How to find the corresponding variable equations of parameters for a system which has equations of parameters and variables? (looking for non-numeric outcome)

Question

Bbb 2022-12-30

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1886587-how-to-find-the-corresponding-variable-equations-of-parameters-for-a-system-which-has-equations-of-p

评论： Bbb 2022-12-31

Hi! I have different parameters and varibles. For them, i am trying to find parameter T1 and T2's equation. In lines 10, 11 and 12 i have found their mathematical value, but how can i find T1 and T2 as variable and parameter equations/ functions ?

syms T1 T2 f1 f2 f3 f4 ;
E1=m1*((-d1.*sin(q1).*q1d.^2)+(d1.*cos(q1).*q1dd))-(f2-f4);
E2=m1*((-d1.*cos(q1).*q1d.^2)-(d1.*sin(q1).*q1dd))-(f3-f1);
E3=T1+(f1*d1.*sin(q1))-(f2.*d1.*cos(q1))+(f3.*d1.*sin(q1))-(f4.*d1.*cos(q1))-(q1dd.*I1);
E4=m2*((-link1max.*sin(q1).*q1d.^2)+(link1max.*cos(q1).*q1dd)-(d2.*sin(q2).*q2d.^2)+(d2.*cos(q2).*q2dd))-(f4-f5);
E5=m2*((-link1max.*cos(q1).*q1d.^2)-(link1max.*sin(q1).*q1dd)-(d2.*cos(q2).*q2d.^2)-(d2.*sin(q2).*q2dd))-(f6-f3);
E6=T2+(f6*d2.*sin(q2))-(f5.*d2.*cos(q2))+(f3.*d2.*sin(q2))-(f4*d2.*cos(q2))-(q2dd.*I2);
[T1,T2,f1,f2,f3,f4]= solve(E3,E6,E2,E4,E5,E1);
torque1(end+1)=eval(T1); %Nm
torque2(end+1)=eval(T2);
force1(end+1)=eval(f1);
force2(end+1)=eval(f2);
force3(end+1)=eval(f3);
force4(end+1)=eval(f4);

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Bbb 2022-12-30

Full code:

height= 1.85; %[m]

mass= 85; %[kg]

tighR=0.08; %[m]

legR= 0.05; %[m]

% x

gaitCycleDuration= 1.4; %[second]

x= linspace(0,1.0,95);

xx= linspace(0,1.00,101);

%HİP

%hip angle

hip_angle= [0.4136 0.4128 0.4121 0.4100 0.4047 0.3958 0.3831 0.3672 0.3485 0.3274 0.3047 0.2805 0.2553 0.2295 0.2030 0.1758 0.1484 0.1208 0.0932 0.0661 0.0396 0.0138 -0.0112 -0.0354 -0.0586 -0.0808 -0.1019 -0.1218 -0.1401 -0.1571 -0.1724 -0.1862 -0.1983 -0.2082 -0.2161 -0.2217 -0.2248 -0.2251 -0.2224 -0.2168 -0.2087 -0.1990 -0.1887 -0.1791 -0.1712 -0.1658 -0.1635 -0.1641 -0.1670 -0.1716 -0.1766 -0.1813 -0.1861 -0.1909 -0.1967 -0.2032 -0.2100 -0.2157 -0.2197 -0.2211 -0.2194 -0.2145 -0.2066 -0.1962 -0.1834 -0.1684 -0.1517 -0.1335 -0.1138 -0.0934 -0.0721 -0.0478 -0.0241 0.0002 0.0250 0.0497 0.0745 0.0990 0.1229 0.1461 0.1686 0.1901 0.2108 0.2306 0.2492 0.2667 0.2829 0.2978 0.3117 0.3245 0.3362 0.3471 0.3571 0.3665 0.3752 0.3831 0.3906 0.3972 0.4030 0.4077 0.4112];

P = polyfit(xx,hip_angle,6);

