Loop-Shaping Synthesis

Shape open-loop frequency response of MIMO feedback control system

In loop-shaping controller synthesis, you specify the shape of the open-loop response you want, and use a loop-shaping function to compute a controller that approximates that shape.

Use ncfsyn for a first cut design that provides some stability margin. For more control of the shapes of system responses, you can instead perform mixed-sensitivity loop shaping with mixsyn. Mixed-sensitivity loop shaping combines performance and stability robustness specifications into one cost function that penalizes both sensitivity and complementary sensitivity.

Functions

ncfsynLoop shaping design using Glover-McFarlane method
mixsynMixed-sensitivity H∞ synthesis method for robust control loop-shaping design
loopsynH∞ optimal controller synthesis for LTI plant
makeweightWeighting function with monotonic gain profile
mkfilterGenerate Bessel, Butterworth, Chebyshev, or RC filter
augwPlant augmentation for weighted mixed-sensitivity H∞ and H2 loop-shaping design

Topics

Tradeoff Between Performance and Robustness

Plant model uncertainty can be a fundamental limiting factor in determining what can be achieved with feedback.

Typical Loop Shapes, S and T Design

To quantify the multivariable stability margins and performance of a system, use the singular values of the closed-loop transfer functions of the system.

Loop-Shaping Controller Design

In loop-shaping controller synthesis, you specify the shape of the open-loop response you want, and use loopsyn to compute a controller that approximates that shape.

Loop-Shaping Control Design of Aircraft Model

This example shows how to use loopsyn to address robustness and performance tradeoffs.

Fine-Tuning the Target Loop Shape to Meet Design Goals

When the initial results from loopsyn are not satisfactory, refine the target loop shape.

Mixed-Sensitivity Loop Shaping

Mixed-sensitivity loop shaping combines robustness specifications for both performance and stability into one cost function that penalizes both sensitivity and complementary sensitivity.

Featured Examples