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. Usediskmargin
to 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.
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 |
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®.