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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. Thedisk marginmeasures 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. Usediskmarginto compute the disk-based gain and phase margins of SISO and MIMO feedback loops.

  • Model gain and phase uncertainty. Use theumargin控制设计块分析the effect of gain and uncertainty on system performance and stability.

Functions

diskmargin Disk-based stability margins of feedback loops
wcdiskmargin Worst-case disk-based stability margins of uncertain feedback loops
diskmarginplot Visualize disk-based stability margins
wcdiskmarginplot Visualize worst-case disk-based stability margins
diskmarginoptions Customize disk-based stability-margin plots
getDGM Convert gain and phase variation into disk-based gain variation
getDPM Disk-based phase variation corresponding to disk-based gain variation
dm2gm Get disk-based margins from disk size and skew
gm2dm Convert disk-based gain margin to disk size and skew

Topics

Stability Analysis Using Disk Margins

Disk margins provide a stronger guarantee of stability than classical gain and phase margins.

Disk Margin and Smallest Destabilizing Perturbation

The smallest destabilizing perturbation associated with the disk margin of a feedback loop is the smallest gain and phase variation that results in closed-loop instability.

Stability Margins of a Simulink Model

Compute classical and disk-based gain and phase margins of a control loop modeled in Simulink®.

Featured Examples