EE-561
From CYPHYNETS
EE-561: Digital Control Systems |
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Instructors
Dr. Abubakr Muhammad, Assistant Professor of Electrical Engineering
Email: abubakr [at] lums.edu.pk
Office: Room 9-351A, 3rd Floor, SSE Bldg
TA: Usaman Bin Sikandar, Mudassar Ejaz
Course Details
Year: 2013-14
Semester: Fall
Category: Graduate
Credits: 3
Elective course for electrical engineering majors
Course Website: http://cyphynets.lums.edu.pk/index.php/EE-561
Course Description
Design and digital implementation of multiple-input, multiple-output (MIMO) linear feedback control systems for specified dynamic response; z-transform and sampling; exposure to embedded control systems; state-space based models; introduction to advanced concepts of multi-variable control. Design and implementation project on real-time digital control.
Objectives
- To build on studentsâ€™ undergraduate exposure to feedback control and teach advanced design techniques
- To impart knowledge of practical issues related to the implementation of feedback controllers using digital processors.
- To introduce advanced techniques of linear multivariable control system design.
- To expose students to aspects of embedded control systems as practiced in robotics, automotive, aerospace, process industries.
- To prepare students for advanced courses in mathematical control theory and practical control engineering.
Learning Outcomes
- Identify state, measurement and control in a given problem.
- Design controllers for linear models of systems using MATLAB and SIMULINK.
- Select and program real-time digital controllers on platforms similar to PC, microcontroller, DSP.
- Predict performance for complex multivariable control tasks.
Pre-requisites
EE-361. Feedback Control Systems
Text book
The course will be taught from the following textbooks.
- FranklinF. Feedback control of dynamic systems by Franklin, Powell and Emami-Naeni (5th edition), Pearson, 2006.
- FranklinD. Digital control of dynamic systems by Franklin, Powell and Workman (3rd edition), Addison Wesley, 2000.
Other important references include
- Astrom. Computer controlled systems by Karl Astrom and Bjorn Witternmark, Prentice Hall, 1997.
- Oppenheim. Signals and Systems by Oppenheim, Wilsky, Nawab (2nd edition), Pearson, 1997.
- Chen. Linear Systems Theory and Design by C.T. Chen. Holt, Rinehart & Winston, 1999.
Grading Scheme
Homeworks+Quiz : 15%
Project: 20%
Midterm: 30%
Final : 35%
Policies and Guidelines
- Quizzes will be announced. There will be no makeup quiz.
- Homework will be due at the beginning of the class on the due date. Late homework will not be accepted.
- You are allowed to collaborate on homework. However, copying solutions is absolutely not permitted. Offenders will be reported for disciplinary action as per university rules.
- Any appeals on grading of homeworks, quiz or midterm scores must be resolved within one week of the return of graded material.
- Attendance is in lectures and tutorials strongly recommended but not mandatory. However, you are responsible for catching the announcements made in the class.
- Many of the homeworks will include MATLAB based computer exercise. Some proficiency in programming numerical algorithms is essential for both the homework and project.
Course Delivery Method
Lectures. Mon, Wed: 11:00am-12:15pm. 10-302. SSE Bldg
Recitations. Fri. 9:00am-9:50am. SC-4. Student Center Bldg.
