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Disk-Based Gain and Phase Margins

Stability margins of feedback loops using disk-based analysis

Disk margins quantify the stability of a closed-loop system against gain or phase variations in the open-loop response. In disk-based margin calculations, the software models such variations as disk-shaped multiplicative uncertainty on the open-loop transfer function. The disk margin measures how much uncertainty the loop can tolerate before going unstable. That uncertainty amount corresponds to minimum gain and phase margins. These disk-based margins take into account all frequencies and loop interactions. Therefore, disk-based margin analysis provides a stronger guarantee of stability than the classical gain and phase margins.

Robust Control Toolbox™ provides tools to:

  • Analyze system stability against gain and phase variations. Use diskmargin to compute the disk-based gain and phase margins of SISO and MIMO feedback loops.

  • Model gain and phase uncertainty. Use the umargin control design block to analyze the effect of gain and uncertainty on system performance and stability.

Functions

diskmarginDisk-based stability margins of feedback loops
wcdiskmarginWorst-case disk-based stability margins of uncertain feedback loops
diskmarginplotVisualize disk-based stability margins (Since R2020a)
wcdiskmarginplotVisualize worst-case disk-based stability margins (Since R2020a)
diskmarginoptionsCustomize disk-based stability-margin plots (Since R2020a)
getDGMConvert gain and phase variation into disk-based gain variation (Since R2020a)
getDPMDisk-based phase variation corresponding to disk-based gain variation (Since R2020a)
dm2gmGet disk-based margins from disk size and skew (Since R2020a)
gm2dmConvert disk-based gain margin to disk size and skew (Since R2020a)

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