Fal!2001 16.3120-2 Simple example: Assume we know that the actual dynamics are GA(s +2Cwns+ but we take the nominal model to be gn= 1 Can explicitly calculate the error E(s), and it is shown in the plot Can also calculate an LTI overbound Eo(s) of the error. Since E(s) is not normally known, it is the bound eo(s that is used in our Lysis tests 10 10 E=G,G.-1 10 G N 10 10 10 10 Freq(rad/sec) Figure 2: Various TF's for the example systemFall 2001 16.31 20—2 • Simple example: Assume we know that the actual dynamics are ω2 n GA(s) = s2(s2 + 2ζωns + ω2 n) but we take the nominal model to be GN = 1/s2. • Can explicitly calculate the error E(s), and it is shown in the plot. • Can also calculate an LTI overbound E0(s) of the error. Since E(s) is not normally known, it is the bound E0(s) that is used in our analysis tests. 103 102 101 100 |G| GN E=GA/GN−1 E0 GA GA GN E E0 10−1 10−2 10−3 10−4 10−1 100 101 Freq (rad/sec) Figure 2: Various TF’s for the example system