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msm/TOOLBOX_Force_Estimation/ESTIMATION_TOOL_constraints_file.m
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PHIts(1,1) =(SCz - OEz - ACx*sin(yc) - TSx*sin(ys) + ACz*cos(xc)*cos(yc) + ACy*cos(yc)*sin(xc) + TSz*cos(xs)*cos(ys) + TSy*cos(ys)*sin(xs))^2/Cts^2 + (SCx - OEx - ACy*(cos(xc)*sin(zc) - cos(zc)*sin(xc)*sin(yc)) + ACz*(sin(xc)*sin(zc) + cos(xc)*cos(zc)*sin(yc)) - TSy*(cos(xs)*sin(zs) - cos(zs)*sin(xs)*sin(ys)) + TSz*(sin(xs)*sin(zs) + cos(xs)*cos(zs)*sin(ys)) + ACx*cos(yc)*cos(zc) + TSx*cos(ys)*cos(zs))^2/Ats^2 + (SCy - OEy + ACy*(cos(xc)*cos(zc) + sin(xc)*sin(yc)*sin(zc)) - ACz*(cos(zc)*sin(xc) - cos(xc)*sin(yc)*sin(zc)) + TSy*(cos(xs)*cos(zs) + sin(xs)*sin(ys)*sin(zs)) - TSz*(cos(zs)*sin(xs) - cos(xs)*sin(ys)*sin(zs)) + ACx*cos(yc)*sin(zc) + TSx*cos(ys)*sin(zs))^2/Bts^2 - 1;
PHIai(1,1) =(SCz - OEz - ACx*sin(yc) - AIx*sin(ys) + ACz*cos(xc)*cos(yc) + AIz*cos(xs)*cos(ys) + ACy*cos(yc)*sin(xc) + AIy*cos(ys)*sin(xs))^2/Cai^2 + (SCx - OEx - ACy*(cos(xc)*sin(zc) - cos(zc)*sin(xc)*sin(yc)) + ACz*(sin(xc)*sin(zc) + cos(xc)*cos(zc)*sin(yc)) - AIy*(cos(xs)*sin(zs) - cos(zs)*sin(xs)*sin(ys)) + AIz*(sin(xs)*sin(zs) + cos(xs)*cos(zs)*sin(ys)) + ACx*cos(yc)*cos(zc) + AIx*cos(ys)*cos(zs))^2/Aai^2 + (SCy - OEy + ACy*(cos(xc)*cos(zc) + sin(xc)*sin(yc)*sin(zc)) - ACz*(cos(zc)*sin(xc) - cos(xc)*sin(yc)*sin(zc)) + AIy*(cos(xs)*cos(zs) + sin(xs)*sin(ys)*sin(zs)) - AIz*(cos(zs)*sin(xs) - cos(xs)*sin(ys)*sin(zs)) + ACx*cos(yc)*sin(zc) + AIx*cos(ys)*sin(zs))^2/Bai^2 - 1;
dPHItsdq(1,1) =(2*(ACy*(sin(xc)*sin(zc) + cos(xc)*cos(zc)*sin(yc)) + ACz*(cos(xc)*sin(zc) - cos(zc)*sin(xc)*sin(yc)))*(SCx - OEx - ACy*(cos(xc)*sin(zc) - cos(zc)*sin(xc)*sin(yc)) + ACz*(sin(xc)*sin(zc) + cos(xc)*cos(zc)*sin(yc)) - TSy*(cos(xs)*sin(zs) - cos(zs)*sin(xs)*sin(ys)) + TSz*(sin(xs)*sin(zs) + cos(xs)*cos(zs)*sin(ys)) + ACx*cos(yc)*cos(zc) + TSx*cos(ys)*cos(zs)))/Ats^2 - (2*(ACy*(cos(zc)*sin(xc) - cos(xc)*sin(yc)*sin(zc)) + ACz*(cos(xc)*cos(zc) + sin(xc)*sin(yc)*sin(zc)))*(SCy - OEy + ACy*(cos(xc)*cos(zc) + sin(xc)*sin(yc)*sin(zc)) - ACz*(cos(zc)*sin(xc) - cos(xc)*sin(yc)*sin(zc)) + TSy*(cos(xs)*cos(zs) + sin(xs)*sin(ys)*sin(zs)) - TSz*(cos(zs)*sin(xs) - cos(xs)*sin(ys)*sin(zs)) + ACx*cos(yc)*sin(zc) + TSx*cos(ys)*sin(zs)))/Bts^2 + (2*(ACy*cos(xc)*cos(yc) - ACz*cos(yc)*sin(xc))*(SCz - OEz - ACx*sin(yc) - TSx*sin(ys) + ACz*cos(xc)*cos(yc) + ACy*cos(yc)*sin(xc) + TSz*cos(xs)*cos(ys) + TSy*cos(ys)*sin(xs)))/Cts^2;
dPHItsdq(1,2) =(2*(ACz*cos(xc)*cos(yc)*cos(zc) - ACx*cos(zc)*sin(yc) + ACy*cos(yc)*cos(zc)*sin(xc))*(SCx - OEx - ACy*(cos(xc)*sin(zc) - cos(zc)*sin(xc)*sin(yc)) + ACz*(sin(xc)*sin(zc) + cos(xc)*cos(zc)*sin(yc)) - TSy*(cos(xs)*sin(zs) - cos(zs)*sin(xs)*sin(ys)) + TSz*(sin(xs)*sin(zs) + cos(xs)*cos(zs)*sin(ys)) + ACx*cos(yc)*cos(zc) + TSx*cos(ys)*cos(zs)))/Ats^2 + (2*(ACz*cos(xc)*cos(yc)*sin(zc) - ACx*sin(yc)*sin(zc) + ACy*cos(yc)*sin(xc)*sin(zc))*(SCy - OEy + ACy*(cos(xc)*cos(zc) + sin(xc)*sin(yc)*sin(zc)) - ACz*(cos(zc)*sin(xc) - cos(xc)*sin(yc)*sin(zc)) + TSy*(cos(xs)*cos(zs) + sin(xs)*sin(ys)*sin(zs)) - TSz*(cos(zs)*sin(xs) - cos(xs)*sin(ys)*sin(zs)) + ACx*cos(yc)*sin(zc) + TSx*cos(ys)*sin(zs)))/Bts^2 - (2*(ACx*cos(yc) + ACz*cos(xc)*sin(yc) + ACy*sin(xc)*sin(yc))*(SCz - OEz - ACx*sin(yc) - TSx*sin(ys) + ACz*cos(xc)*cos(yc) + ACy*cos(yc)*sin(xc) + TSz*cos(xs)*cos(ys) + TSy*cos(ys)*sin(xs)))/Cts^2;
dPHItsdq(1,3) =(2*(ACz*(sin(xc)*sin(zc) + cos(xc)*cos(zc)*sin(yc)) - ACy*(cos(xc)*sin(zc) - cos(zc)*sin(xc)*sin(yc)) + ACx*cos(yc)*cos(zc))*(SCy - OEy + ACy*(cos(xc)*cos(zc) + sin(xc)*sin(yc)*sin(zc)) - ACz*(cos(zc)*sin(xc) - cos(xc)*sin(yc)*sin(zc)) + TSy*(cos(xs)*cos(zs) + sin(xs)*sin(ys)*sin(zs)) - TSz*(cos(zs)*sin(xs) - cos(xs)*sin(ys)*sin(zs)) + ACx*cos(yc)*sin(zc) + TSx*cos(ys)*sin(zs)))/Bts^2 - (2*(ACy*(cos(xc)*cos(zc) + sin(xc)*sin(yc)*sin(zc)) - ACz*(cos(zc)*sin(xc) - cos(xc)*sin(yc)*sin(zc)) + ACx*cos(yc)*sin(zc))*(SCx - OEx - ACy*(cos(xc)*sin(zc) - cos(zc)*sin(xc)*sin(yc)) + ACz*(sin(xc)*sin(zc) + cos(xc)*cos(zc)*sin(yc)) - TSy*(cos(xs)*sin(zs) - cos(zs)*sin(xs)*sin(ys)) + TSz*(sin(xs)*sin(zs) + cos(xs)*cos(zs)*sin(ys)) + ACx*cos(yc)*cos(zc) + TSx*cos(ys)*cos(zs)))/Ats^2;
