fRP – IQClab

The function [bound,muinfo,RPmargin]=fRP(M,om) computes the robust performance margins for the uncertain plant $M$ and for the frequency grid $\omega=[\omega_1,\ldots,\omega_N]$ . It returns the $\mu$ -ssv upper- and lower-bounds by means of the mussv command from the Robust Control Toolbox. The outputs are:

bound: A structure with the lower- and upper-bounds for each frequency $\omega\in[\omega_1,\ldots,\omega_N]$ .
muinfo: The $\mu$ -information obtained during the computations.
RPmargin: The robust performance margins.

If specifying the 3rd inputs as $fRP(M,om,U_\mathrm{sc})</em>$ , one can rescale the analysis as follows. Given the uncertain plant

$M=\left(\begin{array}{cc}M_{11}&M_{12}\\ M_{21}&M_{22}\end{array}\right)$

the uncertainty scaling factor, $<em>U_\mathrm{sc}</em>$ , scales the size of the uncertainty such that

$\mu_\mathbf{\Delta}(M_{11}(i\omega))\leq\dfrac{\gamma}{U_\mathrm{sc}}$ , $\mu_\mathbf{\Delta}(M(i\omega))\leq\gamma$ for all $\Delta\in\mathbf{\Delta}$ with $\|\Delta\|_\infty<\dfrac{U_\mathrm{sc}}{\gamma}$ .

If not specified, $U_\mathrm{sc}$ is set to its default value $U_\mathrm{sc}=1$ .

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