Basis of Control Theory

Chris Hung (Rocket and Optimization)

Tutoring method

Structure

Concept
Overview
Thesis
Application
Current situation
Solving Problems or Implementation
Homework
Preview of future lessons

The lesson will surround applications in space engineering

You can search for the papers I cited
Please ask anytime you don't understand

What is Control system

Mathematical modeling

Think of the world in terms of dynamic system
Represent it with Differential Equations
e.g.
- Romantic relationship
- Spread of COVID-19
- Rocket equation
- Schrödinger equation
Humans not only want to predict the model but also manipulate it.
=> Control System

https://www.weforum.org/agenda/2022/02/covid-19-top-news-omicron-coronavirus-7-february-2022/

https://en.wikipedia.org/wiki/Sigmoid_function

Dynamic mathematic model for the free flight phase of a sounding rocket

Peng W, Zhang Q, Yang T, Feng Z. A high-precision dynamic model of a sounding rocket and rapid wind compensation method research. Advances in Mechanical Engineering. July 2017. doi:10.1177/1687814017713944

An overview of Control Theory

Actively
- Impose some control logic in a certain preplanned way
- Black box method: Measure the system and make decisions based on the system response to what you input
Passively
- System optimization
- e.g., Attack angle for winds of a rocket

An overview of Control Theory

Open-loop

Requires constant input of energy
if not, the system will become unstable
The system must be totally certain in order to preplan

Closed-loop feedback control

Requires sensors to measure the output
feedback the error to the controller
Why feedback?
- Instability
- Uncertainty
- Disturbance
- Efficient

System Structure

https://www.samsongroup.com/document/l101en.pdf

Simple feedback control systems

Their control device is made of the controller only
They are the most classic ones in the field of adaptive control.
However, in the case of non-adaptive neural control, since the quality of their performance relies heavily on the fidelity of the model used for the design of the controller, they can only be used if the model is very accurate and if the effect of disturbances is small.

Internal model control systems

They are characterized by a control device consisting of the controller and of a predictive model of the process, the internal model.
The internal model loop uses the difference between the outputs of the process and of the internal model. This difference represents the effect of disturbances and of a mismatch of the model.

www.mathworks.com

Rivals, Isabelle & Personnaz, Léon. (2000). Nonlinear Internal Model Control using Neural networks : application to Processes with Delay and Design Issues. IEEE transactions on neural networks / a publication of the IEEE Neural Networks Council. 11. 80-90. 10.1109/72.822512.

Homework: Memorize these terms

https://www.srecwarangal.ac.in/ece-itl/CS%20SUMMARY.pdf

The Map of Control Theory

https://engineeringmedia.com/map-of-control

Map of satellite GNC

https://doi.org/10.1016/j.actaastro.2015.10.010

Peter Z. Schulte, David A. Spencer, Development of an integrated spacecraft Guidance, Navigation, & Control subsystem for automated proximity operations, Acta Astronautica, Volume 118, 2016, Pages 168-186, ISSN 0094-5765, https://doi.org/10.1016/j.actaastro.2015.10.010.

Application of Guidance & Control

Guidance and Control

a branch of engineering dealing with the design of systems to control the movement of vehicles, especially, automobiles, ships, aircraft, and spacecraft.

Guidance refers to the determination of the desired path of travel (the "trajectory") from the vehicle's current location to a designated target, as well as desired changes in velocity, rotation and acceleration for following that path.
Control refers to the manipulation of the forces, by way of steering controls, thrusters, etc., needed to execute guidance commands while maintaining vehicle stability.

https://en.wikipedia.org/wiki

GNC Engineer Salaries in the U.S.

Median annual earnings at $41,535 in 2020 for workers aged 15 and over with earnings and $56,287 in 2020 for those who worked full-time, year-round.