angelodamante/furuta_pendulum

Model the Furuta Pendulum with Simulink and Matlab.

Furuta Pendulum

Modeling and controller for Furuta Pendulum with Simulink, Matlab R2020a and Stateflow.

Main for complete system

System description

To compute the mathematical model of the pendulum, we refer to the figure below

Parameters of model

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.

Motion Equations

We use second species Lagrange equations

obtain the following dynamic model

with

implemented as

Explicit angles

the model obtained is

State Simulation

Use model "furuta_check" to verify the correctness with measurements made in laboratory.

Transfer Function

Linearizing around null theta angle, obtain follow function transfer,

PID controller

Utilizing the PID-Tuner obtain follow PID controller

and the firs controller to mantein null theta angle

Swing-Up

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