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 ===Course Description===   ===Course Description=== 
  [[Image:digconlogo1.jpgright350px]]
 
   
 ===Objectives===   ===Objectives=== 
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 ! WEEK !! TOPICS !! REFERENCES   ! WEEK !! TOPICS !! REFERENCES 
     
   align ="left"  Week 1. Aug 19  +   align ="left"  Week 1. 
  align ="left"  '''Lecture 1'''. Introduction to concepts of control, feedback, feedforward, uncertainty and robustness;    align ="left"  '''Lecture 1'''. Introduction to concepts of control, feedback, feedforward, uncertainty and robustness; 
   +   align ="left"  
  '''Recitation'''. Review of SISO continuoustime signals and systems;
 +  
   +  
   align ="left"  FranklinF Ch1;  +  
     
   align ="left"  Week 2. Aug 26
 
   align ="left"  '''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 pseudoalgorithm for controller implementation;
 
   align ="left"  FranklinD 2, FranklinF 4.4
 
  
 
   align ="left"  Week 3. Sept 2
 
   align ="left"  '''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 Ztransform;
 
 
 
  '''Lecture 5'''. Solution of difference equations by Ztransform method; transfer functions; integrator approximation in transform domain; continuoustodiscrete approximations for controller synthesis by emulation; block diagram representations using delays, summers and gain
 
 
 
  '''Recitation / Seminar.''' Feedback control scheduling of crane control systems. [[Media:lumscssseminarsfall2013sept6.pdfAnnouncement]]. [[Media:oumairseminarslidesfall2013sept6.pdfSlides]]
 
   align ="left"  FranklinD Ch 3
 
  [[Media:EE561fall2013HW1.pdfHome work #1]]
 
 
 
  [[Media:EE561fall2013HW1sol.pdfHome work #1 solutions]]
 
  
 
   align ="left"  Week 4. Sept 9
 
   align ="left"  '''Lecture 6'''. Impulse response and convolution in discretetime systems; tests for linearity timeinvariance, stability, causality; basic block diagrams; canonical forms;
 
 
 
  '''Lecture 7'''. Frequency response of discretetime LTI systems; Discretetime Fourier transform; relation to Ztransform; time and frequency analysis of prototypical first order and second order discretetime systems;
 
 
 
  '''Lecture 8'''. Comparison of Ztransform and Laplace transform of sampled signals; mapping between splane and zplane; mappings induced by Euler and trapezoidal approximations; Tustin's approximation of a continuoustime first order system; distortion in frequency response due to trapezoidal approximation;
 
 
 
   align ="left"  FranklinD Ch 3; Oppenheim 5.1.1, 6.6.2; FranklinD 6.1;
 
  [[Media:EE561fall2013HW2.pdfHome work #2]]
 
 
 
  [[Media:EE561fall2013HW2sol.pdfHome work #2 solutions]]
 
  
 
   align ="left"  Week 5. Sept 16
 
   align ="left"  '''Lecture 9'''. Example on frequency response distortion(contd.); introduction to state space analysis; idea of a state; statespace model of Newtonian mechanics;
 
 
 
   align ="left"  FranklinD 6.1; FranklinF Ch 7;
 
  
 
   align ="left"  Week 6. Sept 23
 
   align ="left"  '''Lecture 10'''. Examples of statespace modeling; block diagrams and statespace 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'''.
 
  [[Media:EE561fall2013Quiz1.pdfQuiz #1]]
 
 
 
  [[Media:EE561fall2013Quiz1sol.pdfQuiz #1 solutions]]
 
   align ="left"  FranklinF Ch 7.2, 7.3;
 
  [[Media:EE561fall2013HW3.pdfHome work #3]]
 
 
 
  [[Media:EE561fall2013HW3sol.pdfHome work #3 solutions]]
 
  
 
   align ="left"  Week 7. Sept 30
 
   align ="left"  '''Lecture 12'''. Controllability (contd.); invariance of controllability condition under invertible transformations; computing dynamic response from stateequations using Laplace transform; relationship between transfer functions and statespace models for a SISO LTI system;
 
 
 
  '''Lecture 13'''. Interpretation of transfer function poles in statespace models (contd.); Interpretation of transfer function zeros in statespace models; constructing explicit transformations to obtain Modal canonical form; poles, modes and eigendecomposition of system matrix; examples;
 
   align ="left"  FranklinF Ch 7.3, 7.4;
 
  
 
   align ="left"  Week 8. Oct 7
 
   align ="left"  '''Lecture 14'''. Problem solving & review session
 
 
 
