Inverted Pendulum Project

This project was used along side studying my Engineering degree specialising in Electronics to learn about control theory and physics in a practical way.

#explain the control theory prolem The inverted pendulum or cart pole is a classic problem in control theory.

#hardware and material requirements

-PLA driven by a DC motor via a toothed belt -3D printer

-rotary encoder opposite the motor (acts as a pulley for the belt and allows us to track the motion of the cart) -second rotary encoder on the cart is a pivot for the pole and measures its angle.

-The motor is controlled by a 32 amp Sabertooth motor controller.

-Monitored the encoders with an Arduino.

piece of extruded aluminum rail called V-Slot, (1.5 m long)

Materials

-V-Slot Linear Rail – 20x20mm - Clear Anodise, 1500mm

-Wisamic Incremental Rotary Encoder Dc5-24V Wide Voltage Power Supply Shaft 6Mm x 2

-20-teeth timing pulley wheel + 5m GT2 toothed belt

-ARDUINO MEGA 2560 REV3 [A000067]

-ICQUANZX DC Gear Motor 12V 200R High Torque Electric Micro Speed Reduction Geared Motor Centric Output Shaft Diameter Gearbox

-L298N DC Motor Driver Module

Method

-The rotary encoders were monitored by an Arduino Uno -Two different controllers (one to pump energy into the system and swing the cart into the upright position, and an linear quadratic regulator to balance it upright) -Python program contains commands the motor controller over serial and can query the Arduino whenever it needs to know the state of the system.

#LQR Controller

-linear quadratic regulator or LQR controller.

Arduino

// Motor A connections int enA = 9; int in1 = 8; int in2 = 7;

// This function lets you control spinning direction of motors void directionControl() { // Set motors to maximum speed // For PWM maximum possible values are 0 to 255 analogWrite(enA, 255);

Pole Rotary Encoder

#define CLK 2 #define DT 3 #define SW 4

DT (Output B) is the same as the CLK output, but it lags the CLK by a 90° phase shift. This output can be used to determine the direction of rotation.

CLK (Output A) is the primary output pulse for determining the amount of rotation. Each time the knob is rotated by one detent (click) in either direction, the ‘CLK’ output goes through one cycle of going HIGH and then LOW.

Math

-q is the position of the cart -θ is the angle of the pole counter-clockwise from vertical -f is the force on the cart -A and B are matrices that define the dynamics -Q and R are matrices that define the cost.