Y = polyval(P,xx);

hip_angle=[Y(3) Y(4:95) Y(3) Y(3)];

figure

grid on;

hold on

plot(x,hip_angle,'k');

xlabel('Gait Cycle (%)')

ylabel('Hip Angle (rad)')

hold off

%hip velocity

P_prime = polyder(P);

hip_velocity = polyval(P_prime,xx);

hip_velocity= [0 hip_velocity(4:96) 0];

figure;

grid on;

hold on

plot(x,hip_velocity,'b');

xlabel('Gait Cycle (%)')

ylabel('Hip Veloicty (rad/s)')

hold off

%hip accelaration

P_primeprime = polyder(P_prime);

hip_acceleration = polyval(P_primeprime,xx);

hip_acceleration= [hip_acceleration(3) hip_acceleration(4:96) hip_acceleration(3)];

figure;

grid on;

hold on

plot(x,hip_acceleration,'b');

xlabel('Gait Cycle (%)')

ylabel('Hip Accelartion (rad/s^2)')

hold off

xxx=linspace(0,1,95);

xxxx=linspace(0,1.02,98);

%KNEE

%knee angle

knee_angle = [0.141575 0.173390 0.208110 0.246116 0.286897 0.329180 0.370968 0.410155 0.445131 0.474860 0.498782 0.516788 0.529155 0.536236 0.538367 0.535901 0.529167 0.518466 0.504447 0.487239 0.466171 0.443262 0.418379 0.392150 0.365140 0.337819 0.310595 0.283848 0.257954 0.233173 0.209699 0.187784 0.167653 0.149496 0.133475 0.119758 0.108498 0.099792 0.093761 0.090577 0.090379 0.093314 0.099529 0.109094 0.122028 0.138319 0.157942 0.180881 0.207177 0.237052 0.251327 0.270526 0.304515 0.345870 0.392038 0.442991 0.498452 0.557778 0.620227 0.685252 0.752074 0.819330 0.885340 0.948415 1.007006 1.059808 1.105818 1.144343 1.174976 1.197558 1.212168 1.219045 1.218579 1.211167 1.197207 1.177086 1.151122 1.119633 1.082898 1.041178 0.994764 0.943959 0.889051 0.830301 0.767978 0.702337 0.633677 0.562432 0.489219 0.415088 0.341775 0.271665 0.207522 0.152104 0.107945 0.076989 0.060235 0.057484 0.067176 0.086535 0.112247];

P = polyfit(xx,knee_angle,6);

Y = polyval(P,xxx);

knee_angle=[Y(2:94) Y(1) Y(2)];

figure

grid on;

hold on

plot(xxx,knee_angle)

xlabel('Gait Cycle (%)')

ylabel('Knee Angle (rad)')

hold off

%knee velocity

P_prime = polyder(P);

knee_velocity = polyval(P_prime,xxxx);

knee_velocity= [knee_velocity(2:94) knee_velocity(1) knee_velocity(2)];

figure;

grid on;

hold on

plot(x,knee_velocity,'b');

xlabel('Gait Cycle (%)')

ylabel('Knee Veloicty (rad/s)')

hold off

%knee accelartion

P_primeprime = polyder(P_prime);

knee_acceleration = polyval(P_primeprime,xxxx);

knee_acceleration= [knee_acceleration(2:91) 149 140 100 knee_acceleration(1)+5 knee_acceleration(2)];

figure;

grid on;

hold on

plot(x,knee_acceleration,'b');

xlabel('Gait Cycle (%)')

ylabel('Knee Accelartion (rad/s^2)')

hold off

link1maxJ=(100/178)*42/100*height; %length of link 1 (thigh + joint length) [m]

link2maxJ=(100/178)*52/100*height; %length of link 2 (joint + leg length) [m]

%To find max and min link lengths for SW, irrelevant with the code

link1min=(100/178)*40/100*1.55;

link2min=(100/178)*45/100*1.55;

link1max=(100/178)*40/100*height;

link2max= (100/178)*45/100*height;

%PARAMETERS

normal_force = [27.838 55.676 83.514 111.352 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 111.352 83.514 55.676 27.838 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0];

friction_force= [13.919 27.838 41.757 55.676 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 55.676 41.757 27.838 13.919 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0];

% m11= 0.167*mass; %mass of total leg [kg]

ml1= 1.877; %mass of the thig link [kg]

ml2= 2.049; %mass of the shank link [kg]

mM1=0.5; %mass of the hip motor [kg]

mM2=0.5; %mass of the knee motor [kg]

m1= 0.105*mass + ml1 + mM1; %mass of thigh leg [kg]

m2= 0.0475*mass + ml2 + mM2; %mass of leg + foot [kg]

d1=link1max/2; % link1/2 [m]

d2=link2max/2; % link2/2 [m]

%MOMENT OF INERTIA

I1=1/3*m1*tighR^2;

