Loop Shaping - guidosassaroli/controlbasics GitHub Wiki

This section formalizes the notion of Loop Shaping for linear control system design. The Loop Shaping approach is inherently two-fold:

1. Shape the open-loop transfer function $P(s)C(s)$ to meet performance and robustness specifications.
2. Compute the compensator $C(s)$ using the nominal product $P(s)C(s)$ and the nominal plant $P(s)$.

This approach applies to single-input, single-output (SISO) systems, but the extension to multi-variable (MIMO) control is also feasible. In MIMO systems, absolute values of transfer functions are replaced with the maximum singular values of transfer matrices.

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Example

The Python example LoopShaping.ipynb demonstrates the modeling and analysis of a basic control system using Loop Shaping. It defines a second-order plant, which represents a stable, overdamped system often seen in mechanical or electrical applications.