How do I use Simulink to create a control system with a 2nd order ODE?

[PhysicsLearner2000]

Homework Statement

I need help in MATLAB simulink tool. How do I use Simulink to create a control system to express a 2nd order differential equation?

Relevant Equations

D(theta) theta'' + C(theta,theta')theta' + G(theta) + F(theta') = Torque

Equation:

, where matrix D, C, G and F can be represented by

I'm supposed to design a control system that looks like this:

I am given that the dynamic model = fcn(D,C,G,dq) where the dq is the same as 𝑞̇ and d2q in the diagram is the same 𝑞̈. The default initial value of [𝑞(0), 𝑞̇(0)] is [0, 0].

My code is here:

function torque = fcn(D,C,G,theta,omega)

% length of the 2 robotic arms

l1 = 1;

l2=1;

r1=l1/2;

r2=l2/2;

% mass of the 2 robotic arms

m1= 5;

m2=5;

% moment of inertia of the 2 robotic arms

I1= (m1*l1^2)/3;

I2 = (m2*l2^2)/3;

p1= m1*r1^2+m2*l1^2+I1;

p2= m2*r2^2+ I2;

p3= m2*l1*r2;

p4= m1*r1+m2*l1;

p5= m2*r2;

% gravitational field strength

g = 9.81

D(theta) = [p1+p2+2*p3*cos(theta(2)) p2+p3*cos(theta(2)); p2+p3*cos(theta(2)) p2];

C(theta, omega) = [-p3*omega(2)*sin(theta(2)) -p3*(omega(1)+omega(2))*sin(theta(2)); p3*omega(1)*sin(theta(2)) 0];

G(theta) = [p4*g*theta((1))+ p5*g*cos(theta(1)+theta(2)); p5*g*cos(theta(1)+theta(2))];

F(omega) = 0

dthetadt = omega;

domegadt = D(theta)\(tau-F(omega)-G(theta)-C(theta,omega)*omega);

% Define Conditions

theta(1) = linspace(0, pi/2,10);

theta(2) = linspace(0,pi/2,10);

Is my code correct? And how to create a control system to represent the 2nd ode equation. Can someone help me? I'm pretty new to SimuLink and Matlab

I need help with SimuLink. It is not working. I need help

 

[Valkarie]

with creating a control system to represent this second ODE equation.First, you should create a Simulink model and insert your ODE equation into it. Make sure to include the necessary blocks for the inputs (D,C,G,dq), outputs (torque), and initial conditions (q(0), dq(0)). You can then add the appropriate blocks for any control system components that you need, such as gain blocks or transfer functions. Finally, you can connect them to the appropriate inputs and outputs, and adjust the parameters of the blocks to get the desired control system.