# Control theory

Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required. This controller monitors the controlled process variable (PV), and compares it with the reference or set point (SP). The difference between actual and desired value of the process variable, called the error signal, or SP-PV error, is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point. Other aspects which are also studied are controllability and observability. Control theory is used in control system engineering to design automation that have revolutionized manufacturing, aircraft, communications and other industries, and created new fields such as robotics. Extensive use is usually made of a diagrammatic style known as the block diagram. In it the transfer function, also known as the system function or network function, is a mathematical model of the relation between the input and output based on the differential equations describing the system. Control theory dates from the 19th century, when the theoretical basis for the operation of governors was first described by James Clerk Maxwell. Control theory was further advanced by Edward Routh in 1874, Charles Sturm and in 1895, Adolf Hurwitz, who all contributed to the establishment of control stability criteria; and from 1922 onwards, the development of PID control theory by Nicolas Minorsky.Although a major application of mathematical control theory is in control systems engineering, which deals with the design of process control systems for industry, other applications range far beyond this. As the general theory of feedback systems, control theory is useful wherever feedback occurs - thus control theory also has applications in life sciences, computer engineering, sociology and operations research. (Wikipedia).

Everything You Need to Know About Control Theory

Control theory is a mathematical framework that gives us the tools to develop autonomous systems. Walk through all the different aspects of control theory that you need to know. Some of the concepts that are covered include: - The difference between open-loop and closed-loop control - How

From playlist Control Systems in Practice

!!Con West 2019 - Wesley Aptekar-Cassels: Robots, rockets, and more! Control theory in 10 minutes!

Presented at !!Con West 2019: http://bangbangcon.com/west Control theory is a branch of science and engineering dedicated to understanding and analyzing systems, how they respond to input, and how to control them. Learning about control theory has changed the way I view the world — having

From playlist !!Con West 2019

Ludovic Rifford : Geometric control and dynamics

Abstract: The geometric control theory is concerned with the study of control systems in finite dimension, that is dynamical systems on which one can act by a control. After a brief introduction to controllability properties of control systems, we will see how basic techniques from control

Transfer Functions: Introduction and Implementation

In this video we introduce transfer functions and show how they can be derived from a set of linear, ordinary differential equations. We also examine how to use a transfer function to predict the output of system to a given input. Topics and time stamps: 0:38 – Example using an aircraft

From playlist Control Theory

What Is PID Control? | Understanding PID Control, Part 1

Chances are you’ve interacted with something that uses a form of this control law, even if you weren’t aware of it. That’s why it is worth learning a bit more about what this control law is, and how it helps. PID is just one form of feedback controller. It is the simplest type of contro

From playlist Understanding PID Control

Eigenvalues and Modes of Linear Systems

In this video we discuss how the eigenvalues of the A matrix lead to the modes of a linear state space system. We will also examine how to chose initial conditions to excite a specific mode. In other words, we use a carefully chosen initial condition to ensure that the state response of

From playlist Control Theory

Control Theory and COVID-19: Sensors

Follow on Twitter: https://twitter.com/eigensteve This video will discuss the critical importance of sensors in controlling COVID-19, along with several current measurement strategies. Website: https://www.eigensteve.com/ Acknowledgements: Consultation and Information: Bing Brunton Pro

From playlist Control Theory and COVID-19

What Control Systems Engineers Do | Control Systems in Practice

The work of a control systems engineer involves more than just designing a controller and tuning it. Over the course of a project, designing the controller might be a relatively small part of your day-to-day job. Depending on the size and phase of the project, your responsibilities and the

From playlist Control Systems in Practice

Controllability of a Linear System: The Controllability Matrix and the PBH Test

In this video we explore controllability of a linear system. We discuss two methods to test for controllability, the controllability matrix as well as the PBH test. Topics and time stamps: 0:00 – Introduction and definition. 1:04 – Controllability of a dog. 3:48 – Controllability matrix.

From playlist Control Theory

Control Theory and COVID-19: Summary

Follow on Twitter: https://twitter.com/eigensteve This video will summarize the COVID-19 and control theory series, providing some key takeaways. Website: https://www.eigensteve.com/ Acknowledgements: Consultation and Information: Bing Brunton Production and Editing: Derek Franz Reso

From playlist Control Theory and COVID-19

Optimal control of spin systems with applications in (...) - D. Sugny - Workshop 2 - CEB T2 2018

Dominique Sugny (Univ. Bourgogne) / 05.06.2018 Optimal control of spin systems with applications in Magnetic Resonance Optimal control can be viewed as a generalization of the classical calculus of variations for problems with dynamical constraints. Optimal control was born in its modern

Control Theory and COVID-19

Follow updates on Twitter: https://twitter.com/eigensteve This series describes a control theory perspective on efforts to manage the COVID-19 pandemic. I will discuss the role of models, the importance of extensive and rapid measurements, and how these imperfect models and measurements

From playlist Control Theory and COVID-19

Marxist Philosophy - Bryan Magee & Charles Taylor (1978)

In this program, Charles Taylor discusses Marxist philosophy with Bryan Magee. This is from a 1977-1978 series on Modern Philosophy called Men of Ideas. You can find more interviews in this series here: https://www.youtube.com/playlist?list=PLhP9EhPApKE9Wx2lorEbG_e6UZJgEW9Vx You can also

Ruzena Bajcsy: "History of Modeling Driving and Drivers Using Control Theory and Safety"

Mathematical Challenges and Opportunities for Autonomous Vehicles 2020 Workshop II: Safe Operation of Connected and Autonomous Vehicle Fleets "History of Modeling Driving and Drivers Using Control Theory and Safety" Ruzena Bajcsy - University of California, Berkeley (UC Berkeley), CITRIS

EEVacademy #6 - PID Controllers Explained

David explains PID controllers. First part of a mini-series on control theory. Forum: http://www.eevblog.com/forum/blog/eevacademy-6-pid-controllers-explained/ EEVblog Main Web Site: http://www.eevblog.com The 2nd EEVblog Channel: http://www.youtube.com/EEVblog2 Support the EEVblog throu

Peter E. Caines: Graphon Mean Field Games and the GMFG Equations

Very large networks linking dynamical agents are now ubiquitous and there is significant interest in their analysis, design and control. The emergence of the graphon theory of large networks and their infinite limits has recently enabled the formulation of a theory of the centralized contr

From playlist Probability and Statistics

Control Theory and COVID-19: Control Design

Follow on Twitter: https://twitter.com/eigensteve This video will discuss several aspects of the COVID-19 control problem, including model predictive control, robustness, and the challenge of time delays in the system. Website: https://www.eigensteve.com/ Acknowledgements: Consultation

From playlist Control Theory and COVID-19

Quantum simulation of lattice gauge theories - requirements, challenges and methods by Erez Zohar

PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (II

From playlist NUMSTRING 2022

!!Con West 2019 - Wesley Aptekar-Cassels: Robots, rockets, and more! Control theory in 10 minutes!

Presented at !!Con West 2019: http://bangbangcon.com/west Control theory is a branch of science and engineering dedicated to understanding and analyzing systems, how they respond to input, and how to control them. Learning about control theory has changed the way I view the world — having

From playlist !!Con West 2019