1. EE 4314: Control Systems Lectures: Tue/Thu, 2:00-3:20, NH 202
Instructor: Indika Wijayasinghe, Ph.D.
Office hours: Tue/Thu 9:00 am – 11:00 am, NH 250, or by appointment.
Course TAs: Raghavendra Sriram, Fahad Mirza
Course info:
Grading policy:
5 Homework – 20%
6 Labs – 20%
Midterm I (in-class) – 20%
Midterm II (take-home) – 20%
Final (in-class) – 20%
Grading criteria: on curve based on class average

2. Syllabus Assignments:
Homework contains both written and/or computer simulations using MATLAB. Submit code to the TA’s if it is part of the assignments.
Lab sessions are scheduled in advance, bi-weekly, so that the TA’s can be in the lab (NH 148). While the lab session is carried out in a group, the Lab report is your own individual assignment.
Examinations: Three exams (two midterms, one final), in class or take home.
In rare circumstances (medical emergencies, for instance) exams may be retaken and assignments can be resubmitted without penalty.
Missed deadlines for take-home exams and homework: Maximum grade drops 15% per late day (every 24 hours late).

3. Honor Code
Academic Dishonesty will not be tolerated. All homework and exams are individual assignments. Discussing homework assignments with your classmates is encouraged, but the turned-in work must be yours. Discussing exams with classmates is not allowed. Your take-home exams and homework will be carefully scrutinized to ensure a fair grade for everyone.
Random quizzes on turned-in work: Every student will be required to answer quizzes in person during the semester for homework and take home exam. You will receive invitations to stop by during office hours. Credit for turned in work may be rescinded for lack of familiarity with your submissions.
Attendance and Drop Policy: Attendance is not mandatory but highly encouraged. If you skip classes, you will find the homework and exams much more difficult. Assignments, lecture notes, and other materials are going to be posted, however, due to the pace of the lectures, copying someone else's notes may be an unreliable way of making up an absence. You are responsible for all material covered in class regardless of absences.

4. Textbooks & Description
G.F. Franklin, J.D. Powell, A. Emami-Naeni, Feedback Control of Dynamic
Systems, 7th Ed., Pearson Education, 2014, ISBN
Other materials (on library reserve)
K. Ogata, Modern Control Engineering, 5-th ed, 2010, Pearson Prentice Hall ISBN13: , ISBN10:
Student Edition of MATLAB Version 5 for Windows by Mathworks, Mathworks Staff, MathWorks Inc.
O. Beucher, M. Weeks, Introduction to Matlab & Simulink, A project approach, 3-rd ed., Infinity Science Press, 2006, ISBN: 
B.W. Dickinson, Systems: Analysis, Design and Computation, Prentice Hall, 1991, ISBN:
R.C. Dorf, R.H. Bishop, Modern Control Systems, 10th ed., Pearson Prentice Hall, 2005, ISBN:
Catalog description:
Catalog description: EE CONTROL SYSTEMS (3-0) Analyses of closed loop systems using frequency response, root locus, and state variable techniques. System design based on analytic and computer methods.
This is an introductory control systems course. It presents a broad overview of control techniques for continuous and discrete linear systems, and focuses on fundamentals such as modeling and identification of systems in frequency and state-space domains, stability analysis, graphical and analytical controller design methods.
The course material is divided between several areas:
Control Systems: classification, modeling, and identification
Basics of Feedback: performance and stability
Control Design Methods: frequency domain, state-space
Programming exercises using MATLAB and Simulink
Laboratory experiments

5. Tentative Course Schedule
Part 1: Introduction to systems & system modeling
Week 1 - January 20, 22, Lectures 1, 2
Introduction to feedback control systems and brief history
History of Feedback Control
Review of basics: Matrix and vector algebra, complex numbers, integrals and series, Differential equations and linear systems
Notes for quick review
Week 2 - January 27, 29, Lectures 3, 4
Lecture 3: Dynamic Models of Mechanical systems.
Lecture 4: Dynamic Models of Mechanical systems
Homework #1 handed out on January 29
Lab #1: Matlab and Simulink Hands on Lab at NH 148
Week 3 - Feb 3, 5, Lectures 5, 6
Lecture 5: Dynamic Models of Circuits
Lecture 6: Dynamic Models of Electromechanical Systems
Week 4 - February 10, 12, Lectures 7, 8
Lecture 7: Dynamic Models of DC motors, thermal and fluid system
Lecture 8: System identification of first and second order systems
Homework #1 due February 12, Homework #2 is posted
Lab #2: Identification of a DC Motor Transfer Function

