27/7/14
D(s)
U(s)
+

Controller
+
+
Recap from MA2006
Plant
Y(s)
Laplace Transform covered in detail in
Year 2 in MA2006
Review required of following topics
Definition
Laplace transformations of basic time functions
Properties
Final value theorem
(Nota)HomeworkProblemSet6
Semester1,AY:2012/13
1
s
DueinWeek lim
s 0
1. Using a straight line approximation, sketch the magnitude of the Bode plots of the openloop and
closed loop transfer function of the system shown in Figure 1.
R(s)
+
1000 ( s 0.01)(
ATTENTION: The Singapore Copyright Act applies to the use of this document. Nanyang Technological University Library
ATTENTION: The Singapore Copyright Act applies to the use of this document. Nanyang Technological University Library
ATTENTION: The Singap
D(s)
U(s)
+

Controller
+
+
Plant
Y(s)
MP3001: Dynamics and Control
Topic 27: Frequency Response Design
Controller Design:
Lead compensation
Tegoeh Tjahjowidodo
Bode
Bode plot of PD compensator
Gc s ( s z c )
to infinity
20dB/decade
20log(zc)
zc
w
The ma
D(s)
U(s)
+

Controller
+
+
Plant
Y(s)
MP3001: Dynamics and Control
Topic 26: Frequency Response Design
Dynamic compensation:
Lag compensator Design
Tegoeh Tjahjowidodo
Bode
Bode plot of PI compensator
Infinite gain at d.c. (0 frequency)
s zc
Gc s
s
Not
D(s)
U(s)
+

Controller
+
+
Plant
Y(s)
MP3001: Dynamics and Control
Topic 25: Frequency Response Design
Design with Bode plots:
Design requirements
Gain Compensation Design
Tegoeh Tjahjowidodo
Good design parameters
parameters
Small steady state error
D(s)
U(s)
+

Controller
+
+
Plant
Y(s)
MP3001: Dynamics and Control
Topic 24: Analysis using Bode plots
Open loop frequency response and
closed loop time response
Tegoeh Tjahjowidodo
Step response and frequency
response
Frequency response analysis and de
MP3001 Dynamics & Control (Semester 1 AY201112)
Answers to Tutorial 7 10
Tutorial 7
1.
The root locus sketching
(i) The starting points are open loop poles at s 1 j1 and s 1 j 2 . As there are no
finite zeros, the ending points must be at infinity
(ii) F
MP3001
TotalMarks:100
MP3001  Dynamics and Control
Continuous Assessment Exercise AY12/13 S1
Due on Week 11 (22 26 Oct 2012)
The cruise control system of a car uses a feedback control algorithm. The system tries to
maintain a constant velocity in the pr
ATTENTION: The Singapore Copyright Act applies to the use of this document. Nanyang Technological University Library
MP3001
NANYANG TECHNOLOGICAL UNIVERSITY
SEMESTER 1 EXAMINATION 20092010
MP3001  DYNAMICS & CONTROL
November/December 2009
Time Allowed:
MP3001  System Dynamics and Control
Tutorial 9 Frequency Response Method
This tutorial is an exercise on Frequency response and would you to be familiar with using semilog
papers as well as understanding the purpose of such plots. Straight lines plot fo
MP3001  System Dynamics and Control
Tutorial 8 Root Locus Controller Design
Stability & performance of closed loop systems are governed by the dominant closed loop poles. In
general, for a pair of dominant closed loop poles so = j, the real part governs
MP3001 Dynamics & Control
Tutorial 7 Root Locus
The root locus can be sketched by applying Evans method and the angle criterion
Q1
The root locus for the system with is given below:
G( s) =
K
( s 2 + 2 s + 2)( s 2 + 2 s + 5)
,
H (s) = 1
Plot of root loci
HomeworkProblemSet5
Semester1,AY:2012/13
DueinWeek12(29/102/11)
1. Sketch the root locus for the system shown in Figure 1.
+
C(s)
s3
s ( s 1)( s 2)( s 4)
R(s)
K
Figure 1. System for question 1.
Answer:
Root Locus
8
6
4
Imaginary Axis
2
0
2
4
6
8
 14
HomeworkProblemSet5
Semester1,AY:2012/13
DueinWeek12(29/102/11)
1. Sketch the root locus for the system shown in Figure 1 (No Matlab)
R(s)
+
K
s3
s ( s 1)( s 2)( s 4)
C(s)
Figure 1. System for question 1.
2. Consider a feedback control system with the for
HomeworkProblemSet4
Semester1,AY:2012/13
DueinWeek10(1519October2012)
Q1.
A DC motor has transfer function s
E a s
Km
s Tm s 1
, where Ea(s) is the applied voltage on
the armature circuit (in Volts), (s) is rotor angular displacement (in radians), Km is
HomeworkProblemSet3
Semester1,AY:2012/13
DueinWeek7(2428September2012)
Q1. Consider the rotational system having a flywheel with inertia J = 100 kg.m2 and viscous damping
coefficient B = 10 Ns/rad shown in Figure 1.
Flywheel
J
B
Figure 1: Rotational syst
D(s)
U(s)
+

