Recent content by Remusco

All I'm trying to do is replicate this YouTube tutorial, but for a uniform pendulum rod, not a point mass...

The physical model result is from my physical rotary inverted pendulum. It is the data I collected with my Arduino. The simulated as shown in the plot is the result from the Newtonian equations. Here I now solve the Newtonian equations for theta_ddot:

Here are the Newton's equations: $$ -T \sin{\left(\theta \right)} - b \theta_{dot} \cos{\left(\theta \right)} - m_{p} x_{ddot} - \frac{1}{2} L m_{p} \cos{\left(\theta \right)} \theta_{ddot} + \frac{1}{2} L m_{p} \theta_{dot}^{2} \sin{\left(\theta \right)} = 0$$ $$-T \cos{\left(\theta \right)} -...

I'm directly controlling phi with my stepper motor. The position, velocity, acceleration. The dynamics of phi are whatever I want them to be, and I'm assuming that the stepper is rigid and does not slow down under changes in torque, which is a valid assumption. This reduces the DOF by one...

Thanks for sending that to me. Great resource. However, I used the exact results in the paper and this is what i get. Still the same thing is happening: import sympy as sp # === Step 1: Define all symbolic variables === theta1, theta2 = sp.symbols('theta1 theta2') theta1_dot, theta2_dot =...

I have built this inverted pendulum system (powered by a stepper motor). I define theta to be the pendulum angle 0 degrees in the vertical position, phi is the motor arm angle. When I let the physical pendulum go at theta = 90 degrees, with the stepper motor turned off, I get: Now if I...

Yes this is what I am looking for. Thanks for clarifying.

I looked all over the internet and I can't find a derivation of this. It is over my head to derive this. This is my system: I want to assume that the pendulum and motor arm are uniform rods. I want to ignore the motor shaft inertia and the rotary encoder inertia since they are negligible. Does...

No, I wrote all of this myself. The only thing I'm not sure about are the inertias.

# System Parameters m_p = 0.1 # Mass of pendulum (kg) m_a = 0.5 # Mass of arm (kg) l_p = 0.2 # Length of pendulum (m) l_a = 0.15 # Length of arm (m) g = 9.81 # Gravity (m/s^2) b = 0.00 # Damping coefficient I_a = (1/3) * m_a * l_a**2 # Arm moment of inertia I_p = (1/3) * m_p *...

I am getting really good results now with this code: import numpy as np import matplotlib.pyplot as plt # System Parameters m_p = 0.1 # Mass of pendulum (kg) m_c = 0.5 # Mass of arm (kg) l_p = 0.2 # Length of pendulum (m) l_a = 0.15 # Length of arm (m) g = 9.81 # Gravity (m/s^2) b =...

I need help calculating inertias for a rotary inverted pendulum system (Furuta pendulum). This is for a school project. The pendulum is a unform rod, and the motor arm is a unform rod. The equations of motion are: Where theta is the angle of the pendulum (0 degrees is in vertical position)...

Do you think my calculation for the inertia seen by the motor shaft is correct? Isn't this just J_p or should this be J_p + m_p*r_a**2?