#http://www.totofweb.net/robots-projet-55.html restart; with(inttrans):

#Fonctions de transfert associ\303\251es \303\240 U et Cr (voir document PDF) Hm:=solve(((laplace(U*Heaviside(t),t,p)-Ke*OmegaM)*Kc/(R+L*p))/(J*p)=OmegaM,OmegaM)/laplace(U*Heaviside(t),t,p); Gm:=solve(((laplace(U*Heaviside(t),t,p)-Ke*OmegaM)*Kc/(R+L*p)-Kcr*OmegaM)/(J*p)=OmegaM,OmegaM)/laplace(U*Heaviside(t),t,p);

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f:=laplace(U*Heaviside(t),t,p)*Hm; # Sans couple r\303\251sistant

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F:=simplify(invlaplace(f,p,t)): #Applications num\303\251riques d'un moteur Maxon Ke := 0.0603: Kc := 0.0603: Kcr:= 0.01: R := 1.91: J := 10^(-4): L := 0.63*10^(-3): U := 12: #Valeur finale Vf:=evalf(limit(F,t=infinity)); #=evalf(limit(p*f,p=0))=U/Ke

NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtaUdGJTY5USNWZkYoLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRigvJSVzaXplR1EjMTJGKC8lJWJvbGRHUSZmYWxzZUYoLyUnaXRhbGljR1EldHJ1ZUYoLyUqdW5kZXJsaW5lR0Y4LyUqc3Vic2NyaXB0R0Y4LyUsc3VwZXJzY3JpcHRHRjgvJStmb3JlZ3JvdW5kR1EqWzAsMCwyNTVdRigvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYoLyUnb3BhcXVlR0Y4LyUrZXhlY3V0YWJsZUdGOC8lKXJlYWRvbmx5R0Y7LyUpY29tcG9zZWRHRjgvJSpjb252ZXJ0ZWRHRjgvJStpbXNlbGVjdGVkR0Y4LyUscGxhY2Vob2xkZXJHRjgvJTBmb250X3N0eWxlX25hbWVHUSoyRH5PdXRwdXRGKC8lKm1hdGhjb2xvckdGRC8lL21hdGhiYWNrZ3JvdW5kR0ZHLyUrZm9udGZhbWlseUdGMi8lLG1hdGh2YXJpYW50R1EnaXRhbGljRigvJSltYXRoc2l6ZUdGNS1JI21vR0YlNjNRIzo9RigvJSVmb3JtR1EmaW5maXhGKC8lJmZlbmNlR0Y4LyUqc2VwYXJhdG9yR0Y4LyUnbHNwYWNlR1EvdGhpY2ttYXRoc3BhY2VGKC8lJ3JzcGFjZUdGW3AvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKG1heHNpemVHUSlpbmZpbml0eUYoLyUobWluc2l6ZUdRIjFGKC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUwZm9udF9zdHlsZV9uYW1lR0ZYLyUlc2l6ZUdGNS8lK2ZvcmVncm91bmRHRkQvJStiYWNrZ3JvdW5kR0ZHLUkjbW5HRiU2OVEsMTk5LjAwNDk3NTJGKEYwRjNGNi9GOkY4RjxGPkZARkJGRUZIRkpGTEZORlBGUkZURlZGWUZlbkZnbi9Gam5RJ25vcm1hbEYoRlxvNyMtX0YpSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNWZkdGKCQiK18oXCsqPiEiKDcjRmVy

#Courbe d'\303\251volution plot([Vf,F(t)],t=0..0.5,gridlines,thickness=[1,2],color=[blue,red]);

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

#RAZ des applications num\303\251riques Ke := 'Ke': Kc := 'Kc': R := 'R': J := 'J': L := 'L': U := 'U':

Hp:=Kp->solve((laplace(OmegaC*Heaviside(t),t,p)-OmegaM)*Kp*Hm=OmegaM,OmegaM)/laplace(OmegaC*Heaviside(t),t,p): Fp:=Kp->simplify(invlaplace(Hp(Kp)*laplace(OmegaC*Heaviside(t),t,p),p,t)): Up:=Kp->simplify(invlaplace(Hp(Kp)*laplace(OmegaC*Heaviside(t),t,p)/Hm,p,t)): Ke := 0.0603: Kc := 0.0603: R := 1.91: J := 10^(-4): L := 0.63*10^(-3): OmegaC:=200: plot([OmegaC,Fp(0.2),Fp(0.5),Fp(1),Fp(2),Fp(5)],t=0..0.04,axis=[gridlines=[10, color=grey]]); plot([Ke*OmegaC,Up(0.2),Up(0.5),Up(1),Up(2),Up(5)],t=0..0.04,axis=[gridlines=[10, color=grey]]);