dPHItsdq(1,4) =(2*(TSy*(sin(xs)*sin(zs) + cos(xs)*cos(zs)*sin(ys)) + TSz*(cos(xs)*sin(zs) - cos(zs)*sin(xs)*sin(ys)))*(SCx - OEx - ACy*(cos(xc)*sin(zc) - cos(zc)*sin(xc)*sin(yc)) + ACz*(sin(xc)*sin(zc) + cos(xc)*cos(zc)*sin(yc)) - TSy*(cos(xs)*sin(zs) - cos(zs)*sin(xs)*sin(ys)) + TSz*(sin(xs)*sin(zs) + cos(xs)*cos(zs)*sin(ys)) + ACx*cos(yc)*cos(zc) + TSx*cos(ys)*cos(zs)))/Ats^2 - (2*(TSy*(cos(zs)*sin(xs) - cos(xs)*sin(ys)*sin(zs)) + TSz*(cos(xs)*cos(zs) + sin(xs)*sin(ys)*sin(zs)))*(SCy - OEy + ACy*(cos(xc)*cos(zc) + sin(xc)*sin(yc)*sin(zc)) - ACz*(cos(zc)*sin(xc) - cos(xc)*sin(yc)*sin(zc)) + TSy*(cos(xs)*cos(zs) + sin(xs)*sin(ys)*sin(zs)) - TSz*(cos(zs)*sin(xs) - cos(xs)*sin(ys)*sin(zs)) + ACx*cos(yc)*sin(zc) + TSx*cos(ys)*sin(zs)))/Bts^2 + (2*(TSy*cos(xs)*cos(ys) - TSz*cos(ys)*sin(xs))*(SCz - OEz - ACx*sin(yc) - TSx*sin(ys) + ACz*cos(xc)*cos(yc) + ACy*cos(yc)*sin(xc) + TSz*cos(xs)*cos(ys) + TSy*cos(ys)*sin(xs)))/Cts^2;
dPHItsdq(1,5) =(2*(TSz*cos(xs)*cos(ys)*sin(zs) - TSx*sin(ys)*sin(zs) + TSy*cos(ys)*sin(xs)*sin(zs))*(SCy - OEy + ACy*(cos(xc)*cos(zc) + sin(xc)*sin(yc)*sin(zc)) - ACz*(cos(zc)*sin(xc) - cos(xc)*sin(yc)*sin(zc)) + TSy*(cos(xs)*cos(zs) + sin(xs)*sin(ys)*sin(zs)) - TSz*(cos(zs)*sin(xs) - cos(xs)*sin(ys)*sin(zs)) + ACx*cos(yc)*sin(zc) + TSx*cos(ys)*sin(zs)))/Bts^2 - (2*(TSx*cos(ys) + TSz*cos(xs)*sin(ys) + TSy*sin(xs)*sin(ys))*(SCz - OEz - ACx*sin(yc) - TSx*sin(ys) + ACz*cos(xc)*cos(yc) + ACy*cos(yc)*sin(xc) + TSz*cos(xs)*cos(ys) + TSy*cos(ys)*sin(xs)))/Cts^2 + (2*(TSz*cos(xs)*cos(ys)*cos(zs) - TSx*cos(zs)*sin(ys) + TSy*cos(ys)*cos(zs)*sin(xs))*(SCx - OEx - ACy*(cos(xc)*sin(zc) - cos(zc)*sin(xc)*sin(yc)) + ACz*(sin(xc)*sin(zc) + cos(xc)*cos(zc)*sin(yc)) - TSy*(cos(xs)*sin(zs) - cos(zs)*sin(xs)*sin(ys)) + TSz*(sin(xs)*sin(zs) + cos(xs)*cos(zs)*sin(ys)) + ACx*cos(yc)*cos(zc) + TSx*cos(ys)*cos(zs)))/Ats^2;
