Advanced System Dynamics and Control (2.151):

This lecture shows how to use state space methods for physical system modeling, analysis, and control. The key questions are centered around system stability (will the system stay where I put it?), controllability (can I affect all of its relevant behavior?), and observability (can I monitor all of its relevant behavior?).

Lecture content

• State-determined systems, linearization.
• Energy-based physical system modeling, port concept.
• Time-domain response, state transition matrix.
• Multiport energy storage, electro-magnetic systems.
• Similarity transformations.
• Modal analysis, eigenstructure.
• Simple thermo-fluid systems.
• Stability, controllability, observability.
• Laplace domain, transfer functions.
• Frequency response functions.
• Linear full state feedback, canonical forms.
• Pole-placement, eigenstructure assignment.
• Optimal control.
• LQ (Linear-Quadratic) regulator design.
• Luenberger observer.
• Random variables.
• Linear stochastic processes.
• Noise propagation in linear systems.
• Stochastic observer (Kalman filter).
• LQG (Linear-Quadratic-Gaussian) design.
• Robust system design, loop transfer recovery.
• Delay and prediction.

Acknowledgements

Thanks to Prof. Neville Hogan, for creating this great lecture. Thanks to all the students for the amazing recitation sessions and interesting discussions during my office hours!

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