Disk-Based Gain and Phase Margins
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
diskmarginto compute the disk-based gain and phase margins of SISO and MIMO feedback loops.
Model gain and phase uncertainty. Use the
umargincontrol design block to analyze the effect of gain and uncertainty on system performance and stability.
|Disk-based stability margins of feedback loops|
|Worst-case disk-based stability margins of uncertain feedback loops|
|Visualize disk-based stability margins|
|Visualize worst-case disk-based stability margins|
|Customize disk-based stability-margin plots|
|Convert gain and phase variation into disk-based gain variation|
|Disk-based phase variation corresponding to disk-based gain variation|
|Get disk-based margins from disk size and skew|
|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®.