6. Tentative Course Schedule
Part 2: Feedback and Its Time Domain Analysis
Week 5 - Feb 17, 19, Lectures 9, 10
Lecture 9:Stability and Mason's rule
Lecture 10: Introduction of state space model
Lab #1 report due February 19
Week 6 - Feb 24, 26, Lectures 11, 12
Lecture 11: State space model
Lecture 12: First analysis of feedback system
Homework #2 due February 26, Homework #3 handed out
Lab #3: Identification of a State-Space Model
Week 7 - Mar 3, 5, Lectures 13, Midterm exam I
Midterm study guide
In-class Midterm I on March 5, covers: system modeling, basic feedback, and state-space methods.
Lab #2 report due March 3 in class
Week 8 - Mar , Spring break
Week 9 - Mar 17, 19, Lecture 14, Lecture 15
Lecture 14: PID control
Lecture 15: Response of State-space equation
Homework #3 due on March 19

7. Tentative Course Schedule
Part 3: Feedback and Design Methods in Frequency Domain
Week 10 - Mar 24, 26, Lectures 16, 17
Lecture 16: Full-state feedback, Ackerman's Formula
Lecture 17: Optimal control - Linear Quadratic Regulation.
Lab #4: Speed Motor Control using PID
Lab #3 report due March 26
Week 11 - Mar 31, Apr 2, Lectures 18, 19
Lecture 18: Root-locus design 1
Lecture 19: Root-locus design 2
Homework #4 handed out on Apr 2
Week 12 - Apr 7, 9, Lectures 20, 21
Lecture 20: Root-locus design 3
Lecture 21: Root-locus design 4
Lab #5: LQR control of Mass-Spring-Damper System
Week 13 - Apr 14, 16, Lectures 22, 23
Midterm II (Take Home), posted April 16, due April 23, covers frequency domain techniques
Lecture 22: Bode plot, PM, GM
Lecture 23: Lead-Lag compensator
Homework #4 due April 16, Homework #5 handed out
Lab #4 report due April 14 in class

8. Tentative Course Schedule
Part 4: Digital Control
Week 14 - Apr 21, 23, Lectures 24, 25
Lecture 24: Nyquist plot
Lecture 25: Nyquist stability criterion
Lab #6: Digital Control
Week 15 - Apr 28, 30, Lectures 26, 27
Lecture 26: Digital Control: Z-transform
Lecture 27: Digital Control: Controller design
Week 16 - May 5, 7, Course recap and exam preparation
Lecture 28: Digital Control
Exam preparation and final study guide
Homework #5 due May 5 at class
Lab #5 report due May 5 at class
Week 17 - May 12
Final exam (in-class) (comprehensive) in class, no calculator
Time: 2:00 pm - 4:30 pm
Bring a 6-page, double-sided cheat sheet, handwriting only
Lab #6 report due May 12

9. Course Objectives
Students should be familiar with the following topics:
Modeling of physical dynamic systems
Block diagrams
Specifications of feedback system performance
Steady-state performance of feedback systems
Stability of feedback systems
Root-locus method of feedback system design
Frequency-response methods
Nyquist’s criterion of feedback loop stability
Design using classical compensators
State variable feedback

10. Textbook Reading and Review
Course Refresher:
Math: complex numbers, matrix algebra, vectors and trigonometry, differential equations.
Programming: MATLAB & Simulink
EE 3317 (Linear Systems), 3318 (Discrete Signals and Systems)
For weeks 1 & 2
Read Chapter 1, Appendix A (Laplace Transformation) of Textbook
Read History of Feedback Control by Frank Lewis
Purpose of weekly assigned textbook readings
To solidify concepts
To go through additional examples
To expose yourselves to different perspectives
Reading is required. Problems or questions on exams might cover reading material not covered in class.

