L2: Requirements
Lecture 2: Requirements
Lecture 2 slides Download Lecture 2 slides
Requirements are fundamental, and should always guide control design.
This lecture provides the tools for discussing and quantifying the behavior and properties of feedback systems.
Preparations
Remind, or familiarize, yourself with
- Analytic/Holomorphic functions
- Complex curve integration: Cauchy's theorem, residues, residue theorem
- Parseval's and Placherel's theorems
- Maximum modulus theorem
Here are some resources:
Complex analysis cheat sheet Links to an external site.
Sven Spannes blixtkurs i komplex integration Links to an external site.
Tank explorations
The tank experiments were made in Julia with Moberg.jl interfacing directly with the tanks. The scripts are here (warning Messy)
tank_setup.jl Download tank_setup.jl Collect static info
tank_noise.jl Download tank_noise.jl Collect noise info
empirical_tfs.jl Download empirical_tfs.jl Naive frequency domain experiments
test_plots.jl Download test_plots.jl Statics plots
tank_noise_plot.jl Download tank_noise_plot.jl Plot noisy data and compute RMS
empirical_tfs_plots.jl Download empirical_tfs_plots.jl Plot empirical transfer functions
Additional Reading
The lecture covers the material
Chapters 2, 10.3, 12.1, 12.2, 12.4, 13.1--13.3 in Feedback systems, Åström Murray Links to an external site.
The proof of the approximate inverse theorem is from KJ 1968 page 241. Note the mistake on the 9th line from the bottom: it's missing a factor two coming from the symmetric derivative
Chapter 8 in Boyd & Barratt Links to an external site.collects mathematical definitions of common (and quite a few esoteric) closed-loop performance specifications. Chapters 9 and 10 discuss robustness specifications (the role of S and T in differential sensitivities) and robustness via gain-bounds.