Schedule
WEEK | TOPICS | REFERENCES |
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Week 1. Aug 19 | Lecture 1. Introduction to concepts of control, feedback, feedforward, uncertainty and robustness;
Recitation. Review of SISO continuous-time signals and systems; | FranklinF Ch1; |
Week 2. Aug 26 | Lecture 2. Review of SISO feedback control; rational LTI systems; geometry of 2nd order poles; error expression in closed loop and open loop systems; sensitivity function; control design objectives;
Lecture 3. Summary of control design; compensators and PID controllers; introduction to sampled data systems; Naive approaches towards emulation; Euler's forward approximation; a pseudo-algorithm for controller implementation; | FranklinD 2, FranklinF 4.4 |
Week 3. Sept 2 | Lecture 4. Digital control by emulation; Euler's forward and backward approximation; trapezoidal rule; approximation of a continuous time compensator; zero order hold (ZOH) and delays; general difference equations; introduction to the Z-transform;
Lecture 5. Solution of difference equations by Z-transform method; transfer functions; integrator approximation in transform domain; continuous-to-discrete approximations for controller synthesis by emulation; block diagram representations using delays, summers and gain Recitation / Seminar. Feedback control scheduling of crane control systems. Announcement. Slides | FranklinD Ch 3 |
Week 4. Sept 9 | Lecture 6. Impulse response and convolution in discrete-time systems; tests for linearity time-invariance, stability, causality; basic block diagrams; canonical forms;
Lecture 7. Frequency response of discrete-time LTI systems; Discrete-time Fourier transform; relation to Z-transform; time and frequency analysis of prototypical first order and second order discrete-time systems; Lecture 8. Comparison of Z-transform and Laplace transform of sampled signals; mapping between s-plane and z-plane; mappings induced by Euler and trapezoidal approximations; Tustin's approximation of a continuous-time first order system; distortion in frequency response due to trapezoidal approximation; | FranklinD Ch 3; Oppenheim 5.1.1, 6.6.2; FranklinD 6.1; |
Week 5. Sept 16 | Lecture 9. Example on frequency response distortion(contd.); introduction to state space analysis; idea of a state; state-space model of Newtonian mechanics; | FranklinD 6.1; FranklinF Ch 7; |
Week 6. Sept 23 | Lecture 10. Examples of state-space modeling; block diagrams and state-space models;
Lecture 11. Control canonical form and modal canonical form for SISO systems; how to find explicit transformations to setup control canonical form; the idea of a controllability matrix; Recitation. Quiz #1 | FranklinF Ch 7.2, 7.3; |
Week 7. Sept 30 | Lecture 12. Controllability (contd.); invariance of controllability condition under invertible transformations; computing dynamic response from state-equations using Laplace transform; relationship between transfer functions and state-space models for a SISO LTI system;
Lecture 13. Interpretation of transfer function poles in state-space models (contd.); Interpretation of transfer function zeros in state-space models; constructing explicit transformations to obtain Modal canonical form; poles, modes and eigen-decomposition of system matrix; examples; | FranklinF Ch 7.3, 7.4; |
Week 8. Oct 7 | Lecture 14. Problem solving & review session | |
Week 9. Oct 14 | Eid/Midterm Break. | |
Week 10. Oct 21 | Lecture 15. Review of canonical forms; the concept of state feedback; pole-placement; Ackermann's formula;
Lecture 16. Review of pole placement; Ackermann's formula and controllability; how to add references for trajectory tracking; state-estimator design; concept of an observer; observer design; observer canonical form; observer design by Ackermann's formula; observability matrix; | FranklinF 7.5.1, 7.5.2; |
Week 11. Oct 28 | Lecture 17. Review of combined state feedback and observor design; definitions of controllability and observability; physical interpretation of observability and controllability; examples of uncontrollable and unobservable systems from circuit theory and mechanics;
Lecture 18. Solutions of continuous-time LTI state-space models; a re-look at forced and natural responses; matrix exponential and its properties; Discrete-time state space models; discretized matrix equivalents of continuous-time LTI models; | FranklinF 7.7.1, 7.8; Chen 4.2; |
Week 12. Nov 4 | Lecture 19. Discrete-time state space models continued; example of double-integrator; a re-look at Zero order hold (ZOH) in state-space models and transfer functions;
Lecture 20. Discrete-time state-space form of Euler and Tustin's approximations; full-state feedback control in discrete-time LTI systems; pole placement; control canonical form; Ackermann's formula re-visited; graphical understanding of z-plane via mapping from s-plane contours of constant damping ratio, natural frequency; Lecture 21 / Recitation. State-space models from difference equations; FIR and IIR filters; state-space modeling example: Laplacian dynamics in networked control systems | FranklinD 4.3.3; 4.3.1; 4.2.3; 8.1; |
Week 13. Nov 11 | Lecture 22. Prediction estimators; observability in discrete-time; observability as a dual concept to controllability; derivation of Ackermann's formula for observer design;
Lecture 23. Discrete-time Regulator design; combining control law and estimator; proof of Separation Principle; regulators reinterpreted as classical z-domain compensators; | FranklinD 8.2.1; 8.3; |
Week 14. Nov 18 | Lecture 24. Adding reference to standard regulator design for trajectory tracking; Feedforward loop for zero tracking error; determination of pre-filter matrices; state-command structure; output command structure;
Lecture 25. Integral control; state augmentation; disturbance estimation; observability and disturbance estimation; Recitation. Jordan decomposition method for handling repeated and complex poles. | FranklinD 8.4; |
Week 15. Nov 25 | Lecture 26. Optimal control in discrete-time; Lagrange multiplier method;
Lecture 27. Linear Quadratic Regulator (LQR); steady-state optimal control; algebraic Ricatti equations; | FranklinD 9.2; |
Week 16. Dec 2 | Lecture 28. Review Lecture
Project Presentations. |