11. Signals and Systems Signal: System: A set of data or information
Examples: audio, video, image, sonar, radar, etc.
It provides information on the status of a physical system.
Any time dependent physical quantity
System:
Object that processes a set of signals (input) to produce another set of signals (outputs).
Examples:
Hardware: Physical components such as electrical, mechanical, or hydraulic systems
Software: Algorithm that computes an output from input signals

12. Signal Classification
Continuous Time vs. Discrete Time
Telephone line signals, Neuron synapse potentials
Stock Market, GPS signals
Analog vs. Digital
Radio Frequency (RF) waves, battery power
Computer signals, HDTV images
Analog, continuous time
Digital, continuous time
Analog, discrete time
Digital, discrete time

13. Signal Classification
Deterministic vs. Random
Predictable: FM Radio Signals
Non-predictable: Background Noise Speech Signals
Periodic vs. Aperiodic
Sine wave
Sum of sine waves with non-rational frequency ratio

14. System Classification
Linear vs. Nonlinear
Linear systems have the property of superposition
If U →Y, U1 →Y1, U2 →Y2 then
U1+U2 → Y1+Y2
A*U →A*Y
Nonlinear systems do not have this property, and the I/O map is represented by a nonlinear mapping.
Examples: Diode, Dry Friction, Robot Arm at High Speeds.
Memoryless vs. Dynamical
A memoryless system is represented by a static (non-time dependent) I/O map: Y=f(U).
Example: Amplifier – Y=A*U, A- amplification factor.
A dynamical system is represented by a time-dependent I/O map, usually a differential equation:
Example: dY/dt=A*u, Integrator with Gain A.
Exact Equation, nonlinear
Approximation around vertical equilibrium, linear

15. System Classification
Time-Invariant vs. Time Varying
Time-invariant system parameters do not change over time. Example: pendulum, low power circuit, robots.
Time-varying systems perform differently over time. Example: human body during exercise, rocket.
Stable vs. Unstable
For a stable system, the output to bounded inputs is also bounded. Example: pendulum at bottom equilibrium
For an unstable system, the ouput diverges to infinity or to values causing permanent damage. Example: Inverted pendulum.
stable
unstable

16. System Modeling
Building mathematical models based on observed data, or other insight for the system.
Parametric models (analytical): ODE, PDE
Non-parametric models: ex: graphical models - plots, or look-up tables.

17. Types of Models White (clear or glass) Box Model Black Box Model
derived from first principles laws: physical, chemical, biological, economical, etc.
Examples: RLC circuits, MSD mechanical models (electromechanical system models).
Black Box Model
model is based solely from measured data
No or very little prior knowledge is used.
Example: regression (data fit)
Gray Box Model
combination of the two
Determination of the model structure relies on prior knowledge while the model parameters are mainly determined by measurement data

18. White Box Systems: Electrical
Defined by Electro-Magnetic Laws of Physics: Ohm’s Law, Kirchoff’s Laws, Maxwell’s Equations
Example: Resistor, Capacitor, Inductor

19. RLC Circuit as a System
Kirchoff’s Voltage Law (KVL):

20. White Box Systems: Mechanical
Newton’s Law:
Mechanical-Electrical Equivalance:
F (force) ~V (voltage)
x (displacement) ~ q (charge)
M (mass) ~ L (inductance)
B (damping) ~ R (resistance)
1/K (compliance) ~ C (capacitance)

21. White Box vs Black Box Models
White Box Models
Black-Box Models
Information Source
First Principle
Experimentation
Advantages
Good Extrapolation
Good understanding
High reliability, scalability
Short time to develop
Little domain expertise required
Works for not well understood systems
Disadvantages
Time consuming and detailed domain expertise required
Not scalable, data restricts accuracy, no system understanding
Application Areas
Planning, Construction, Design, Analysis, Simple Systems
Complex processes
Existing systems
This course deals with both white and black models which are linear

22. Linear System
Why study continuous linear analysis of signals and systems when many systems are nonlinear in practice?
Basis for digital signals and systems
Many dynamical systems are nonlinear but some techniques for analysis of nonlinear systems are based on linear methods
Methods for linear systems often work reasonably well, for nonlinear systems as well
If you don’t understand linear dynamical systems you certainly can’t understand nonlinear systems

23. LTI Models State space form of linear time varying dynamical system
dx/dt= A(t)x(t) + B(t)u(t),
y(t) = C(t)x(t) + D(t)u(t)
where:
x(t) = state vector (n-vector)
u(t) = control vector (m-vector)
y(t) = output vector (p-vector)
A(t) = nxn system matrix, B(t) = nxm input matrix
C(t) = pxn output matrix, D(t) = pxm matrix