Controller
+
+
Plant
Y(s)
MP3001: Dynamics and Control
Topic 22: Frequency Response Method
Bode Plots II: General Properties
Prof. Tegoeh Tjahjowidodo
Scope
Combining the basic Bode plots an example
Straight lines in place of actual magnit
D(s)
U(s)
+

Controller
+
+
Plant
Y(s)
MP3001: Dynamics and Control
Topic 21: Frequency Response Method
Bode Plots I: Graphs of basic transfer functions
Tegoeh Tjahjowidodo
Scope
Introduction background to Bode plots
Bode plots of standard systems
Int
8/6/2012
D(s)
U(s)
+

Controller
+
+
Plant
Stability analysis in complex plane
Y(s)
Stability of linear closed loop system can
be determined from location of the closed
th
loop system poles in splane
MP3001: Dynamics and Control
Topic 8: RouthHurwitz
8/5/2012
D(s)
U(s)
+

Controller
+
+
Plant
Time response
Y(s)
Given a system
R(s)
MP3001: Dynamics and Control
Topic 7: System Response and
Stability
G(s)
C(s)
need to study the performance of the system
before controlling it
Prof. Jaspreet Singh Dhupia
8/5/2012
D(s)
U(s)
+

Controller
+
+
Plant
Linearization of nonlinear math
models
Y(s)
Most physical systems tend to have some
nonlinearity
nonlinearity
Around a small operating region, system can be
assumed to behave almost like linear function
Linea
8/5/2012
D(s)
U(s)
+

+
+
Controller
Plant
Governing Eqns. for Electrical Sys.
Y(s)
Kirchhoffs current law; KCL (node law)
Net current flowing into the node/ out of the
node = 0
MP3001: Dynamics and Control
Topic 5: Mathematical Modeling
of Electrical
8/5/2012
D(s)
U(s)
+

Controller
+
+
Plant
Constituents of Mechanical
Systems
Y(s)
Inertia elements
Mass (kg) or Moment of Inertia (kgm2)
Spring elements
Deformed by an external force (torque) where the
deformation (angular disp.) is directly propor
8/5/2012
D(s)
U(s)
+
Controller
+
+
Plant
Why develop a mathematical model?
Y(s)
Systems that need to be studied, analyzed or
controlled can be of different types (e mechanical
controlled can be of different types (e.g. mechanical,
electrical, hydraulic
8/5/2012
D(s)
U(s)
+

Controller
+
+
Recap from MP2007
Plant
Y(s)
Laplace Transform covered in detail in
Year 2 in MP2007
MP2007
Review required of following topics
MP3001: Dynamics and Control
Topic 2: Review of Laplace Transform
Prof. Jaspreet Singh