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Mathematical Models

Mathematical Models. SYSTEMS AND CONTROL I ECE 09.321 09/04/07 – Lecture 1 ROWAN UNIVERSITY College of Engineering Prof. John Colton DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING Fall 2007 - Semester One. Welcome to Systems and Control I. Course Learning Objectives

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Mathematical Models

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  1. Mathematical Models SYSTEMS AND CONTROL I ECE 09.321 09/04/07 – Lecture 1 ROWAN UNIVERSITY College of Engineering Prof. John Colton DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING Fall 2007 - Semester One

  2. Welcome to Systems and Control I Course Learning Objectives • Develop mathematical tools for analysis and design of modern feedback control systems • Apply these tools to many types of closed loop feedback control systems, evaluating the beneficial effects that feedback provides for steady–state and transient performance of these systems • Evaluate the beneficial implications of feedback on system performance, including sensitivity to parameter variation, tracking, and disturbance rejection • Develop the design criteria and tools for optimizing closed loop system performance and ensuring system stability • Develop tools for frequency response analysis and design of feedback control systems. • Use MATLAB for assignments and lab projects to supplement direct calculations

  3. Systems and Control I Topics • Historical Perspective • Mathematical models and tools: differential equations of physical systems, Laplace transforms, convolution integral and impulse response, transfer functions, block diagram manipulation, and signal flow graphs • Closed loop system performance: sensitivity reduction, disturbance rejection, transient performance and steady-state error, use of s-plane for analysis and design, cost of feedback, design criteria and tools, frequency response methods • Stability of feedback control systems: stability concepts, Routh-Hurwitz Stability Criterion, root locus design methods, Bode diagrams, phase and gain margin, Nyquist stability criterion • Design of feedback control systems

  4. Course Potpourri • Lectures M/W 9:50 AM-10:40 AM Rowan 102 • Laboratories T 3:15 PM-6:00 PM Rowan 239 • Course Website: users.rowan.edu/~colton/fall07/systems/index.html • Required Text: Modern Control Systems, Dorf and Bishop, 11th Edition 2007, ISBN: 0132270285 • Syllabus: see website (read ahead in text – Chapters 1/2) • Problem Sets: see website (issued each Wednesday, due 9:50 AM the next Monday – show all work for any credit, no credit for late problem sets) • Labs: see website (labs conducted Tuesday, reports due 12:15 PM the next Tuesday – lab report format, no credit for late lab reports • Course announcements: made regularly in class • Email: check regularly (daily)

  5. Learning Evaluation Grading Policy • 6 Quizzes 30% • Final Exam 40% • Assignments and labs 30% • Problem Sets and Class participation (15%) • Lab Reports, participation, homework (15%)

  6. Introduction to Control Systems • Historical perspective • Introduction to Feedback Control Systems • Closed loop system examples

  7. Historical Perspective • 13.7B BC Big Bang • 13.4B Stars and galaxies form • 5B Birth of our sun • 3.8B Early life begins • 700M First animals • 200M Mammals evolve • 65M Dinosaurs extinct • 600K Homo sapiens evolve

  8. Feedback Control Systems emerge rather recently • 1600 Drebbel Temperature regulator • 1781 Pressure regulator for steam boilers • 1765 Polzunov water level float regulator

  9. Closed loop example: Polzunov’s Water level float regulator

  10. Feedback Control Systems emerge rather recently • 1600 Drebbel Temperature regulator • 1681 Pressure regulator for steam boilers • 1765 Polzunov water level float regulator • 1769 James Watt’s Steam Engine and Governor

  11. Closed loop example: James Watt’s flyball governor

  12. Feedback Control Systems emerge rather recently • 1600 Drebbel Temperature regulator • 1681 Pressure regulator for steam boilers • 1765 Polzunov water level float regulator • 1769 James Watt’s Steam Engine and Governor • 1868 James Clerk Maxwell formulates a mathematical model for governor control of a steam engine • 1927 Harold Black discovers and patents the feedback amplifier • 1927 Hendrik Bode analyzes feedback amplifiers • 1932 Nyquist develops methods for analyzing feedback amplifier stability

  13. Open loop and closed loop control systems Open Loop System

  14. Open loop and closed loop control system models Open Loop System Closed Loop System

  15. Example: Feedback Control Amplifiers

  16. Feedback Control Systems emerge rather recently • 1600 Drebbel Temperature regulator • 1681 Pressure regulator for steam boilers • 1765 Polzunov water level float regulator • 1769 James Watt’s Steam Engine and Governor • 1868 James Clerk Maxwell formulates a mathematical model for governor control of a steam engine • 1927 Harold Black discovers and patents the feedback amplifier • 1927 Hendrik Bode analyzes feedback amplifiers • 1932 Nyquist develops methods for analyzing feedback amplifier stability • 1940s Norbert Wiener leads gun positioning effort; feedback control engineering becomes an engineering discipline • 1950s Increased use of Laplace transform, s-plane, root locus • 1960s Sputnik, highly accurate control systems for space vehicles, • robotics, and missiles • 1980s Routine use of digital computers as control elements • 1990s Feedback control in automobiles, automation, planetary exploration

  17. Example: Feedback in everyday life

  18. Quotable Quotes • “Take warning! Alternating currents are dangerous! They are fit only for powering the electric chair. The only similarity between an AC and a DC lighting system is that they both start from the same coal pile.” Thomas Edison – Pamphlet of 1887 • “Heavier than air flying machines are impossible” Lord Kelvin – Royal Society 1895 • “There is no likelihood man can ever tap the power of the atom” Robert Milliken Nobel Laureate Physics 1923

  19. Multivariable Control System Model

  20. Multivariable Control System

  21. Robotics A robot is a programmable computer integrated with a machine

  22. Example: Disk Drive

  23. Example: Automatic Parking Control

  24. Feedback Control: Benefits and cost Benefits: Cost:

  25. Feedback Control: Benefits and cost Benefits: Cost: • Reduction of sensitivity to process parameters • Disturbance rejection • More precise control of process at lower cost • Performance and robustness not otherwise achievable

  26. Feedback Control: Benefits and cost Benefits: Cost: • Reduction of sensitivity to process parameters • Disturbance rejection • More precise control of process at lower cost • Performance and robustness not otherwise achievable • More mathematical sophistication • Large loop gain to provide substantial closed loop gain • Stabilizing closed loop system • Achieving proper transient and steady-state response

  27. Homework for next week • See website for Problem Set 1 • Due Monday 09/10 8 AM • Show all work for any credit • See website for Lab Assignment 1 • Mostly reading tutorials • Report due Monday 09/10 12:15 PM

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