1_Introduction.pdf 1 Dynamics and Control Topic 1: Introduction 2 Tentative Lecture Schedule 3 What is Control? Think of some “control” examples: • From your study • From industry • From real-life Commonly used terms in “control”? 4 Open Loop Control vs. Closed Loop Control? Open Loop Control: • There is no feedback • Calibration is the key! • Can be sensitive to disturbances 5 Open Loop Control: • Objective: make bread toasted • Control action: set timer • Control result (performance)? • How to improve the performance? • Use temp sensor • Use microprocessor and actuator to control the spring • Worth it? Feedback Closed Loop Control: • There is a feedback (sensor) • Compare actual behavior with desired behavior • Make corrections based on the error • The sensor is the key element of a feedback control • Design a proper control algorithm is the focus of this subject! Room Temp Control: Open or Closed? • Feedback? • Control objective? • Controller? • System/plant? • Disturbance? Applications of Feedback Control • Manufacturing Applications of Feedback Control • Robotics UNDERWATER ROBOT Applications of Feedback Control • Aerospace and Astronautics Applications of Feedback Control: BIG DOG in Action BOSTON DYNAMICS Sensing Actuation Control Plant ControlSystem = + + + BIG DOG CONTROL: Block Diagram DISTURBANCE Environment Foot Trajectory Planning Desired Walking Speed REFERENCE Joint angles & velocities Robot Joint torques Robot Robot Virtual Leg IK Virtual Leg FK Virtual Leg VM PD Servo Virtual Leg Coords Virtual Leg Forces State Machine Leg State Gait Coordination Mechanisms Influences to/from other legs + IK=inverse kinematics FK=forward kinematics VM=virtual model Exercise: • Use Block Diagram to represent this driving system • Indicate: sensor, actuator, control, plant, reference & disturbance Brain Hand Foot Eye Car _ Desired Direction Desired Speed Direction Speed Controller Actuators Plant Error Disturbances Sensor Control Actuation Sensor Plant _ Reference Response Error General Block Diagram Representation Feedback Control Concept Not limited to engineering systems only! Human Grasping Motion Feedback Control Concept…cont’d Not limited to engineering systems only! e.g. Taking Dynamics & Control… Two Main Criteria of Good Feedback Control • Acceptable Dynamic Responses • Stability Crash of SAAB JAS-39 due to instability Systematic Control Design Process Goa.

1. 1_Introduction.pdf
1
Dynamics and Control
Topic 1: Introduction
2
Tentative Lecture Schedule
3
What is Control?
Think of some “control” examples:
• From your study
• From industry
• From real-life

2. Commonly used terms in “control”?
4
Open Loop Control vs. Closed Loop Control?
Open Loop Control:
• There is no feedback
• Calibration is the key!
• Can be sensitive to disturbances
5
Open Loop Control:
• Objective: make bread toasted
• Control action: set timer
• Control result (performance)?
• How to improve the performance?
• Use temp sensor
• Use microprocessor and actuator to control the spring
• Worth it?

3. Feedback
Closed Loop Control:
• There is a feedback (sensor)
• Compare actual behavior with desired behavior
• Make corrections based on the error
• The sensor is the key element of a feedback control
• Design a proper control algorithm is the focus of this
subject!
Room Temp Control: Open or Closed?
• Feedback?
• Control objective?
• Controller?
• System/plant?
• Disturbance?
Applications of Feedback Control

4. • Manufacturing
Applications of Feedback Control
• Robotics
UNDERWATER ROBOT
Applications of Feedback Control
• Aerospace and Astronautics

5. Applications of Feedback Control: BIG DOG in Action
BOSTON DYNAMICS
Sensing Actuation Control Plant ControlSystem = +
+ +
BIG DOG CONTROL: Block Diagram
DISTURBANCE
Environment
Foot
Trajectory
Planning
Desired
Walking

6. Speed
REFERENCE
Joint angles
& velocities
Robot
Joint
torques
Robot Robot
Virtual
Leg IK
Virtual
Leg FK
Virtual
Leg VM
PD
Servo
Virtual
Leg Coords
Virtual
Leg Forces
State
Machine
Leg State

7. Gait
Coordination
Mechanisms
Influences to/from other legs
+
IK=inverse kinematics
FK=forward kinematics
VM=virtual model
Exercise:
• Use Block Diagram to represent this driving system
• Indicate: sensor, actuator, control, plant, reference &
disturbance
Brain Hand Foot
Eye
Car _
Desired
Direction

8. Desired
Speed
Direction
Speed
Controller Actuators
Plant
Error Disturbances
Sensor
Control Actuation
Sensor
Plant
_
Reference Response
Error
General Block Diagram Representation

9. Feedback Control Concept
Not limited to engineering systems only!
Human Grasping Motion
Feedback Control Concept…cont’d
Not limited to engineering systems only!
e.g. Taking Dynamics & Control…
Two Main Criteria of Good Feedback Control
• Acceptable Dynamic Responses
• Stability
Crash of SAAB JAS-39 due to instability
Systematic Control Design Process
Goals of This Course

10. To learn the basics of feedback control systems
1. Modeling as a transfer function and a block diagram
• Laplace transform (Mathematics!)
• Mechanical, electrical, electromechanical systems
2. Analysis
• Step response, frequency response
• Stability: Routh-Hurwitz criterion, (Nyquist criterion)
3. Design
• Root locus technique, frequency response technique,
• PID control, lead/lag compensator
4. Programming ability / Actual Implementation
• Matlab
• Simulink
Course Roadmap
Recap today’s topics
+
Questions?
Block Diagrams
Recap today’s topics
+