24. Linear Systems in Practice
Most linear systems encountered are time-invariant: A, B, C, D are constant, i.e., don’t depend on time
Examples: second-order electromechanical systems with constant coefficients (mass, spring stiffness, etc)
when there is no input u (hence, no B or D) system is called autonomous
Examples: filters, uncontrolled systems
when u(t) and y(t) are scalar, system is called single-input, single-output (SISO)
when input & output signal dimensions are more than one, MIMO (Multi-Input-Multi-Output)
Example: Aircraft – MIMO

25. Linear System Description in Frequency Domain

26. Block Diagrams Block Diagram Model:
Helps understand flow of information (signals) through a complex system
Helps visualize I/O dependencies
Elements of block diagram:
Lines: Signals
Blocks: Systems
Summing junctions
Pick-off points
Transfer Function Summer/Difference Pick-off point U U2 + U1
U1+U2 U U +

27. Block Diagram: Simplification Rules

28. Block Diagram: Reduction Rules

29. Block Diagram: Reduction Rules

30. Automatic Control
Control: process of making a system variable converge to a reference value
Tracking control (servo): reference value = changing
Regulation control: reference value = constant (stabilization)
Open Loop vs. closed loop control + y + y r
Controller
K(s)
Plant
G(s)
Controller
K(s) +
Plant
G(s) r -
- No output measurement
- Known system
- No disturbance
Sensor Gain
H(s)

31. Feedback Control Role of feedback:
Reduce sensitivity to system parameters (robustness)
Disturbance rejection
Track desired inputs with reduced steady state errors, overshoot, rise time, settling time (performance)
Systematic approach to analysis and design
Select controller based on desired characteristics
Predict system response to some input
Speed of response (e.g., adjust to workload changes)
Approaches to assessing stability

32. Feedback System Block Diagram
Temperature control system
Control variable: temperature
Initial set temp=55F, At time=6, set temp=65F

33. Feedback System Block Diagram
Process: house
Actuator: furnace
Sensor: Thermostat
Controller: computes control input
Actuator: a device that influences the controlled variable of the process
Disturbance: heat loss (unknown, undesired)

34. Key Transfer Functions
Reference + S
Controller
Plant –
Transducer
Jlh: Can we make the diagram bigger and the title smaller?

35. Basic Control Actions: u(t)
Jlh: Can we give more intuition on control actions. This seems real brief considering its importance.

36. Summary of Basic Control
Proportional control
Multiply e(t) by a constant
PI control
Multiply e(t) and its integral by separate constants
Avoids bias for step
PD control
Multiply e(t) and its derivative by separate constants
Adjust more rapidly to changes
PID control
Multiply e(t), its derivative and its integral by separate constants
Reduce bias and react quickly

37. Feedback System Block Diagrams
Automobile Cruise Control
disturbance
Input
Output

38. Brief History of Feedback Control
The key developments in the history of mankind that affected the progress of feedback control were:
1. The preoccupation of the Greeks and Arabs with keeping accurate track of time. This represents a period from about 300 BC to about 1200 AD. (Primitive period of AC)
2. The Industrial Revolution in Europe, and its roots that can be traced back into the 1600's. (Primitive period of AC)
3. The beginning of mass communication and the First and Second World Wars. (1910 to 1945). (Classical Period of AC)
4. The beginning of the space/computer age in (Modern Period of AC).

39. Primitive Period of AC
Float Valve for tank level regulators Drebbel incubator furnace control (1620)
(antiquity)

40. Primitive Period of AC
James Watt Fly-Ball Governor For regulating steam engine speed (late 1700’s)

41. Classical Period of AC
Most of the advances were done in Frequency Domain.
Stability Analysis: Maxwell, Routh, Hurwitz, Lyapunov (before 1900).
Electronic Feedback Amplifiers with Gain for long distance communications (Black, 1927)
Stability analysis in frequency domain using Nyquist criterion (1932), Bode Plots (1945).
PID controller (Callender, 1936) – servomechanism control
Root Locus (Evans, 1948) – aircraft control

42. Modern Period of AC Time domain analysis (state-space)
Bellmann, Kalman: linear systems (1960)
Pontryagin: Nonlinear systems (1960) – IFAC
Optimal controls
H-infinity control (Doyle, Francis, 1980’s) – loop shaping (in frequency domain).
MATLAB (1980’s to present) has implemented math behind most control methods.