Fal!2001 Unstructured Uncertainty Mode/ 0.3120-4 Standard error model lumps all errors in the system into the actu- ator dynamics Could just as easily use the sensor dynamics, and for MImo systems, we typically use both 1(s)=GN(s)(1+E(s) E(s) is any stable TF that satisfies the magnitude bound E(ju)≤|Eo(ju) E G Called an unstructured modeling error and or uncertainty With a controller Gc(s), we have that GPGc= gnGc(l+e)= Lp= ln(1+e) Which is a set of possible perturbed loop transfer functions Can use Eo( ja) to accentuate the model uncertainty in certain frequency ranges(percentage errorFall 2001 16.31 20—4 Unstructured Uncertainty Model • Standard error model lumps all errors in the system into the actu￾ator dynamics. — Could just as easily use the sensor dynamics, and for MIMO systems, we typically use both. Gp(s) = GN(s)(1 + E(s)) — E(s) is any stable TF that satisfies the magnitude bound |E(jω)| ≤ |E0(jω)| ∀ω u E G - - - ? y • Called an unstructured modeling error and/or uncertainty. — With a controller Gc(s), we have that GpGc = GNGc(1 + E) ⇒ Lp = LN(1 + E) — Which is a set of possible perturbed loop transfer functions. • Can use |E0(jω)| to accentuate the model uncertainty in certain frequency ranges (percentage error)