ME 6401: Linear Control Systems
Offered Every Fall

Credit Hours: 3-0-3
Prerequisite: ME 3015 or equivalent, or with the consent of the instructor
Catalog Description: Theory and applications of linear systems, state space, stability, feedback controls, observers, LQR, LQG, Kalman Filters.
Textbook: Chi-Tsong Chen, Linear System Theory and Design, 3rd Edition, Oxford University Press, 1998.
Ferenc Sidarovszky and Terry Bahill, Linear System Theory, Second Edition, CRC Press, 1999.
Instructors: Wayne Book, Ye-Hwa Chen (Fall 2003, Fall 2004), Kok-Meng Lee, Nader Sadegh (Fall 2003), William Singhose (Fall 2004).

Goals:

Evaluation procedures:

Homework:
15%
Project:
15%
Two tests:
20% (each)
Final:
30%

Mode of instruction:

Lectures 100%

Topical Outline:

  • State space representations.
  • Linearization.
  • State equation implementation.
  • State equation solution.
     
  • Transfer matrix properties.
  • Linear time-invariant system.
  • Linear periodic systems.
     
  • Internal stability.
  • Lyapunov stability criteria.
  • Additional stability criteria.
     
  • Controllability.
  • Observability
     
  • Realizability.
  • Transfer function realizability.
     
  • Minimal realization.
  • Time-varying realizations.
  • Time-invariant realizations.
     
  • Input-output stability.
  • Bounded-input bounded-output stability.
  • Relation to exponential stability.
     
  • Controller observer form.
  • Observer form.
     
  • Linear feedback.
  • Effect of feedback.
  • Feedback stabilization.
  • Eigenvalue assignment.
  • Noninterconnecting control.
     
  • State observation.
  • Observers.
  • Output feedback stabilization.
     
  • Reduced dimension observers.
  • Servomechanism problem.
     
  • Linear quadratic regulator (LQR).
  • Suboptimal design.
     
  • Linear quadratic Gaussian (LQG) design.
  • The separation principle.
  • LQG/Loop-Transfer Recovery.
     
  • Stochastic process.
  • Kalman optimal filter derivation.
  • Kalman optimal filter formulation.
     
  • Implementation of the Kalman filter.
  • Kalman filter with colored noise.
  • Suboptimal steady state Kalman filter.
     
    • _______________________
    Revised June 2004