dPHItsdq(1,6) =(2*(TSz*(sin(xs)*sin(zs) + cos(xs)*cos(zs)*sin(ys)) - TSy*(cos(xs)*sin(zs) - cos(zs)*sin(xs)*sin(ys)) + TSx*cos(ys)*cos(zs))*(SCy - OEy + ACy*(cos(xc)*cos(zc) + sin(xc)*sin(yc)*sin(zc)) - ACz*(cos(zc)*sin(xc) - cos(xc)*sin(yc)*sin(zc)) + TSy*(cos(xs)*cos(zs) + sin(xs)*sin(ys)*sin(zs)) - TSz*(cos(zs)*sin(xs) - cos(xs)*sin(ys)*sin(zs)) + ACx*cos(yc)*sin(zc) + TSx*cos(ys)*sin(zs)))/Bts^2 - (2*(TSy*(cos(xs)*cos(zs) + sin(xs)*sin(ys)*sin(zs)) - TSz*(cos(zs)*sin(xs) - cos(xs)*sin(ys)*sin(zs)) + TSx*cos(ys)*sin(zs))*(SCx - OEx - ACy*(cos(xc)*sin(zc) - cos(zc)*sin(xc)*sin(yc)) + ACz*(sin(xc)*sin(zc) + cos(xc)*cos(zc)*sin(yc)) - TSy*(cos(xs)*sin(zs) - cos(zs)*sin(xs)*sin(ys)) + TSz*(sin(xs)*sin(zs) + cos(xs)*cos(zs)*sin(ys)) + ACx*cos(yc)*cos(zc) + TSx*cos(ys)*cos(zs)))/Ats^2;
dPHItsdq(1,7) =0;
dPHItsdq(1,8) =0;
dPHItsdq(1,9) =0;
dPHItsdq(1,10) =0;
dPHItsdq(1,11) =0;
dPHIaidq(1,1) =(2*(ACy*cos(xc)*cos(yc) - ACz*cos(yc)*sin(xc))*(SCz - OEz - ACx*sin(yc) - AIx*sin(ys) + ACz*cos(xc)*cos(yc) + AIz*cos(xs)*cos(ys) + ACy*cos(yc)*sin(xc) + AIy*cos(ys)*sin(xs)))/Cai^2 - (2*(ACy*(cos(zc)*sin(xc) - cos(xc)*sin(yc)*sin(zc)) + ACz*(cos(xc)*cos(zc) + sin(xc)*sin(yc)*sin(zc)))*(SCy - OEy + ACy*(cos(xc)*cos(zc) + sin(xc)*sin(yc)*sin(zc)) - ACz*(cos(zc)*sin(xc) - cos(xc)*sin(yc)*sin(zc)) + AIy*(cos(xs)*cos(zs) + sin(xs)*sin(ys)*sin(zs)) - AIz*(cos(zs)*sin(xs) - cos(xs)*sin(ys)*sin(zs)) + ACx*cos(yc)*sin(zc) + AIx*cos(ys)*sin(zs)))/Bai^2 + (2*(ACy*(sin(xc)*sin(zc) + cos(xc)*cos(zc)*sin(yc)) + ACz*(cos(xc)*sin(zc) - cos(zc)*sin(xc)*sin(yc)))*(SCx - OEx - ACy*(cos(xc)*sin(zc) - cos(zc)*sin(xc)*sin(yc)) + ACz*(sin(xc)*sin(zc) + cos(xc)*cos(zc)*sin(yc)) - AIy*(cos(xs)*sin(zs) - cos(zs)*sin(xs)*sin(ys)) + AIz*(sin(xs)*sin(zs) + cos(xs)*cos(zs)*sin(ys)) + ACx*cos(yc)*cos(zc) + AIx*cos(ys)*cos(zs)))/Aai^2;
dPHIaidq(1,2) =(2*(ACz*cos(xc)*cos(yc)*cos(zc) - ACx*cos(zc)*sin(yc) + ACy*cos(yc)*cos(zc)*sin(xc))*(SCx - OEx - ACy*(cos(xc)*sin(zc) - cos(zc)*sin(xc)*sin(yc)) + ACz*(sin(xc)*sin(zc) + cos(xc)*cos(zc)*sin(yc)) - AIy*(cos(xs)*sin(zs) - cos(zs)*sin(xs)*sin(ys)) + AIz*(sin(xs)*sin(zs) + cos(xs)*cos(zs)*sin(ys)) + ACx*cos(yc)*cos(zc) + AIx*cos(ys)*cos(zs)))/Aai^2 + (2*(ACz*cos(xc)*cos(yc)*sin(zc) - ACx*sin(yc)*sin(zc) + ACy*cos(yc)*sin(xc)*sin(zc))*(SCy - OEy + ACy*(cos(xc)*cos(zc) + sin(xc)*sin(yc)*sin(zc)) - ACz*(cos(zc)*sin(xc) - cos(xc)*sin(yc)*sin(zc)) + AIy*(cos(xs)*cos(zs) + sin(xs)*sin(ys)*sin(zs)) - AIz*(cos(zs)*sin(xs) - cos(xs)*sin(ys)*sin(zs)) + ACx*cos(yc)*sin(zc) + AIx*cos(ys)*sin(zs)))/Bai^2 - (2*(ACx*cos(yc) + ACz*cos(xc)*sin(yc) + ACy*sin(xc)*sin(yc))*(SCz - OEz - ACx*sin(yc) - AIx*sin(ys) + ACz*cos(xc)*cos(yc) + AIz*cos(xs)*cos(ys) + ACy*cos(yc)*sin(xc) + AIy*cos(ys)*sin(xs)))/Cai^2;
dPHIaidq(1,3) =(2*(ACz*(sin(xc)*sin(zc) + cos(xc)*cos(zc)*sin(yc)) - ACy*(cos(xc)*sin(zc) - cos(zc)*sin(xc)*sin(yc)) + ACx*cos(yc)*cos(zc))*(SCy - OEy + ACy*(cos(xc)*cos(zc) + sin(xc)*sin(yc)*sin(zc)) - ACz*(cos(zc)*sin(xc) - cos(xc)*sin(yc)*sin(zc)) + AIy*(cos(xs)*cos(zs) + sin(xs)*sin(ys)*sin(zs)) - AIz*(cos(zs)*sin(xs) - cos(xs)*sin(ys)*sin(zs)) + ACx*cos(yc)*sin(zc) + AIx*cos(ys)*sin(zs)))/Bai^2 - (2*(ACy*(cos(xc)*cos(zc) + sin(xc)*sin(yc)*sin(zc)) - ACz*(cos(zc)*sin(xc) - cos(xc)*sin(yc)*sin(zc)) + ACx*cos(yc)*sin(zc))*(SCx - OEx - ACy*(cos(xc)*sin(zc) - cos(zc)*sin(xc)*sin(yc)) + ACz*(sin(xc)*sin(zc) + cos(xc)*cos(zc)*sin(yc)) - AIy*(cos(xs)*sin(zs) - cos(zs)*sin(xs)*sin(ys)) + AIz*(sin(xs)*sin(zs) + cos(xs)*cos(zs)*sin(ys)) + ACx*cos(yc)*cos(zc) + AIx*cos(ys)*cos(zs)))/Aai^2;
dPHIaidq(1,4) =(2*(AIy*cos(xs)*cos(ys) - AIz*cos(ys)*sin(xs))*(SCz - OEz - ACx*sin(yc) - AIx*sin(ys) + ACz*cos(xc)*cos(yc) + AIz*cos(xs)*cos(ys) + ACy*cos(yc)*sin(xc) + AIy*cos(ys)*sin(xs)))/Cai^2 - (2*(AIy*(cos(zs)*sin(xs) - cos(xs)*sin(ys)*sin(zs)) + AIz*(cos(xs)*cos(zs) + sin(xs)*sin(ys)*sin(zs)))*(SCy - OEy + ACy*(cos(xc)*cos(zc) + sin(xc)*sin(yc)*sin(zc)) - ACz*(cos(zc)*sin(xc) - cos(xc)*sin(yc)*sin(zc)) + AIy*(cos(xs)*cos(zs) + sin(xs)*sin(ys)*sin(zs)) - AIz*(cos(zs)*sin(xs) - cos(xs)*sin(ys)*sin(zs)) + ACx*cos(yc)*sin(zc) + AIx*cos(ys)*sin(zs)))/Bai^2 + (2*(AIy*(sin(xs)*sin(zs) + cos(xs)*cos(zs)*sin(ys)) + AIz*(cos(xs)*sin(zs) - cos(zs)*sin(xs)*sin(ys)))*(SCx - OEx - ACy*(cos(xc)*sin(zc) - cos(zc)*sin(xc)*sin(yc)) + ACz*(sin(xc)*sin(zc) + cos(xc)*cos(zc)*sin(yc)) - AIy*(cos(xs)*sin(zs) - cos(zs)*sin(xs)*sin(ys)) + AIz*(sin(xs)*sin(zs) + cos(xs)*cos(zs)*sin(ys)) + ACx*cos(yc)*cos(zc) + AIx*cos(ys)*cos(zs)))/Aai^2;