I2=1/3*m2*legR^2; %rod moment of inertia [kg/m^2]

n=0;

torque1= [];

torque2= [];

force1= [];

force2= [];

force3= [];

force4= [];

for n= 0: length(hip_angle)-1

n= n+1;

q1= hip_angle(n);

q1d= hip_velocity(n);

q1dd= hip_acceleration(n);

q2= knee_angle(n);

q2d= knee_velocity(n);

q2dd= knee_acceleration(n);

f5= friction_force(n);

f6= normal_force(n);

syms T1 T2 f1 f2 f3 f4 ;

E1=m1*((-d1.*sin(q1).*q1d.^2)+(d1.*cos(q1).*q1dd))-(f2-f4);

E2=m1*((-d1.*cos(q1).*q1d.^2)-(d1.*sin(q1).*q1dd))-(f3-f1);

E3=T1+(f1*d1.*sin(q1))-(f2.*d1.*cos(q1))+(f3.*d1.*sin(q1))-(f4.*d1.*cos(q1))-(q1dd.*I1);

E4=m2*((-link1max.*sin(q1).*q1d.^2)+(link1max.*cos(q1).*q1dd)-(d2.*sin(q2).*q2d.^2)+(d2.*cos(q2).*q2dd))-(f4-f5);

E5=m2*((-link1max.*cos(q1).*q1d.^2)-(link1max.*sin(q1).*q1dd)-(d2.*cos(q2).*q2d.^2)-(d2.*sin(q2).*q2dd))-(f6-f3);

E6=T2+(f6*d2.*sin(q2))-(f5.*d2.*cos(q2))+(f3.*d2.*sin(q2))-(f4*d2.*cos(q2))-(q2dd.*I2);

[T1,T2,f1,f2,f3,f4]= solve(E3,E6,E2,E4,E5,E1);

torque1(end+1)=eval(T1); %Nm

torque2(end+1)=eval(T2);

force1(end+1)=eval(f1);

force2(end+1)=eval(f2);

force3(end+1)=eval(f3);

force4(end+1)=eval(f4);

end

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Answer 1

Sulaymon Eshkabilov 2022-12-30

There are several variables are not defined at all and thus, your set equations are not solviable as defined in your code, e.g.:

m1=?; m2=?;

d1=?; d2=?;

q1=?; q2 = ?;

q1d = ?;

q1dd=?;

I1 = ?;

I2 = ?; link1max = ?

...

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Bbb 2022-12-30

yes, i wouldn't want to add full code thinking it would be irrelevant if the answer is just a syntax. full code is

height= 1.85; %[m]

mass= 85; %[kg]

tighR=0.08; %[m]

legR= 0.05; %[m]

% x

gaitCycleDuration= 1.4; %[second]

x= linspace(0,1.0,95);

xx= linspace(0,1.00,101);

%HİP

%hip angle

hip_angle= [0.4136 0.4128 0.4121 0.4100 0.4047 0.3958 0.3831 0.3672 0.3485 0.3274 0.3047 0.2805 0.2553 0.2295 0.2030 0.1758 0.1484 0.1208 0.0932 0.0661 0.0396 0.0138 -0.0112 -0.0354 -0.0586 -0.0808 -0.1019 -0.1218 -0.1401 -0.1571 -0.1724 -0.1862 -0.1983 -0.2082 -0.2161 -0.2217 -0.2248 -0.2251 -0.2224 -0.2168 -0.2087 -0.1990 -0.1887 -0.1791 -0.1712 -0.1658 -0.1635 -0.1641 -0.1670 -0.1716 -0.1766 -0.1813 -0.1861 -0.1909 -0.1967 -0.2032 -0.2100 -0.2157 -0.2197 -0.2211 -0.2194 -0.2145 -0.2066 -0.1962 -0.1834 -0.1684 -0.1517 -0.1335 -0.1138 -0.0934 -0.0721 -0.0478 -0.0241 0.0002 0.0250 0.0497 0.0745 0.0990 0.1229 0.1461 0.1686 0.1901 0.2108 0.2306 0.2492 0.2667 0.2829 0.2978 0.3117 0.3245 0.3362 0.3471 0.3571 0.3665 0.3752 0.3831 0.3906 0.3972 0.4030 0.4077 0.4112];

P = polyfit(xx,hip_angle,6);