11. Questions?
Homework 1 - Part A
1. Find 2 open-loop control examples and 2 closed-loop
control examples in your daily life. Represent these
examples using block diagram. Clearly indicate Control
Reference, Controller, Plant, Actuator, Feedback Element
in the block diagram.
2. Compared to open-loop control, discuss the pros and cons
of feedback control.
3. What are the two main criteria in feedback control design?
4. Describe the procedures of feedback control system
design.
1_MathReview.pdf
1
Dynamics and Control
• Math Preparation
(Review of Complex Number)

12. • Complex Number in Matalb
Week Topics Exam Reading
1 Introduction Ch 1-2
2 Math Review Ch 1-2
3 Modelling (Frequency + Time Domain) Ch 2
4 Time Response Ch 4
5 Block Diagram M-Exam 1 Ch 5
6 Stability Ch 6
7 Midterm Review + Make up Ch 1-6
8 Experiment
9 Spring Break
10 Steady State Errors Ch 7
11 Root Locus Ch 8
12 Design Via Root Locus M-Exam 2 Ch 9
13 Design Via Root Locus Ch 9
14 Frequency Response Ch 10

13. 15 Design Via Frequency Response Ch 11
16 Final Review + Make up Ch 7-11
17 Final Exam Final Exam
2
Tentative Lecture Schedule
2
Math Prerequisites
1. Complex Numbers
2. Linear Ordinary Differential Equations
3. Laplace Transform to Solve ODE’s
4. Partial Fraction Expansion
5. Linearization
WARNING!!
THIS IS A VERY MATH INTENSIVE COURSE!
It is your responsibility to review these topics.
We assume that you have passed all the pre-
required calculus courses and already have a
GOOD command of all these prerequisites.

14. ADD/DROP deadline is Sept 8!
Complex Number: A Little History
Math is used to explain our universe. When a recurring
phenomenon is seen and can’t be explained by our present
mathematics, new systems of mathematics are derived.
In the real number
system, we can’t
take the square
root of negatives,
therefore the
complex number
system was
created.
Girolamo’s Problem
40
10

15. xy
yx
In The Great Art, published in 1545, Girolamo Cardano
discusses the
following problem.
To find x and y, use substitution.
04010
40)10(
2
xx
xx
Apply the Quadratic Formula.
155
2
)40()1(41010
2

16. Due to the symmetry in the problem, x and y take on ± values.
5 10 15 20
2
4
6
8
10
12
No Intersection!
Bombelli And Imaginary Numbers
1
1
1
1
4

17. 3
2
i
ii
i
i
Rafael Bombelli in the 1560’s figured out a way to work with
imaginary
numbers. Definition of Imaginary unit, i
Using these rules, Bombelli worked Cardano’s cubic solutions
to arrive
at real results.
Complex Numbers: Definition
A complex number consists of a real and an imaginary

18. term:
� + ��
where � and � are real numbers and � is the imaginary
unit.
Both real numbers and imaginary numbers have
specific physical meanings in control engineering
Complex Numbers: Addition and Subtraction
Add/subtract real to real, and imaginary to imaginary
Example: (6 + 7i) + (3 - 2i)
(6 + 3) + (7i - 2i) = 9 + 5i
When subtracting, DON’T FORGET to distribute the
negative sign!
Example: (3+2i) – (5 – i)
(3 – 5) + (2i – (-i)) = -2 + 3i
Complex Numbers: Multiplication

19. Complex Numbers: Division/Simplification
• In order to simplify complex numbers (they must
always be in the form a + bi, you must multiply by the
complex conjugate:
2
3 8i (4 3i)
(3 8i) (4 3i)
4 3i (4 3
12 41i
i)
12 9i 32i 24i
16 9
25
12 41i
25 25

20. Exercise 1
Simplify:
Solution
:
i

21. i
4
23
2
2
13 2i 3 2i 4 i 12 11i 2i
4 i 4 i 4 i
0 11
i
17 1716 i

22. Complex Numbers: Geometrical Interpretation
Jean-Robert Argand in 1806 came up with the idea of a
geometrical interpretation of complex numbers. Replace the x-
axis with the real part of complex numbers, and the y-axis with
the imaginary part.
Thus, � = � + �� has the graphical interpretation:
Complex Numbers: Trigonometric and Polar Forms

23. A complex number can be represented in the trigonometric
form:
� = ����⁡(�)
� = ����⁡(�)
� = � + �� = ���� � + ���� � �
Recall Euler’s formula:
��� = ���� + �����
Based on this, a complex number can
also be represented in polar form:
� = ���� = �∠ �
r

24. Complex Numbers: Angle of Quadrants
Conjugate Pair
Complex Numbers: Angle of Quadrants

25. Conjugate Pair
Exercise 2:
Represent these complex numbers in polar form

27. First key in these complex numbers in Matlab
21505.24
88302
65
2
4
3
60
21
izzez
jzezz

28. i
i
The variable z in function compass (z)
can be a single variable, or an array.
In this example, it is an array , holding
6 elements
Homework 1 - Part B

29. 1. Practice all the exercises in this PPT.
For the following problems 2-7, you need to verify your
solutions in Matlab.
2. For this complex number, �⁡ − ⁡��, give its exponential
form.