dPHIaidq(1,5) =(2*(AIz*cos(xs)*cos(ys)*cos(zs) - AIx*cos(zs)*sin(ys) + AIy*cos(ys)*cos(zs)*sin(xs))*(SCx - OEx - ACy*(cos(xc)*sin(zc) - cos(zc)*sin(xc)*sin(yc)) + ACz*(sin(xc)*sin(zc) + cos(xc)*cos(zc)*sin(yc)) - AIy*(cos(xs)*sin(zs) - cos(zs)*sin(xs)*sin(ys)) + AIz*(sin(xs)*sin(zs) + cos(xs)*cos(zs)*sin(ys)) + ACx*cos(yc)*cos(zc) + AIx*cos(ys)*cos(zs)))/Aai^2 + (2*(AIz*cos(xs)*cos(ys)*sin(zs) - AIx*sin(ys)*sin(zs) + AIy*cos(ys)*sin(xs)*sin(zs))*(SCy - OEy + ACy*(cos(xc)*cos(zc) + sin(xc)*sin(yc)*sin(zc)) - ACz*(cos(zc)*sin(xc) - cos(xc)*sin(yc)*sin(zc)) + AIy*(cos(xs)*cos(zs) + sin(xs)*sin(ys)*sin(zs)) - AIz*(cos(zs)*sin(xs) - cos(xs)*sin(ys)*sin(zs)) + ACx*cos(yc)*sin(zc) + AIx*cos(ys)*sin(zs)))/Bai^2 - (2*(AIx*cos(ys) + AIz*cos(xs)*sin(ys) + AIy*sin(xs)*sin(ys))*(SCz - OEz - ACx*sin(yc) - AIx*sin(ys) + ACz*cos(xc)*cos(yc) + AIz*cos(xs)*cos(ys) + ACy*cos(yc)*sin(xc) + AIy*cos(ys)*sin(xs)))/Cai^2;
dPHIaidq(1,6) =(2*(AIz*(sin(xs)*sin(zs) + cos(xs)*cos(zs)*sin(ys)) - AIy*(cos(xs)*sin(zs) - cos(zs)*sin(xs)*sin(ys)) + AIx*cos(ys)*cos(zs))*(SCy - OEy + ACy*(cos(xc)*cos(zc) + sin(xc)*sin(yc)*sin(zc)) - ACz*(cos(zc)*sin(xc) - cos(xc)*sin(yc)*sin(zc)) + AIy*(cos(xs)*cos(zs) + sin(xs)*sin(ys)*sin(zs)) - AIz*(cos(zs)*sin(xs) - cos(xs)*sin(ys)*sin(zs)) + ACx*cos(yc)*sin(zc) + AIx*cos(ys)*sin(zs)))/Bai^2 - (2*(AIy*(cos(xs)*cos(zs) + sin(xs)*sin(ys)*sin(zs)) - AIz*(cos(zs)*sin(xs) - cos(xs)*sin(ys)*sin(zs)) + AIx*cos(ys)*sin(zs))*(SCx - OEx - ACy*(cos(xc)*sin(zc) - cos(zc)*sin(xc)*sin(yc)) + ACz*(sin(xc)*sin(zc) + cos(xc)*cos(zc)*sin(yc)) - AIy*(cos(xs)*sin(zs) - cos(zs)*sin(xs)*sin(ys)) + AIz*(sin(xs)*sin(zs) + cos(xs)*cos(zs)*sin(ys)) + ACx*cos(yc)*cos(zc) + AIx*cos(ys)*cos(zs)))/Aai^2;
dPHIaidq(1,7) =0;
dPHIaidq(1,8) =0;
dPHIaidq(1,9) =0;
dPHIaidq(1,10) =0;
dPHIaidq(1,11) =0;
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