Fal!2001 16.3120-1 Model Uncertain Prior analysis assumed a perfect model. What if the model is in correct= actual system dynamics GA(s)are in one of the sets Multiplicative model G,(s=GN(s(1+E(s)) Additive model Gp(S)=GN(S)+E(s) where 1. GN(s)is the nominal dynamics(known 2. E(s) is the modeling error- not known directly, but bound Eo(s) known(assumed stable) where E(ju)≤|Eo(ju) If Eo(jw) small, our confidence in the model is high = nominal model is a good representation of the actual dynamics If Eo(jw)large, our confidence in the model is low = nominal mode is not a good representation of the actual dynamics Figure 1: Typical system TF with multiplicative uncertaintyFall 2001 16.31 20—1 Model Uncertainty • Prior analysis assumed a perfect model. What if the model is in￾correct ⇒ actual system dynamics GA(s) are in one of the sets — Multiplicative model Gp(s) = GN(s)(1 + E(s)) — Additive model Gp(s) = GN(s) + E(s) where 1. GN(s) is the nominal dynamics (known) 2. E(s) is the modeling error — not known directly, but bound E0(s) known (assumed stable) where |E(jω)| ≤ |E0(jω)| ∀ω • If E0(jω) small, our confidence in the model is high ⇒ nominal model is a good representation of the actual dynamics • If E0(jω) large, our confidence in the model is low ⇒ nominal model is not a good representation of the actual dynamics G 100 N 10−1 10−2 10−3 10−4 10−5 10−6 10−1 100 101 102 multiplicative uncertainty Freq (rad/sec) |G| Figure 1: Typical system TF with multiplicative uncertainty