
Spring 2016
Lab #3
Lab Objectives
In this lab you will use the data provided in Lab 1 to fit discrete-time models that are not based
on physical models (like the fact that the essential pieces of the low-pass filter are