ME 6401: Linear Control Systems

Offered Every Fall


Credit Hours: 3-0-3
Prerequisites: 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.
Textbooks: 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, Kok-Meng Lee, Nader Sadegh, William Singhose
Goals: To be familiar with the theory and applications of linear systems, state space (controllability, observability, realization), stability, feedback control, observers, LQR, LQG, and Kalman filter.
Topics:
  • 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.
  • Grading Scheme (%):

    Homework

    15

    Projects

    15 

    Exams x2

    20 (each)

    Final

    30