Y = polyval(P,xx);

hip_angle=[Y(3) Y(4:95) Y(3) Y(3)];

figure

grid on;

hold on

plot(x,hip_angle,'k');

xlabel('Gait Cycle (%)')

ylabel('Hip Angle (rad)')

hold off

%hip velocity

P_prime = polyder(P);

hip_velocity = polyval(P_prime,xx);

hip_velocity= [0 hip_velocity(4:96) 0];

figure;

grid on;

hold on

plot(x,hip_velocity,'b');

xlabel('Gait Cycle (%)')

ylabel('Hip Veloicty (rad/s)')

hold off

%hip accelaration

P_primeprime = polyder(P_prime);

hip_acceleration = polyval(P_primeprime,xx);

hip_acceleration= [hip_acceleration(3) hip_acceleration(4:96) hip_acceleration(3)];

figure;

grid on;

hold on

plot(x,hip_acceleration,'b');

xlabel('Gait Cycle (%)')

ylabel('Hip Accelartion (rad/s^2)')

hold off

xxx=linspace(0,1,95);

xxxx=linspace(0,1.02,98);

%KNEE

%knee angle

knee_angle = [0.141575 0.173390 0.208110 0.246116 0.286897 0.329180 0.370968 0.410155 0.445131 0.474860 0.498782 0.516788 0.529155 0.536236 0.538367 0.535901 0.529167 0.518466 0.504447 0.487239 0.466171 0.443262 0.418379 0.392150 0.365140 0.337819 0.310595 0.283848 0.257954 0.233173 0.209699 0.187784 0.167653 0.149496 0.133475 0.119758 0.108498 0.099792 0.093761 0.090577 0.090379 0.093314 0.099529 0.109094 0.122028 0.138319 0.157942 0.180881 0.207177 0.237052 0.251327 0.270526 0.304515 0.345870 0.392038 0.442991 0.498452 0.557778 0.620227 0.685252 0.752074 0.819330 0.885340 0.948415 1.007006 1.059808 1.105818 1.144343 1.174976 1.197558 1.212168 1.219045 1.218579 1.211167 1.197207 1.177086 1.151122 1.119633 1.082898 1.041178 0.994764 0.943959 0.889051 0.830301 0.767978 0.702337 0.633677 0.562432 0.489219 0.415088 0.341775 0.271665 0.207522 0.152104 0.107945 0.076989 0.060235 0.057484 0.067176 0.086535 0.112247];

P = polyfit(xx,knee_angle,6);

Y = polyval(P,xxx);

knee_angle=[Y(2:94) Y(1) Y(2)];

figure

grid on;

hold on

plot(xxx,knee_angle)

xlabel('Gait Cycle (%)')

ylabel('Knee Angle (rad)')

hold off

%knee velocity

P_prime = polyder(P);

knee_velocity = polyval(P_prime,xxxx);

knee_velocity= [knee_velocity(2:94) knee_velocity(1) knee_velocity(2)];

figure;

grid on;

hold on

plot(x,knee_velocity,'b');

xlabel('Gait Cycle (%)')

ylabel('Knee Veloicty (rad/s)')

hold off

%knee accelartion

P_primeprime = polyder(P_prime);

knee_acceleration = polyval(P_primeprime,xxxx);

knee_acceleration= [knee_acceleration(2:91) 149 140 100 knee_acceleration(1)+5 knee_acceleration(2)];

figure;

grid on;

hold on

plot(x,knee_acceleration,'b');

xlabel('Gait Cycle (%)')

ylabel('Knee Accelartion (rad/s^2)')

hold off

link1maxJ=(100/178)*42/100*height; %length of link 1 (thigh + joint length) [m]

link2maxJ=(100/178)*52/100*height; %length of link 2 (joint + leg length) [m]

%To find max and min link lengths for SW, irrelevant with the code

link1min=(100/178)*40/100*1.55;

link2min=(100/178)*45/100*1.55;

link1max=(100/178)*40/100*height;

link2max= (100/178)*45/100*height;

%PARAMETERS

normal_force = [27.838 55.676 83.514 111.352 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 139.19 111.352 83.514 55.676 27.838 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0];

friction_force= [13.919 27.838 41.757 55.676 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 69.595 55.676 41.757 27.838 13.919 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0];

