Frequency Domain LQR

Document #:

LIGO-T1300301-v1

Document type:

T - Technical notes

Abstract:

Notes on designing optimal control using cost functions in the frequency domain. The optimization algorithm is the Linear Quadratic Regulator (LQR) method. LQR is inherently a time domain method, so the challenge for frequency domain cost functions is converting them to the time domain and applying them correctly to the LQR algorithm.

There are two examples here:
1. Estimator/observer design for suspension modal damping
2. Cavity feedback (hierarchical control) for a double pendulum

Each example has a pdf doc, matlab code example, and the latex source files for the pdf.

Files in Document:

• Frequency Domain LQR Modal Damping Estimator Example (Frequency Domain LQR Estimator.pdf, file is not accessible)

Other Files:

• Frequency Domain LQR Hierarchical Control Example - Class Project (16323_Report.pdf, file is not accessible)
• Frequency Domain LQR Hierarchical Control Example - Class Project Latex files (16323_Report_LaTeX_Files.zip, file is not accessible)
• Frequency Domain LQR Hierarchical Control Example - Class Project MATLAB files (FrequencyDomainLQR_HierarchicalControlExample_ClassPro...zip, file is not accessible)
• Frequency Domain LQR Modal Damping Estimator Example - Latex source files (FrequencyDomainLQR_EstimatorExample_LaTeX_Files.zip, file is not accessible)
• Frequency Domain LQR Modal Damping Estimator Example - Matlab Files (FrequencyDomainLQR_19March2013.zip, file is not accessible)
• pair.m (pair.m, file is not accessible)

Topics:

• Meeting
• Basic R&D

Authors:

• Brett Shapiro

Notes and Changes:

* To use the modal damping estimator matlab files, uncompress the attached folder
FrequencyDomainLQR_19March2013.zip
and open FreqDomainQuadEstimator.m.

* To use the hierarchical control matlab files from the class project, uncompress the attached folder
FrequencyDomainLQR_HierarchicalControlExample_ClassProject_MATLAB_Files.zip
and open Main.m

* some of the code calls pair.m, attached here as a separate file.

Referenced by:

• LIGO-G1400100-v1: LQR Linear Quadratic Regulator - A state space optimal control technique
• LIGO-G1500454-v1: Controls Workshop at the GWADW 2015