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Course Description:
Learn methods of designing automatic control systems that use digital computers to implement control laws: utilize a parallel treatment of continuous and discrete systems to understand the similarities and differences; develop methods to model and predict the behavior of digital systems. Topics will include real-time control of dynamic systems using digital computers; Z-transform methods; discrete equivalents to continuous systems; sampled data systems; root locus and frequency response methods; state-space design techniques; sample rate selection; and problems with discretization and numerical round-off.
Faculty/Manager:
Richard Longman
Contact Information:
Richard Longman
email: rwl4@columbia.eduCredits for Course: 3 Viewing Schedule: 1 lecture per week Prerequisites: An undergraduate course in signals and systems or classical control systems.
Applicable Degree Program: MS program in Mechanical Engineering
MS program in Electrical Engineering
Most courses 4000-level and above can be credited to all degree programs. All courses are subject to advisor approval.Required Text(s): Kuo, Benjamin C. "Digital Control Systems." Saunders College Publishing, 2nd edition. ISBN 0-03-012884-6
Homework: 11 assignments Midterm Exam: 150 minutes, closed book. Final Exam: 3 hours, closed book. Grading: 10% Homework
45% Midterm exam
45% Final exam Notes: Course Outline
1
Introduction to feedback and digital feedback control (Chapter 1)
2
Digital controllers as difference equations, solution of difference equations (Chapter 2, pp. 13-28)
3
Forced response in digital equations
4
Laplace transforms, solution of difference equations using z transforms (Chapter 3.1, 3.2, 3.4; Chapter4, pp. 124-129)
5
Block diagram manipulation, finding system response using z transfer functions (Chapter 3.5 - 3.7)
6
Converting continuous elements following zero order holds to digital form, behavior between samples, closed loop difference equation (chapter 4.3 - 4.4)
7
Predicting closed loop response of digital control systems with digital controllers and continuous plants
8
Midterm
9
Stability of digital control systems (chapter 6.7.1, 6.7.2)
10
State space models of digital control systems. Solutions (Chapter 3.3, 5.1 - 5.9, 5.11, 5.12)
11
State transition matrix. Response between samples. Skip step and multiple sample rates (Chapter 5.17, 5.18)
12
Unsynchronized sampling. Identification
13
Frequency Response Methods
FINAL EXAM
* The information contained in this syllabus is subject to change at any time.