T H I R T E E N
Digital Control Systems
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Transient Design via Gain
a. From the answer to the antenna control challenge in Chapter 5, the equivalent
Root Locus : Design
Design Example :
The differential equation of a DC motor is given by
Motor speed
Applied voltage
Determining the parameters and inserting their actual
values we have
The transfer f
Nyquist Plots / Nyquist Stability Criterion
Given
Nyquist plot is a polar plot for
vs
using the Nyquist contour (K=1 is assumed)
Applying the Nyquist criterion to the Nyquist plot we can
determine the
Lead Compensator
Design Example :
For the system with the following block diagram
representation
Find
so that the dominant closed loop poles are at
Solution : Start with
Compensator design with
is not
Time Response
After the engineer obtains a mathematical representation
of a subsystem, the subsystem is analyzed for its transient
and steadystate responses to see if these characteristics
yield the d
Modeling
This lecture we will consentrate on how to do system
modeling based on two commonly used techniques
In frequency domain using Transfer Function (TF)
representation
In time domain via using St
Frequency Response Analysis
Consider
let the input be in the form
Assume that the system is stable and the steady state
response of the system to a sinusoidal inputdoes not
depend on the initial condi
Stability
This lecture we will concentrate on
How to determine the stability of a system represented as
a transfer function
How to determine the stability of a system represented in
state-space
How to
Block Diagram Representation
This lecture we will concentrate on
Representing system components with block diagrams
Analyze and design transient response for systems
consisting of multiple subsystems
Root Locus
This lecture we will learn
What is root locus
How to sketch root-locus
How to determine the closed loop poles via root locus
How to use root locus to describe the transient
response, and st
T H R E E
Modeling in the Time Domain
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: State-Space Representation
. Ea(s) 150 For the power amplifier, V (s) = s+150 . Taking the inverse Laplace t
F O U R
Time Response
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Open-Loop Response
The forward transfer function for angular velocity is, 0(s) 24 G(s) = V (s) = (s+150)(s+1.32) P a. 0(t) =
F I V E
Reduction of Multiple Subsystems
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Designing a Closed-Loop Response
a. Drawing the block diagram of the system:
Pots
Pre amp
Power amp
Motor
T W O
Modeling in the Frequency Domain
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Transfer Functions
Finding each transfer function: Vi(s) 10 = ; i(s) Vp(s) Pre-Amp: V (s) = K; i Ea(s) 150
T W E L V E
Design via State Space
SOLUTION TO CASE STUDY CHALLENGE
Antenna Control: Design of Controller and Observer
a. We first draw the signal-flow diagram of the plant using the physical variable
O N E
Introduction
ANSWERS TO REVIEW QUESTIONS
1. Guided missiles, automatic gain control in radio receivers, satellite tracking antenna 2. Yes - power gain, remote control, parameter conversion; No -
E L E V E N
Design via Frequency Response
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Gain Design
a. The required phase margin for 25% overshoot ( = 0.404), found from Eq. (10.73), is 43.49o
T E N
Frequency Response Techniques
SOLUTION TO CASE STUDY CHALLENGE
Antenna Control: Stability Design and Transient Performance
First find the forward transfer function, G(s). Pot: K1 = Preamp: K Pow
E I G H T
Root Locus Techniques
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Transient Design via Gain
a. From the Chapter 5 Case Study Challenge: 76.39K G(s) = s(s+150)(s+1.32) 1 Since Ts =
N I N E
Design via Root Locus
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Lag-Lead Compensation
76.39K a. Uncompensated: From the Chapter 8 Case Study Challenge, G(s) = s(s+150)(s+1.32) = 71
S E V E N
Steady-State Errors
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Steady-State Error Design via Gain
76.39K a. G(s) = s(s+150)(s+1.32) . System is Type 1. Step input: e() = 0; Ramp i
S I X
Stability
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Stability Design via Gain
From the antenna control challenge of Chapter 5, 76.39K T(s) = 3 s +151.32s2+198s+76.39K Make a Routh ta
ELM 322, Control Systems
Control Systems
Spring 2015
Dr. Erkan Zergerolu
202 Computer Engineering Department
Email: ezerger@bilmuh.gyte.edu.tr
CLASS TIME: See the Schedule
OFFICE HOURS: To be announce