Modeling and controller for Furuta Pendulum with Simulink, Matlab R2020a and Stateflow.
To compute the mathematical model of the pendulum, we refer to the figure below
The parameters measured in laboratory are:
- pendulum mass m_p = 0.3 kg
- pendulum length l_p = 0.205 m
- brace mass m_b = 1 kg
- brace length l_b = 0.3 m
- puntiform mass M = 1 kg
- inertial moment J = 0.1531 kg*m^2
- gravity g = 9.81 m*s^-2
For constant transduction:
- torque drive constant k = 2.7 Nm/V
- transduction drive constant k_i = 2.667 A/V
- gearbox transmission ratio k_g = 15
- motor torque constant k_t = 0.1 Nm/A
For frictions:
- viscous friction on brace b_phi = 0.337 Nms/rad
- viscous friction on brace p_theta = 0.035 Nms/rad
This parameters are declared in callbacks of simulink model.
We use second species Lagrange equations
obtain the following dynamic model
with
implemented as
the model obtained is
Use model "furuta_check" to verify the correctness with measurements made in laboratory.
Linearizing around null theta angle, obtain follow function transfer,
Utilizing the PID-Tuner obtain follow PID controller
and the firs controller to mantein null theta angle
For Swing-Up problem, the idea has been that of to introduce a wave signal for motor and a control for monitoring theta angle.
using stateflow, implement an alternative mode of swing-up controller
