Lista Modelagem

Curso de Engenharia Elétrica ProfaDrªSelene Dias Ricardo de Andrade Disciplina Modelagem de Sistemas Dinâmicos Lista 02 de exercícios Resolva as questões a seguir e poste no Moodle em pdf Enviar de forma manuscrita 1 Determine a função de transferência 𝐺1𝑠 𝑋2𝑠 𝐹𝑠 para o sistema mecânico translacional mostrado na Figura 01 Figura 01 Figura 02 2 Com base na função de transferência do exercício anterior determine os polos e zeros apresente seus valores numéricos e realize o mapeamento no plano complexo 3 Determine a função de transferência 𝐺3𝑠 𝜃2𝑠 𝑇𝑠 para o sistema mecânico rotacional mostrado na Figura 03 Figura 03 4 Determine a função de transferência 𝐺2𝑠 𝑉𝐿𝑠 𝑉𝑠 para o sistema elétrico mostrado na Figura 02 Modelagem de Sistemas Dinâmicos 27 de novembro de 2025 1 M1 1 M2 1 fv1 1 fv2 1 fv3 1 fv4 1 k 1 b fv1 fv2 fv3 b 1 1 1 b 2 1 b 3 M1 ddotx1t Ft bdotx1t dotx2t kx1t x2t M2 ddotx2t bdotx1t dotx2t kx1t x2t fv4 dotx2t M1 ddotx1t Ft b dotx1t b dotx2t kx1t kx2t M1 ddotx1t Ft b dotx1t b dotx2t kx1t kx2t M2 ddotx2t b dotx1t b dotx2t kx1t kx2t fv4 dotx2t 1 cdot ddotx1t Ft 3dotx1t 3 dotx2t 1 cdot x1t 1 cdot x2t 1 cdot ddotx2t 3dotx1t 3 dotx2t 1 cdot x1t 1 cdot x2t 1 cdot dotx2t ddotx1t Ft 3dotx1t 3 dotx2t x1t x2t ddotx2t 3dotx1t 3 dotx2t x1t x2t dotx2t ddotx1t 3dotx1t x1t 3 dotx2t x2t Ft ddotx2t 3dotx1t 4 dotx2t x1t x2t 0 mathcalLddotx1t 3dotx1t x1t 3 dotx2t x2t mathcalLFt mathcalLddotx1t 3mathcalLdotx1t mathcalLx1t 3mathcalLdotx2t mathcalLx2t mathcalLFt s2 X1s 3s X1s X1s 3s X2s X2s Fs s2 X1s 3s X1s X1s s2 3s 1 X1s 3s X2s X2s 3s 1 X2s s2 3s 1 X1s 3s 1 X2s Fs mathcalLddotx2t 3dotx1t 4 dotx2t x1t x2t mathcalL0 mathcalLddotx2t 3mathcalLdotx1t 4mathcalLdotx2t mathcalLx1t mathcalLx2t 0 s2 X2s 3s X1s 4s X2s X1s X2s 0 3s X1s X1s 3s 1 X1s s2 X2s 4s X2s X2s s2 4s 1 X2s 3s 1 X1s s2 4s 1 X2s 0 3s 1 X1s s2 4s 1 X2s 3s 1 X1s s2 4s 1 X2s X1s fracs2 4s 13s 1 X2s s2 3s 1 X1s 3s 1 X2s Fs s2 3s 1 leftfracs2 4s 13s 1 X2s right 3s 1 X2s Fs fracs2 3s 1s2 4s 13s 1 X2s 3s 1 X2s Fs 3s 1 frac3s 13s 13s 1 frac3s 123s 1 fracs2 3s 1s2 4s 13s 1 X2s frac3s 123s 1 X2s Fs s2 3s 1s2 4s 1 3s 12 3s 1 X2s Fs X2s Fs 3s 1 s2 3s 1s2 4s 1 3s 12 s2 3s 1 s2 4s 1 s2 s2 s2 4s s2 1 3s s2 3s 4s 3s 1 1 s2 1 4s 1 1 s4 4s3 s2 3s3 12s2 3s s2 4s 1 s4 4s3 3s3 s2 12s2 s2 3s 4s 1 s4 7s3 1s2 12s2 1s2 7s 1 s4 7s3 14s2 7s 1 3s 12 3s 13s 1 3s 3s 3s 1 1 3s 1 1 9s2 3s 3s 1 9s2 6s 1 s2 3s 1s2 4s 1 3s 12 s4 7s3 14s2 7s 1 9s2 6s 1 s4 7s3 14s2 7s 1 9s2 6s 1 s4 7s3 14s2 9s2 7s 6s 1 1 s4 7s3 5s2 1s 0 s4 