Everything You Need to Know About Control Theory

Summary

El vídeo explica la teoría de control, esencial para diseñar sistemas autónomos. Se discuten métodos de control abierto y cerrado, la importancia de los modelos matemáticos, y cómo se aplican para controlar dinámicamente diferentes sistemas. Se exploran controladores como PID y controladores no lineales, así como técnicas de planificación y estimación de estado. El vídeo también destaca la necesidad de análisis y simulación para garantizar que los sistemas cumplan con los requisitos deseados.

Takeaways

• 🧠 La teoría de control es un marco matemático que proporciona herramientas para desarrollar sistemas autónomos.
• 🚗 Un sistema dinámico es algo que queremos controlar automáticamente, como un edificio, una columna de destilación o un automóvil.
• 🔄 Los sistemas pueden verse afectados por entradas controladas (U) y perturbaciones no deseadas (D).
• 🔄 Un controlador de retroalimentación (o de bucle cerrado) utiliza tanto la referencia como el estado actual del sistema para determinar las entradas de control apropiadas.
• 🔄 Los controladores de avance (o de bucle abierto) generan la señal de control sin necesidad de medir el estado real del sistema.
• 🔄 Los modelos matemáticos son cruciales para casi todos los aspectos de la teoría de control, ya que se utilizan para el diseño de controladores, estimación de estado, planificación y análisis.
• 🔍 La identificación del sistema se puede realizar mediante principios físicos o a través de datos para ajustar un modelo a los datos.
• 🔄 El control de retroalimentación es un mecanismo auto-corregido que puede hacer que un sistema sea más estable, pero también puede cambiar su dinámica y estabilidad.
• 🛠 Hay una variedad de tipos de controladores de retroalimentación, como los controladores lineales, no lineales, robustos, adaptativos, óptimos, predictivos e inteligentes.
• 📈 La planificación es esencial para definir la referencia que el controlador debe seguir, y es donde se determina qué debe hacer el sistema.
• 🔬 La estimación de estado es necesaria para manejar las mediciones ruidosas y garantizar que el controlador tenga una estimación precisa del estado del sistema.

Q & A

¿Qué es la teoría de control y cómo se relaciona con la creación de sistemas autónomos?

La teoría de control es un marco matemático que proporciona herramientas para desarrollar sistemas autónomos, como un automóvil que conduce solo, un edificio con control de temperatura o una columna de destilación eficiente.

¿Cuáles son las dos fuentes de entradas que afectan a un sistema dinámico en la teoría de control?

Las dos fuentes de entradas son las entradas de control (U), que son intencionadas para afectar el sistema, y las perturbaciones (D), que son fuerzas no deseadas que afectan al sistema.

¿Qué es un controlador de bucle abierto y cómo funciona?

Un controlador de bucle abierto, también conocido como controlador de retroalimentación directa, toma la referencia (R) de lo que se desea que haga el sistema y genera la señal de control sin necesidad de medir el estado actual del sistema.

¿Por qué pueden ser necesarios modelos matemáticos en la teoría de control?

Los modelos matemáticos son necesarios para entender y predecir el comportamiento del sistema, diseñar controladores, estimar el estado del sistema, planificar y analizar el rendimiento y la estabilidad del sistema.

¿Qué es un controlador de retroalimentación y cómo difiere de un controlador de bucle abierto?

Un controlador de retroalimentación, o bucle cerrado, utiliza tanto la referencia como el estado actual del sistema para determinar las entradas de control. Esto difiere del controlador de bucle abierto, que no necesita medir el estado actual del sistema.

¿Qué son los controladores lineales y no lineales y cuándo se usan?

Los controladores lineales, como el PID y la retroalimentación de estado completo, se usan cuando se asume que el comportamiento general del sistema es lineal. Los controladores no lineales, como los controladores de encendido/apagado y el control de modo deslizante, se utilizan cuando el sistema no es lineal.

¿Qué es la planificación en el contexto de la teoría de control y por qué es importante?

La planificación es el proceso de determinar un plan o ruta para que el sistema siga, considerando obstáculos, reglas y capacidades físicas. Es importante porque el controlador necesita un plan para generar comandos que lleven al sistema a cumplir sus objetivos.

¿Qué es la estimación de estado y por qué es crucial en los sistemas de retroalimentación?

La estimación de estado es el proceso de determinar el estado actual del sistema a partir de mediciones con ruido. Es crucial porque los controladores de retroalimentación necesitan conocer el estado del sistema para ajustar las entradas de control de manera efectiva.

¿Cómo se puede analizar y simular un sistema controlado para garantizar que cumpla con los requisitos?