% m11= 0.167*mass; %mass of total leg [kg]

ml1= 1.877; %mass of the thig link [kg]

ml2= 2.049; %mass of the shank link [kg]

mM1=0.5; %mass of the hip motor [kg]

mM2=0.5; %mass of the knee motor [kg]

m1= 0.105*mass + ml1 + mM1; %mass of thigh leg [kg]

m2= 0.0475*mass + ml2 + mM2; %mass of leg + foot [kg]

d1=link1max/2; % link1/2 [m]

d2=link2max/2; % link2/2 [m]

%MOMENT OF INERTIA

I1=1/3*m1*tighR^2;

I2=1/3*m2*legR^2; %rod moment of inertia [kg/m^2]

n=0;

torque1= [];

torque2= [];

force1= [];

force2= [];

force3= [];

force4= [];

for n= 0: length(hip_angle)-1

n= n+1;

q1= hip_angle(n);

q1d= hip_velocity(n);

q1dd= hip_acceleration(n);

q2= knee_angle(n);

q2d= knee_velocity(n);

q2dd= knee_acceleration(n);

f5= friction_force(n);

f6= normal_force(n);

syms T1 T2 f1 f2 f3 f4 ;

E1=m1*((-d1.*sin(q1).*q1d.^2)+(d1.*cos(q1).*q1dd))-(f2-f4);

E2=m1*((-d1.*cos(q1).*q1d.^2)-(d1.*sin(q1).*q1dd))-(f3-f1);

E3=T1+(f1*d1.*sin(q1))-(f2.*d1.*cos(q1))+(f3.*d1.*sin(q1))-(f4.*d1.*cos(q1))-(q1dd.*I1);

E4=m2*((-link1max.*sin(q1).*q1d.^2)+(link1max.*cos(q1).*q1dd)-(d2.*sin(q2).*q2d.^2)+(d2.*cos(q2).*q2dd))-(f4-f5);

E5=m2*((-link1max.*cos(q1).*q1d.^2)-(link1max.*sin(q1).*q1dd)-(d2.*cos(q2).*q2d.^2)-(d2.*sin(q2).*q2dd))-(f6-f3);

E6=T2+(f6*d2.*sin(q2))-(f5.*d2.*cos(q2))+(f3.*d2.*sin(q2))-(f4*d2.*cos(q2))-(q2dd.*I2);

[T1,T2,f1,f2,f3,f4]= solve(E3,E6,E2,E4,E5,E1);

torque1(end+1)=eval(T1); %Nm

torque2(end+1)=eval(T2);

force1(end+1)=eval(f1);

force2(end+1)=eval(f2);

force3(end+1)=eval(f3);

force4(end+1)=eval(f4);

end

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Answer 2

Sulaymon Eshkabilov 2022-12-30

在 MATLAB Online 中打开

If I have understood your question correctly, you are trying to save the equations. If this is the case, then you should amend your code with the followings:

...
    syms T1 T2 f1 f2 f3 f4 ;
E1(n)=m1*((-d1.*sin(q1).*q1d.^2)+(d1.*cos(q1).*q1dd))-(f2-f4);
E2(n)=m1*((-d1.*cos(q1).*q1d.^2)-(d1.*sin(q1).*q1dd))-(f3-f1);
E3(n)=T1+(f1*d1.*sin(q1))-(f2.*d1.*cos(q1))+(f3.*d1.*sin(q1))-(f4.*d1.*cos(q1))-(q1dd.*I1);
E4(n)=m2*((-link1max.*sin(q1).*q1d.^2)+(link1max.*cos(q1).*q1dd)-(d2.*sin(q2).*q2d.^2)+(d2.*cos(q2).*q2dd))-(f4-f5);
E5(n)=m2*((-link1max.*cos(q1).*q1d.^2)-(link1max.*sin(q1).*q1dd)-(d2.*cos(q2).*q2d.^2)-(d2.*sin(q2).*q2dd))-(f6-f3);
E6(n)=T2+(f6*d2.*sin(q2))-(f5.*d2.*cos(q2))+(f3.*d2.*sin(q2))-(f4*d2.*cos(q2))-(q2dd.*I2);
[T1,T2,f1,f2,f3,f4]= solve(E1(n),E2(n),E3(n),E4(n),E5(n),E6(n));
...
    

All your equations are stored under variables: E1, E2, ... E6.

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Bbb 2022-12-31

unfortunately no, like i said i don't want numeric value. i want T1 and T2 as equations in terms of E1,E2,...,E6's eqquations. For example T1= m2*link1max- sin(q1)... etc. Something like this.

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