notes - Notes for ECE-320 Fall 2004 by R. Throne The...

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Unformatted text preview: Notes for ECE-320 Fall 2004 by R. Throne The following pages contain a first attempt at writing notes for ECE-320. The topics we cover in ECE-320 are not covered in any single book. These notes are not complete, especially the sections on root locus design and design using Bode plots. The major sources for these notes are Analog and Digital Control System Design , by C. T. Chen. Sanders College Publishing. 1993. Linear Control Systems , by Rohrs, Melsa, and Schulz. McGraw-Hill, 1993. Modern Control Engineering , by Ogata. Prentice-Hall, 2002. Modern Control Systems , by Dorf and Bishop. Prentice-Hall, 2005. 1 Contents 1 Table of Laplace Transforms 4 2 Laplace Transform Review 5 2.1 Poles and Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Proper and Strictly Proper Transfer Functions . . . . . . . . . . . . . . . . . . . 5 2.3 Impulse Response and Transfer Functions . . . . . . . . . . . . . . . . . . . . . 5 2.4 Partial Fractions with Distinct Poles . . . . . . . . . . . . . . . . . . . . . . . . 6 2.5 Partial Fractions with Distinct and Repeated Poles . . . . . . . . . . . . . . . . 9 2.6 Complex Conjugate Poles: Completing the Square . . . . . . . . . . . . . . . . . 14 2.7 Complex Conjugate Poles-Again . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3 Final Value Theorem 20 4 Step Response and Position Error, Ramp Response and Velocity Error 21 4.1 Step Response and Position Error . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.2 Ramp Response and Velocity Error . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5 Response of a Ideal Second Order System 28 5.1 Step Response of an Ideal Second Order System . . . . . . . . . . . . . . . . . . 28 5.2 Time to Peak, T p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 5.3 Percent Overshoot, PO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.4 Settling Time, T s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5.5 Constraint Regions in the s-Plane . . . . . . . . . . . . . . . . . . . . . . . . . . 33 5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 6 Characteristic Polynomial, Modes, and Stability 42 6.1 Characteristic Polynomial, Equation, and Modes . . . . . . . . . . . . . . . . . . 42 6.2 Characteristic Mode Reminders . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 6.3 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 6.4 Settling Time and Dominant Poles . . . . . . . . . . . . . . . . . . . . . . . . . 44 7 Basic Feedback Configuration 46 8 Model Matching 47 8.1 ITAE Optimal Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 8.2 Quadratic Optimal Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 8.3 Summary and Caveates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8....
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notes - Notes for ECE-320 Fall 2004 by R. Throne The...

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