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: http://www.uta.edu/ee/ngs/ee4314_control/ 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

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).

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 Credit for turned in work may be rescinded for lack of familiarity with your submissions.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.

Textbooks & Description G.F. Franklin, J.D. Powell, A. Emami-Naeni, Feedback Control of Dynamic Systems, 7th Ed., Pearson Education, 2014, ISBN 978-0-13-349659-8 Other materials (on library reserve) K. Ogata, Modern Control Engineering, 5-th ed, 2010, Pearson Prentice Hall ISBN13:9780136156734, ISBN10:0136156738 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: 978-1-934015-04-9 B.W. Dickinson, Systems: Analysis, Design and Computation, Prentice Hall, 1991, ISBN: 0-13-338047-5. R.C. Dorf, R.H. Bishop, Modern Control Systems, 10th ed., Pearson Prentice Hall, 2005, ISBN: 0-13-145733-0 Catalog description: Catalog description: EE 4314. 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

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

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 9 - 13, 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

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

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

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

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 http://arri.uta.edu/acs/history.htm 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.

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

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

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

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

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

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.

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

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

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

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)

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

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

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

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

Linear System Description in Frequency Domain

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 +

Block Diagram: Simplification Rules

Block Diagram: Reduction Rules

Block Diagram: Reduction Rules

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)

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

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

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)

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

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

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

Feedback System Block Diagrams Automobile Cruise Control disturbance Input Output

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 1957. (Modern Period of AC).

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

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

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

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.