7s3 5s2 s s4 7s3 5s2 s s4 7s3 5s2 s1 s s3 7s s2 5s s 1 s ss3 7s2 5s 1 5 X2sFs 3s 1 s4 7s3 5s2 s X2sFs 3s 1 ss3 7s2 5s 1 G1s X2sFs 3s 1 s s3 7s2 5s 1 6 2 G1s X2sFs 3s 1 s s3 7s2 5s 1 Ns 3s 1 Ds s s3 7s2 5s 1 Ns 0 3s 1 0 3s 1 1 0 1 3s 1 3s 3 1 3 s 13 Ds 0 s s3 7s2 5s 1 0 s 0 s3 7s2 5s 1 0 ss3 7s2 5s 1 s s3 s 7s2 s 5s s 1 s4 7s3 5s2 s Ds s s3 7s2 5s 1 s4 7s3 5s2 s Ds 0 s4 7s3 5s2 s 0 s4 7s3 5s2 s1 0 ss3 7s2 5s 1 0 s 0 s3 7s2 5s 1 0 s3 7s2 5s 1 0 sp2 62223 sp3 03889 00974j sp4 03889 00974j z1 13 z1 03333 p1 0 p2 62223 p3 03889 00974j p4 03889 00974j z1 13 p1 0 p2 62223 p3 03889 00974j p4 03889 00974j ℑs ℜs 3 J1 1 J2 1 D1 1 D2 1 K 1 J1θ1t Tt D1θ1t Kθ1t θ2t J2θ2t Kθ1t θ2t D2θ2t 1θ1t Tt 1θ1t 1θ1t θ2t 1θ2t 1θ1t θ2t 1θ2t θ1t Tt θ1t θ1t θ2t θ2t θ1t θ2t θ2t θ1t θ1t θ1t θ2t Tt θ2t θ2t θ2t θ1t 0 ℒθ1t s2Θ1s ℒθ1t sΘ1s ℒθ1t Θ1s ℒθ2t s2Θ2s ℒθ2t sΘ2s ℒθ2t Θ2s ℒTt Ts ddot heta1t dot heta1t heta1t heta2t Tt Downarrow mathcalL s2Theta1s sTheta1s Theta1s Theta2s Ts s2Theta1s sTheta1s Theta1s lefts2 s 1rightTheta1s lefts2 s 1rightTheta1s Theta2s Ts ddot heta2t dot heta2t heta2t heta1t 0 Downarrow mathcalL s2Theta2s sTheta2s Theta2s Theta1s 0 s2Theta2s sTheta2s Theta2s lefts2 s 1rightTheta2s Theta1s lefts2 s 1rightTheta2s 0 Theta1s lefts2 s 1rightTheta2s Theta1s lefts2 s 1rightTheta2s lefts2 s 1rightTheta1s Theta2s Ts lefts2 s 1rightleftlefts2 s 1rightTheta2sright Theta2s Ts lefts2 s 1right2Theta2s Theta2s Ts leftlefts2 s 1right2 1rightTheta2s Ts fracTheta2sTs frac1lefts2 s 1right2 1 lefts2 s 1right2 lefts2 s 1rightlefts2 s 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fracVbss 0 fracVcs Vss fracVcss Vcs Vbs 0 Vbs Vs Vbs Vcs fracVbss 0 fracVcs Vss fracVcss Vcs Vbs 0 Vbs Vs Vbs Vcs fracVbss 0 frac2Vcs Vss Vcs Vbs 0 Vbs Vs Vbs Vcs fracVbss 0 Vbs Vbs Vcs Vs fracVbss 0 2Vbs Vcs Vs fracVbss 0 s2Vbs Vcs Vs Vbs 0 2sVbs sVcs sVs Vbs 0 Vbs2s 1 sVcs sVs 0 Vbs2s 1 sVcs sVs Vbs fracsVcs sVs2s 1 frac2Vcs Vss Vcs Vbs 0 frac2Vcs Vss Vcs fracsVcs sVs2s 1 0 frac2Vcs Vss Vcs fracsVcs sVs2s 1 frac2Vcs Vss fracVcsss fracsVcs sVs2s 1 frac2Vcs Vs Vcsss fracsVcs sVs2s 1 fracVcs2 s Vss fracsVcs sVs2s 1 2s 1Vcs2 s Vs ssVcs sVs 2s 12 sVcs 2s 1Vs s2Vcs s2Vs 2s 12 s 2s cdot 2 2s cdot s 1 cdot 2 1 cdot s 4s 2s2 2 s 2s2 4s s 2 2s2 5s 2 2s2 5s 2Vcs 2s 1Vs s2Vcs s2Vs 2s2 5s 2Vcs s2Vcs 2s 1Vs s2Vs Vcs2s2 5s 2 s2 Vs2s 1 s2 2s2 5s 2 s2 2s2 s2 5s 2 s2 5s 2 2s 1 s2 s2 2s 1 Vcss2 5s 2 Vss2 2s 1 fracVcsVs fracs2 2s 1s2 5s 2 G2s fracVLsVs fracVcsVs fracs2 2s 1s2 5s 2 boxedG2s fracVLsVs fracs2 2s 1s2 5s 2