Se pueden usar herramientas de análisis, como diagramas de Bode, gráficos de Nyquist y simulaciones en Matlab y Simulink, para verificar la estabilidad, el rendimiento y asegurar que el sistema funcione según lo previsto.

¿Cuáles son algunas técnicas de control que se mencionan en el guion y cómo se relacionan con diferentes tipos de sistemas?

Se mencionan técnicas como el control PID, el control de ganancia programada, el control fuzzy, el aprendizaje por refuerzo, el control predictivo y el control inteligente. Estas técnicas se relacionan con diferentes sistemas dependiendo de sus características, la presencia de incertidumbre y las necesidades específicas de control.

Outlines

00:00

🔍 Introducción a la Teoría de Control

Este párrafo introduce la teoría de control como un marco matemático esencial para el desarrollo de sistemas autónomos. Se describe cómo la teoría de control puede ser aplicada a diferentes sistemas, como un automóvil, un edificio o una columna de destilación. Se explica que los sistemas pueden ser afectados por entradas controladas (como el volante o el acelerador en un automóvil) y por disturbios no deseados (como el viento o las imperfecciones en la carretera). Además, se plantea la pregunta de cómo un algoritmo puede determinar las entradas de control necesarias sin conocer constantemente el estado actual del sistema.

05:01

🔧 Control de Bucles Abiertos y Bucles Cerrados

Se contrastan los controladores de bucles abiertos (también conocidos como controladores de retroalimentación directa) con los controladores de bucles cerrados (control de retroalimentación o control de retroalimentación). Los controladores de bucles abiertos toman una referencia y generan una señal de control sin medir el estado real del sistema, mientras que los controladores de bucles cerrados utilizan tanto la referencia como el estado actual del sistema para determinar las entradas de control. Se discuten las ventajas y desventajas de cada tipo de control, y se enfatiza la importancia de comprender la dinámica del sistema y el entorno para implementar un control efectivo.

10:01

🛠 Diversidad en los Métodos de Control de Retroalimentación

Este párrafo explora la variedad de algoritmos de control de retroalimentación, que van desde controladores lineales como el PID y el retroalimentación de estado completo hasta controladores no lineales como los controladores de encendido/apagado y los controladores de modo deslizante. Se mencionan controladores robustos, adaptativos, óptimos y predictivos, así como controladores inteligentes como los controladores basados en datos. Se destaca la importancia de elegir el controlador adecuado en función del sistema que se está controlando y los objetivos deseados.

15:01

📈 Planificación, Estimación de Estado y Análisis del Sistema

Se abordan los aspectos adicionales de la teoría de control, como la planificación, la estimación de estado y el análisis del sistema. La planificación es crucial para definir la referencia que el controlador debe seguir. La estimación de estado es necesaria para manejar la retroalimentación del estado del sistema a pesar de la presencia de ruido en las mediciones. Finalmente, el análisis del sistema es esencial para garantizar que el sistema diseñado cumpla con los requisitos establecidos. Se sugiere que los modelos matemáticos son fundamentales en todos estos aspectos de la teoría de control.

🔗 Recursos y Referencias para Aprender Más

El último párrafo ofrece recursos adicionales para aprender más sobre la teoría de control, incluyendo enlaces a otros videos de Matlab Tech Talks que cubren temas específicos mencionados en el video. Se menciona que hay videos disponibles para temas como el control de retroalimentación, el control de bucles cerrados, la identificación de sistemas y más. También se proporciona un enlace a un recorrido en Resourceum.org que organiza todos los recursos mencionados en el video.

Keywords

💡Control Theory

La Teoría del Control es un marco matemático utilizado para desarrollar sistemas autónomos. En el vídeo, se menciona que proporciona las herramientas para controlar dinámicamente sistemas como automóviles autónomos, edificios con sistemas de temperatura o columnas de destilación. Se utiliza para diseñar y analizar cómo un sistema debe reaccionar ante diferentes entradas para alcanzar un objetivo deseado.

💡Dynamical System

Un Sistema Dinámico es cualquier cosa que se puede controlar automáticamente, como un edificio, una columna de destilación o un automóvil. Se ve afectado por entradas externas, que pueden ser intencionadas (control inputs) o no intencionadas (disturbances). En el vídeo, se discute cómo estos sistemas dinámicos pueden ser controlados y modelados para predecir y ajustar su comportamiento.

💡Control Inputs (U)

Las Entradas de Control son las acciones intencionadas que se toman para afectar el sistema, como mover el volante o presionar el acelerador en un automóvil. El vídeo explica cómo estas entradas son fundamentales para la teoría del control, ya que son las que el controlador manipula para alcanzar el objetivo deseado.

