Lecture notes and recordings for ECE5530: Multivariable Control Systems II

To play any of the lecture recording files (below), QuickTime is required. This software may be downloaded (free) from http://www.apple.com/quicktime/download/. Each of the recordings is on the order of 20 to 30 minutes long, and between about 40 and 50 Mb in size.

If you are not registered at UCCS to take this course for credit, and if you wish to do so, please contact Dr. Gregory Plett using the information provided in the Section 0 notes.

This course can be taken at the graduate level as part of the Masters of Science in Electrical Engineering option in Battery Controls. See the IDEATE web site for more details.

0. Course introduction and syllabus. [PDF]
• 0: Course introduction and syllabus.
1. Introduction and review of multivariable control. [PDF]
• 1.1: State-space dynamic systems (continuous-time).
• 1.2: State-space dynamic systems (discrete-time); stability.
• 1.3: Observability and controllability.
• 1.4: Controller design.
• 1.5: Closed-loop estimator design.
• 1.6: Vector and signal norms; MIMO frequency response.
• 1.7: System norms.
2. Vector random processes. [PDF]
• 2.1: Scalar random variables.
• 2.2: Vector random variables.
• 2.3: Uncorrelated versus independent.
• 2.4: Functions of random variables.
• 2.5: Conditioning.
• 2.6: Vector random (stochastic) processes.
• 2.7: Discrete-time systems with random inputs.
• 2.8: Continuous-time systems with random inputs.
• 2.9: Relating Ξ_w to S_w precisely: A trick.
• 2.10: Shaping filters.
3. Linear Quadratic Regulator. [PDF]
• 3.1: Cost functions; deterministic LQR problem.
• 3.2: Optimization via calculus of variations.
• 3.3: LQR problem solved via calculus of variations.
• 3.4: Solving the Riccati equation.
• 3.5: Symmetric root locus.
• 3.6: Stochastic LQR.
• 3.7: LQR solution via dynamic programming.
• 3.8: Infinite-horizon discrete-time LQR.
4. Least-Squares Estimation. [PDF]
• 4.1: Deterministic least squares.
• 4.2: Stochastic least squares.
• 4.3: Metrics for our estimates.
• 4.4: Recursive estimation.
• 4.5: Example: Equation-error system identification.
5. Linear Quadratic Estimator. [PDF]
• 5.1: Setting up the optimal state estimator?
• 5.2: Deriving the optimal state estimator?
• 5.3: Kalman filter loop.
• 5.4: Continuous-time filters.
• 5.5: Steady-state Kalman filters.
• 5.6: Frequency-domain interpretation.
• 5.7: Symmetric root locus.
• 5.8: Relationship between LQE and LQR.
6. Linear Quadratic Gaussian. [PDF]
• 6.1: Deriving LQG via separation principle.
• 6.2: Satellite tracking example.
• 6.3: Steady-state LQG control and the compensator.
• 6.4: Reference tracking.
• 6.5: Designing for disturbance rejection.
7. Introduction to robust control. [PDF]
• 7.1: Review of SISO Nyquist stability.
• 7.2: Robustness of LQR.
• 7.3: Robustness of LQG; Loop-transfer recovery.
• 7.4: Modeling uncertainty.
• 7.5: Four classic problems.
• 7.6: Robust stability [analysis; unstructured].
• 7.7: Robust stability [analysis; structured].
• 7.8: Performance robustness [analysis].
8. H_∞ full-information control and estimation. [PDF]
• 8.1: Differential games.
• 8.2: Full-information control.
• 8.3: The Hamiltonian equation.
• 8.4: Riccati equation to find state feedback.
• 8.5: H_∞ estimation.
9. H_∞ output-feedback controller. [PDF]
• 9.1: Setting up the problem.
• 9.2: H_∞ output-feedback control as an estimation problem.
• 9.3: Finite-time and steady-state control.
• 9.4: μ synthesis.
• 9.5: Fitting a transfer function to D-scales and inverse D-scales.
• 9.6: Controller order reduction.