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#Courbes montrant l'apparition d'oscillations plot([OmegaC,Fp(5),Fp(20),Fp(50)],t=0..0.005,axis=[gridlines=[10, color=grey]]); plot([Ke*OmegaC,Up(5),Up(20),Up(50)],t=0..0.005,axis=[gridlines=[10, color=grey]]);

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#Courbes ne d\303\251passant pas les valeurs maximales plot([OmegaC,Fp(0.05),Fp(0.1),Fp(0.15)],t=0..0.2,axis=[gridlines=[10, color=grey]]); plot([Ke*OmegaC,Up(0.05),Up(0.1),Up(0.15)],t=0..0.2,axis=[gridlines=[10, color=grey]]);

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

Ke := 'Ke': Kc := 'Kc': R := 'R': J := 'J': L := 'L': OmegaC:='OmegaC':

Hpi:=(Kp,Ki)->solve((laplace(OmegaC*Heaviside(t),t,p)-OmegaM)*(Kp+Ki/p)*Hm=OmegaM,OmegaM)/laplace(OmegaC*Heaviside(t),t,p): Fpi:=(Kp,Ki)->simplify(invlaplace(Hpi(Kp,Ki)*laplace(OmegaC*Heaviside(t),t,p),p,t)): Upi:=(Kp,Ki)->simplify(invlaplace(Hpi(Kp,Ki)*laplace(OmegaC*Heaviside(t),t,p)/Hm,p,t)): Ke := 0.0603: Kc := 0.0603: R := 1.91: J := 10^(-4): L := 0.63*10^(-3): OmegaC:=200: #courbes d'\303\251volution et tensions correspondantes plot([OmegaC,Fpi(1,0),Fpi(1,100),Fpi(1,320),Fpi(1,1000)],t=0..0.05,axis=[gridlines=[10, color=grey]]); plot([Ke*OmegaC,Upi(1,0),Upi(1,320),Upi(1,100),Upi(1,1000)],t=0..0.05,axis=[gridlines=[10, color=grey]]);

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#valeurs ne d\303\251passant par la zone limite d'endommagement plot([OmegaC,Fpi(0.15,0),Fpi(0.15,2),Fpi(0.15,4),Fpi(0.15,8)],t=0..0.2,axis=[gridlines=[10, color=grey]]); plot([Ke*OmegaC,Upi(0.15,0),Upi(0.15,2),Upi(0.15,4),Upi(0.15,8)],t=0..0.2,axis=[gridlines=[10, color=grey]]);

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

Ke := 'Ke': Kc := 'Kc': R := 'R': J := 'J': L := 'L': OmegaC:='OmegaC':

Hpid:=(Kp,Ki,Kd)->solve((laplace(OmegaC*Heaviside(t),t,p)-OmegaM)*(Kp+Ki/p+p*Kd)*Hm=OmegaM,OmegaM)/laplace(OmegaC*Heaviside(t),t,p): Fpid:=(Kp,Ki,Kd)->simplify(invlaplace(Hpid(Kp,Ki,Kd)*laplace(OmegaC*Heaviside(t),t,p),p,t)): Upid:=(Kp,Ki,Kd)->simplify(invlaplace(Hpid(Kp,Ki,Kd)*laplace(OmegaC*Heaviside(t),t,p)/Hm,p,t)): Ke := 0.0603: Kc := 0.0603: R := 1.91: J := 10^(-4): L := 0.63*10^(-3): OmegaC:=200: #Courbes respectant la zone de fonctionnement normale du moteur #elles peuvent sembler aberrantes, mais c'est en fait le r\303\251sultat de la discontinuit\303\251 de la d\303\251riv\303\251e de l'erreur en 0 plot([OmegaC,Fpid(0.15,8,0),Fpid(0.15,8,0.01)],t=0..0.2,axis=[gridlines=[10, color=grey]]); plot([Ke*OmegaC,Upid(0.15,8,0),Upid(0.15,8,0.01)],t=0..0.2,axis=[gridlines=[10, color=grey]]);

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