37 lines
1.9 KiB
Markdown
37 lines
1.9 KiB
Markdown
# Table of Contents for 3 Notes
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## Files
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- [[Feedback Control Theory.md]]
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- [[How is robust control validation done?.md]]
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- [[Robust Control.md]]
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- [[What is gain scheduling?.md]]
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## Summary
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This is a comprehensive set of notes on Feedback Control Theory, covering various topics such as sensitivity and complementary sensitivity functions, robustness and stability, and uncertainty and perturbation. Here's a brief summary of the key points:
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**Sensitivity and Complementary Sensitivity Functions**
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* The sensitivity function S is defined as 1/(1+L), where L is the loop gain.
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* The complementary sensitivity function T is defined as L/(1+L).
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* These functions are used to analyze the performance of a feedback system.
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**Robustness and Stability**
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* A controller C is robust to a set of plants $\mathcal{P}$ with respect to a characteristic if this characteristic holds for every plant in $\mathcal{P}$.
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* A system is robustly stable if it is internally stable for every plant in the set $\mathcal{P}$: $|| \Delta W_2 T ||_\infty < 1$.
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* Nominal performance is achieved simultaneously when $|| \text{max} (|W_1S|, |W_2 T|)||_\infty < 1$.
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**Uncertainty and Perturbation**
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* The multiplicative disk perturbation is defined as $\tilde P = (1+\Delta W_2)P$, where P is a nominal plant transfer function.
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* $||\Delta||_\infty <1$ ensures that the system remains stable for all plants in the set $\mathcal{P}$.
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**Key Concepts**
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* Robustness: the distance between L and -1 for all frequencies, which determines how much room there is for plant perturbation before becoming unstable.
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* Uncertainty profile: $|W_2(j\omega)|$ describes a disk in the complex plane that indicates the maximum amount of uncertainty allowed.
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Overall, these notes provide a solid foundation for understanding the concepts and techniques used in feedback control theory, particularly in the context of robustness and stability analysis.
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