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.


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

Featured Examples