Fall 2001 6.3119-3 Typically pick simple forms for weighting functions(first or second order), and then cascade them as necessary. Basic one W(Ss)=s/+uB +Wba M A Freq(rad/sec) Figure 1: Example of a standard performance weighting filter. Typically have A≤1,M>1,and|1/W≈1atuB Thus we can test whether Ws(jw)(jw)<1, Vw by Forming a state space model of the combined system Ws(s)S(s) Use the bounded gain theorem with y=1 Typically use a bisection section of y to find Ws(ja)S(ja)lmaxFall 2001 16.31 19–3 • Typically pick simple forms for weighting functions (first or second order), and then cascade them as necessary. Basic one: Ws(s) = s/M + ωB s + ωBA 10−2 10−1 100 101 102 10−2 10−1 100 101 Freq (rad/sec) |1/W s | A ωb M Figure 1: Example of a standard performance weighting filter. Typically have A 1, M > 1 , and |1/Ws| ≈ 1at ωB • Thus we can test whether |Ws(jω)S(jω)| < 1, ∀ω by: – Forming a state space model of the combined system Ws(s)S(s) – Use the bounded gain theorem with γ = 1 – Typically use a bisection section of γ to find |Ws(jω)S(jω)|max