  [[Media:EE561fall2013midterm.pdfMidterm Exam]]
 
 
 
  [[Media:EE561fall2013midtermsol.pdfMidterm Exam solutions]]
 
 
 
   align ="left" 
 
  
 
   align ="left"  Week 9. Oct 14
 
   align ="left"  '''Eid/Midterm Break'''.
 
   align ="left" 
 
  
 
   align ="left"  Week 10. Oct 21
 
   align ="left"  '''Lecture 15'''. Review of canonical forms; the concept of state feedback; poleplacement; Ackermann's formula;
 
  '''Lecture 16'''. Review of pole placement; Ackermann's formula and controllability; how to add references for trajectory tracking; stateestimator design; concept of an observer; observer design; observer canonical form; observer design by Ackermann's formula; observability matrix;
 
   align ="left"  FranklinF 7.5.1, 7.5.2;
 
 
 
  [[Media:EE561fall2013HW4.pdfHome work #4]]
 
 
 
  [[Media:EE561fall2013HW4sol.pdfHome work #4 solutions]]
 
  
 
   align ="left"  Week 11. Oct 28
 
   align ="left"  '''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 continuoustime LTI statespace models; a relook at forced and natural responses; matrix exponential and its properties; Discretetime state space models; discretized matrix equivalents of continuoustime LTI models;
 
   align ="left"  FranklinF 7.7.1, 7.8; Chen 4.2;
 
  
 
   align ="left"  Week 12. Nov 4
 
   align ="left"  '''Lecture 19'''. Discretetime state space models continued; example of doubleintegrator; a relook at Zero order hold (ZOH) in statespace models and transfer functions;
 
 
 
  '''Lecture 20'''. Discretetime statespace form of Euler and Tustin's approximations; fullstate feedback control in discretetime LTI systems;
 
  pole placement; control canonical form; Ackermann's formula revisited; graphical understanding of zplane via mapping from splane contours of constant damping ratio, natural frequency;
 
 
 
  '''Lecture 21 / Recitation'''. Statespace models from difference equations; FIR and IIR filters; statespace modeling example: Laplacian dynamics in networked control systems
 
   align ="left"  FranklinD 4.3.3; 4.3.1; 4.2.3; 8.1;
 
  
 
   align ="left"  Week 13. Nov 11
 
   align ="left"  '''Lecture 22'''. Prediction estimators; observability in discretetime; observability as a dual concept to controllability; derivation of Ackermann's formula for observer design;
 
 
 
  '''Lecture 23'''. Discretetime Regulator design; combining control law and estimator; proof of Separation Principle; regulators reinterpreted as classical zdomain compensators;
 
 
 
  [[Media:EE561fall2013quiz2.pdfQuiz #2]]
 
 
 
  [[Media:EE561fall2013quiz2sol.pdfQuiz #2 solutions]]
 
 
 
   align ="left"  FranklinD 8.2.1; 8.3;
 
 
 
  [[Media:EE561fall2013HW5.pdfHome work #5]]
 
 
 
  [[Media:EE561fall2013HW5sol.pdfHome work #5 solutions]]
 
  
 
   align ="left"  Week 14. Nov 18
 
   align ="left"  '''Lecture 24'''. Adding reference to standard regulator design for trajectory tracking; Feedforward loop for zero tracking error; determination of prefilter matrices; statecommand 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.
 
 
 
   align ="left"  FranklinD 8.4;
 
 
 
  [http://math.rwinters.com/E21b/supplements/newbasis.pdf Notes on Jordan decomposition.]
 
  
 
   align ="left"  Week 15. Nov 25
 
   align ="left"  '''Lecture 26'''. Optimal control in discretetime; Lagrange multiplier method;
 
 
 
  '''Lecture 27'''. Linear Quadratic Regulator (LQR); steadystate optimal control; algebraic Ricatti equations;
 
 
 
   align ="left"  FranklinD 9.2;
 
  [[Media:EE561fall2013HW6.pdfHome work #6]]
 
 
 
  [[Media:EE561fall2013HW6sol.pdfHome work #6 solutions]]
 
  
 
   align ="left"  Week 16. Dec 2
 
   align ="left"  '''Lecture 28'''. Review Lecture
 
 
 
  [[Media:EE561fall2013Quiz3.pdfQuiz #3]]
 
 
 
  '''Project Presentations'''.
 
 
 
   align ="left" 
 
  
 
 }   } 