Linear Systems and Control: A First Course (Course notes for AAE 564) Martin Corless School of Aeronautics & Astronautics Purdue University West Lafayette, Indiana
[email protected] August 25, 2008 Contents 1 Introduction 1 1.1 Ingredients..................................... 4 1.2 Somenotation................................... 4 1.3 MATLAB ..................................... 4 2 State space representation of dynamical systems 5 2.1 Linearexamples.................................. 5 2.1.1 Afirstexample .............................. 5 2.1.2 Theunattachedmass........................... 6 2.1.3 Spring-mass-damper ........................... 6 2.1.4 Asimplestructure ............................ 7 2.2 Nonlinearexamples............................... 8 2.2.1 Afirstnonlinearsystem ......................... 8 2.2.2 Planarpendulum ............................. 9 2.2.3 Attitudedynamicsofarigidbody. .. 9 2.2.4 Bodyincentralforcemotion. 10 2.2.5 Ballisticsindrag ............................. 11 2.2.6 Doublependulumoncart . .. .. 12 2.2.7 Two-linkroboticmanipulator . .. 13 2.3 Discrete-timeexamples . ... 14 2.3.1 Thediscreteunattachedmass . 14 2.4 Generalrepresentation . ... 15 2.4.1 Continuous-time ............................. 15 2.4.2 Discrete-time ............................... 18 2.4.3 Exercises.................................. 20 2.5 Vectors....................................... 22 2.5.1 Vector spaces and IRn .......................... 22 2.5.2 IR2 andpictures.............................. 24 2.5.3 Derivatives ...............................