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Control of Inverted Pendulum System (Real Time)

 Inverted pendulum


The rotary pendulum device is shown in Fig1 below. The motor is mounted vertically in a metal chamber. An L-shaped arm is connected to the motor shaft and pivots between ±180 degrees. A pendulum is suspended on a horizontal axis at the end of the arm. The pendulum angle is measured by an encoder. The control variable is the input voltage to the pulse-width modulated amplifier that drives the motor. The output variables are the angle of the pendulum and the angle of the motor.


Fig1. The QNET rotary pendulum control trainer (ROTPENT).




 General Overview

The photograph in Figure2 shows an overview and the general layout of the QNET Rotary Pendulum Control Trainer (ROTPENT) system.

Fig 2. General layout of QNET ROTPENT



Fig 3. Components of QNET-ROTPENT pendulum assembly.



The ROTPENT components in Figure 2 and Figure 3 are located and identified by a unique ID in Table 1


Description                         ID         Description                                                                      
1 DC motor 8 Pendulum link
 2 High-resolution encoder that measured arm angle 9 Pendulum weight
3 Motor metal chamber 10 PCI connector to NI ELVIS: for interfacing QNET module with DAC.
4 Rotary arm pivot 11 QNET PWM/Encoder board
5 Rotary arm 12 24V bulk power jack
6 Pendulum encoder 13 Fuse
7 Pendulum pivot 14 +B, +15V, -15V, +5V LEDs




The specifications of the ROTPENT system model parameters are given in Table 2.

Value Unit
Rm Motor armature resistance. 3.30 ohms
Kt Motor torque constant. 0.0280 N.m
Km Motor back-emf constant (same as Kt in SI units). 0.0280 V/(rad/s)
Jm Moment of inertia of motor rotor. 9.64e-6 kg.m2
Jeq Equivalent moment of inertia about motor shaft pivot axis. 1.23e-4 kg.m2
Marm Mass of the arm. 0.0280 kg
r Length of arm pivot to pendulum pivot. 0.0826 m
Beq Arm viscous damping. 0.000 N.m/(rad/s)
Mp Mass of the pendulum link and weight combined. 0.0270 kg
Lp Total length of pendulum. 0.191 m
lp Length of pendulum center of mass from pivot 0.153 m
Jp Pendulum moment of inertia about its pivot axis. 1.20e-4 kg.m2
Bp Pendulum viscous damping. 0.000 N.m/(rad/s)


 There are two experiments: simple modeling and swing-up control. The experiments can be performed independently.





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