Double Inverted Pendulum

2020-12-03T12:04:44Z

BarendCoetzee: Created page with "== Introduction == This control rig consists of a cart on a linear rail that can moved in 1D by using DC motor. The cart has a free moving arm attached to it, an angle encoder..."

== Introduction ==
This control rig consists of a cart on a linear rail that can moved in 1D by using DC motor. The cart has a free moving arm attached to it, an angle encoder is used to measure the angle between the cart and the first arm.
A second arm is attached to the end of the first arm, a second angle encoder is used to measure the angle between the first and second arm. Where these two angles are used to calculate the control moves to bring to stability.

==2020 - Bernard Coetzee==
'''Build'''
[[File:3D_Model.png|500px|left|thumb]]

The rig was built by previous students, where the base consists of a wooden board and the rest of the structured is made from polycarbonate sheet.

A Raspberry Pi 3 is used to perform all the input and output operations to and from the process, as well as computational tasks. The inputs to this system consist of the following:
# Distance to end of board, busing a time of flight (IR) sensor
# Angle between the cart and the first arm
# Angle between the first and second arm

These are then used to determine the control moves by moving the cart. This is accomplished by using the DC (MWP) motor.

All control measurement and control operations are carried out using Python 3 on the Raspberry Pi. To control the DC motor an Arduino shield is used.

'''Modelling'''

Since this rig is inherently unstable, the system needs to be modelled in order with the aim of moving the zeros from the RHP to the LHP. In this case the MV is the movement of the cart by means of the DC motor, thus the motor's direction and duty cycle. Since this system is non-linear and step test is not a practical method of obtaining a system model, a mathematical model had to be derived from first principals using the Lagrange method.
This yielded a state space representation of the system which could be used in Python to implement the controller.

'''Control'''
Several controllers were implemented with increasing levels of complexity. The first controller was a (PI) Proportional Integral controller, with only the first arm. This was to firstly test and validate all the different component could communication and their values historized, and secondly to get a grip on the controllability of the system. The PI controller worked but had very poor disturbance rejection abilities.
Once this was completed, An MPC controller was designed for the single arm, and then for both the single arm and for two arms. It was found that the time required to get the MPC output is to long to be practical

PMC Lab

2020-12-03T12:02:43Z

BarendCoetzee: /* Rigs */

The Process Modelling & Control lab currently contains five working rigs. The [[Opto 22]] unit is usually refered to as the sixth rig. Equipment on the rigs (and in the lab) is discussed in the lab equipment section. The lab manual is available [[Media:labmanual.pdf| here]]. New users wanting to set up computers and software should have a look at [[PMC Lab Users|this page]].

== Rigs ==
For the rigs in the Tribology labs, see [[Tribology|this page]].

<big>'''[[Acetone Flashing]]'''</big>

The acetone flashing rig is a four by four control problem. You can find the documentation [https://drive.google.com/open?id=197S7vxDqJp_X41LAvZFYRfnl9P7wuSnb here].

<big>'''[[pH Loop]]'''</big>

This rig demonstrates pH control. You can find the documentation [https://drive.google.com/open?id=19L2OCUjSNSugsQk4jKBRBbkjbt11HVza here].

<big>'''[[Temperature Control]]'''</big>

The temperature control rig was rebuilt by Ivan and David in 2005. You can find the documentation [https://drive.google.com/open?id=1JbOB6-6fxGMyvYjgvlBAwYgiqd97Yfwq here].

<big>'''[[Level and Flow]]'''</big>

Level and Flow is one of our favourite rigs. You can find the documentation [https://drive.google.com/open?id=1XHBrkO8PCHQKCRljF4-D0qIjiQCUUhpe here].

<big>'''Distillation Columns'''</big>

There are two distillation columns in the chemical engineering laboratories;
* documentation for the [[small distillation column]] (in the PM&C lab) can be found [https://drive.google.com/open?id=1A2yNQfkMiBDit-BQ9CCWk5oqQ182NL5G here].
* information on the column [[big distillation column]] (between the 3rd year labs and the PM&C lab) .
<big>'''[[Slug Flow]]'''</big>

This unit, copied from a setup done by Ingvald Bårdsen under supervision of Espen Storkaas and Heidi Sivertsen at [http://www.ntnu.no/indexe.php NTNU], models severe slugging behaviour in a pipeline/riser system.
* the original information is hosted at http://www.nt.ntnu.no/users/skoge/diplom/prosjekt03/bardsen/ (this will, if anything, improve your Norwegian)
* our lab documentation is available [https://drive.google.com/open?id=1cOBXPwDX-QkzQmU1M2OXC6oWKena9lPs here].

<big>'''[[Dual Fluidised Bed System]]'''</big>

This unit, intended to produce bio-oils from woody biomass, is still under construction by Stephen Swart and Prof. Heydenrych. It is intended to be completed by 2012, with the design outlined in [https://drive.google.com/open?id=1aSxt4bjZz08prpvXHOf-uvAIFtDC_elU Swart (2010)]. The documentation can be found [https://drive.google.com/open?id=1QNU4wAVI8ehaXwKxTsR5li5O6n2Jr36s here].

<big>'''[[Ball and Plate Control Rig]]'''</big>

This rig is a rapid prototyping and test unit for control systems, consisting of the task of stabilisation and reference tracking of an open loop unstable system.

<big>'''[[Quadcopter]]'''</big>

Implement an Arduino Uno based control system to stabilise the quadcopter in a hover position.

<big>'''[[Bioreactor]]'''</big>

This rig is part of a joint effort between the Bioreaction Engineering group and the PM&C group. The reactor produces fumaric acid from glucose in a continuous process using <i> Rhizopus oryzae </i>.

<big>'''[[Double Inverted Pendulum ]]'''</big>

This rig consists of a cart on a linear rail that can move in 1D by using a DC motor. The cart has a free moving arm attached to it, an angle encoder is used to measure the angle between the cart and the first arm.
A second arm is attached to the end of the first arm, a second angle encoder is used to measure the angle between the first and second arm. Control is implemented on a Raspberry Pi 3, with the aim of balancing the two arms in the vertical position.

== Lab equipment ==

Equipment for the rigs are (should be) documented on their respective pages. Some additional equipment in the PMC lab include;
* [[PMC testing equipment|Testing equipment]]

== Contact Details ==

<big>'''[[Burkett Valves]]'''</big>

<big>'''[[Opto Controls]]'''</big>

<big>'''[[Mantech Electronics]]'''</big>

Chemical Engineering @ UP wiki - User contributions [en]

Double Inverted Pendulum

PMC Lab