Linear Control Systems: With solved problems and MATLAB examples

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Springer Science & Business Media, Dec 31, 2001 - Technology & Engineering - 381 pages
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Anyone seeking a gentle introduction to the methods of modern control theory and engineering, written at the level of a first-year graduate course, should consider this book seriously. It contains:
  • A generous historical overview of automatic control, from Ancient Greece to the 1970s, when this discipline matured into an essential field for electrical, mechanical, aerospace, chemical, and biomedical engineers, as well as mathematicians, and more recently, computer scientists;
  • A balanced presentation of the relevant theory: the main state-space methods for description, analysis, and design of linear control systems are derived, without overwhelming theoretical arguments;
  • Over 250 solved and exercise problems for both continuous- and discrete-time systems, often including MATLAB simulations; and
  • Appendixes on MATLAB, advanced matrix theory, and the history of mathematical tools such as differential calculus, transform methods, and linear algebra.

Another noteworthy feature is the frequent use of an inverted pendulum on a cart to illustrate the most important concepts of automatic control, such as:
  • Linearization and discretization;
  • Stability, controllability, and observability;
  • State feedback, controller design, and optimal control; and
  • Observer design, reduced order observers, and Kalman filtering.

Most of the problems are given with solutions or MATLAB simulations. Whether the book is used as a textbook or as a self-study guide, the knowledge gained from it will be an excellent platform for students and practising engineers to explore further the recent developments and applications of control theory.
 

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Contents

Historical overview of automatic control
3
11 Automatic control before the 1930s
5
12 Classical period of automatic control
12
13 Beginnings of modern control theory
18
Modern control theory
23
21 Statespace representation
25
22 System properties
34
23 State feedback and optimal control
62
46 Stability
239
47 Controllability and observability
244
48 Canonical realizations
251
49 State feedback
255
410 Optimal control
259
411 State observers
263
412 Kalman filter
265
413 Reducedorder observers
272

24 State observers and estimators
68
Part II Solved problems
71
Continuous linear systems
73
31 Simple differential equations
75
32 Matrix theory
83
33 Systems of linear differential equations
95
34 Inputoutput representation
98
35 Statespace representation
113
36 Stability
128
37 Controllability and observability
134
38 Canonical realizations
152
39 State feedback
166
310 Optimal control
178
311 State observers
186
312 KalmanBucy filter
194
313 Reducedorder observers
199
Discrete linear systems
207
41 Simple difference equations
209
42 More matrix theory
217
43 Systems of linear difference equations
220
44 Inputoutput representation
222
45 Statespace representation
235
Exercise problems
273
Part III Appendixes
287
A quick introduction to MATLAB
289
A2 Basic matrix operations
290
A3 Plotting graphs
294
A4 Data analysis
295
A5 Data management and IO operations
296
Mathematical preliminaries
305
B2 Differential and difference equations
306
B3 Laplace and ztransforms
312
B4 Matrices and determinants
318
Results from advanced matrix theory
325
C2 Diagonal and Jordan forms
330
C3 Similarity of matrices
334
C4 Symmetric and Hermitian matrices
340
C5 Quadratic forms and definiteness
345
C6 Some special matrices
353
C7 Rank pseudoinverses SVD and norms
355
C8 Problems
365
Bibliography
371
Index
375
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