Control Parameterization and Loop Shaping

This course teaches two transformative concepts and tools in designing feedback controllers for linear systems: Youla-Kucera (YK) parameterization and loop shaping. The first topic, YK parameterization, provides a powerful formula that describes all possible stabilizing feedback controllers for any given plant. The second topic, loop shaping, gives a graphical control synthesis broadly used in industrial servo control. Along with these two core topics, this course will also offer students with new opportunities to understand the principles of feedback controls, limits of performance, digital filter design, and approximation theory.

Prerequisites

Undergraduate Course in Linear Systems and Classical Control

Textbook

Notes will be distributed.

References

• DFT08: Feedback Control Theory by Doyle, Francis, and Tannenbaum, 2008. NY: Dover Publications.

• Gene F. Franklin, J. David Powell, and Michael Workman. Digital Control of Dynamic Systems, 3rd Edition. Ellis-Kagle Press.
• Oppenheim, Alan V., and Ronald W. Schafer. 2009. Discrete-Time Signal Processing. Prentice Hall.

Course agenda

• Week 1: closed-loop stability
  • Reading: DFT08 Chapter 3.1, 3.2
• Week 2: Discretization
  • discretization and digital control
  • ZOH
  • HW
• Week 3: principles of feedback design
• Week 4: linearization
  • Lecture: linearization notes, slides
  • Presentation template: modeling, simulation, and analysis of practical systems
• Week 5 and week 6: all-stabilizing control parameterization
  • Reading: Chapter 5 DFT08
  • HW 2
• Week 7 and week 8: pseudo YK parameterization and Q design
  • lecture:
    • intrinsic signal models
    • X. Chen, T. Jiang, M. Tomizuka (2015). Pseudo Youla-Kucera Parameterization with Control of the Waterbed Effect for Local Loop Shaping, Automatica 62, 177-183.
    • X. Chen, M. Tomizuka (2015). Overview and New Results in Disturbance Observer based Adaptive Vibration Rejection with Application to Advanced Manufacturing, International Journal of Adaptive Control and Signal Processing, 29, 1459-1474.
  • Reading: - X. Chen, M. Tomizuka (2014). New Repetitive Control with Improved Steady-State Performance and Accelerated Transient, IEEE Transactions on Control Systems Technology, 22(2), 664-675.
  • HW 3
• Week 9: model inversion
• Week 10: project
• Exam week: project presentation