💡Disturbances (D)

Los Disturbances son fuerzas no deseadas que afectan al sistema, como el viento o las bump en la carretera para un automóvil. El vídeo destaca la importancia de manejar estos disturbios en la teoría del control para asegurar que el sistema funcione según lo planeado a pesar de las condiciones externas imprevisibles.

💡System State (X)

El Estado del Sistema se refiere a las condiciones actuales del sistema, como la velocidad y la dirección de un automóvil. El vídeo discute cómo el control理论 se utiliza para gestionar y ajustar el estado del sistema a lo largo del tiempo en respuesta a las entradas y las perturbaciones.

💡Open Loop Controller

Un Controlador de Bucles Abiertos, también conocido como Controlador de Avance, es un tipo de controlador que genera señales de control basadas únicamente en las referencias deseadas sin necesitar medir el estado actual del sistema. El vídeo lo ejemplifica con el control de un automóvil que mantiene una velocidad constante sin medir su velocidad actual.

💡Feedback Control

El Control de Retroalimentación, o Bucles Cerrados, es un método donde el controlador utiliza tanto la referencia como el estado actual del sistema para determinar las entradas de control. El vídeo lo presenta como una solución para sistemas que no son robustos ante perturbaciones y donde es necesario un controlador que auto-corrija en respuesta a desviaciones del estado deseado.

💡Mathematical Model

Un Modelo Matemático es una representación matemática de un sistema que se utiliza para predecir su comportamiento y diseñar controladores. El vídeo destaca la importancia de los modelos en la teoría del control, ya que son esenciales para la identificación del sistema, el diseño del controlador y la estimación del estado.

💡State Estimation

La Estimación del Estado es el proceso de estimar el estado actual del sistema a partir de mediciones que pueden ser ruidosas. El vídeo lo menciona como un área importante de la teoría del control, ya que es necesario para proporcionar una retroalimentación precisa al controlador a pesar de la presencia de ruido en los sensores.

💡Planning

La Planificación es el proceso de determinar una secuencia de acciones para alcanzar un objetivo específico. En el vídeo, se destaca la importancia de la planificación en la teoría del control, ya que es necesaria para crear una referencia que el controlador siga, como en el caso de un automóvil autónomo que debe planificar un camino para llegar a su destino evitando obstáculos.

Highlights

Control theory is essential for designing autonomous systems.

A dynamical system can be affected by control inputs and disturbances.

Automating a process involves determining control inputs without constant state knowledge.

Open loop controllers, or feed forward controllers, generate control signals without measuring the system state.

Feed forward controllers require a good understanding of system dynamics.

System identification is crucial for developing models used in control theory.

Feedback control, or closed loop control, uses the current state of the system to adjust control inputs.

Feedback control is a self-correcting mechanism but can be dangerous if not designed properly.

There are various types of feedback controllers, including linear, non-linear, robust, adaptive, optimal, and intelligent.

Planning is necessary to create a reference for the control system to follow.

State estimation is required to accurately estimate the system state from noisy measurements.

Analysis, simulation, and testing ensure the designed system meets requirements.

Mathematical models are used throughout control theory for design, estimation, planning, and analysis.

Matlab Tech talks cover various topics in control theory, providing in-depth knowledge.

Resource links and a journey at resourcium.org are provided for further learning.

Transcripts

an important question that has to be

answered when you're designing an

autonomous system is how do you get that

system to do what you want I mean how do

you get a car to drive on its own how do

you manage the temperature of a building

or how do you separate liquids into

their component parts efficiently with a

distillation column

and to answer those questions we need

control theory

control theory is a mathematical

framework that gives us the tools to

develop autonomous systems and in this

video I want to walk through everything

you need to know about control theory so

I hope you stick around for it I'm Brian

and welcome to a Matlab Tech talk

we can understand all of control theory

using a simple diagram and to begin

let's just start with a single dynamical

system

this system is the thing that we want to

automatically control like a building or

a distillation column or a car it can

really be anything but the important

thing is that the system can be affected

by external inputs and in general we can

think of the inputs as coming from two

different sources there are the control

inputs U that we intentionally use to

affect the system for a car these are

things like moving the steering wheel

and hitting the brake and pressing on

the accelerator pedal and then there are

unintentional inputs these are the

disturbances D and they are forces that

we don't want affecting the system but

they do anyway these are things like

wind and bumps in the road

now the inputs enter the system interact

with the internal Dynamics and then the

system State X changes over time

so for a car we move the steering wheel

and we press the pedals which turn the

wheels and revs the engine producing

forces and torques on that vehicle and

then combined with the forces and

torques from the disturbances the car

changes its speed position and direction

now if we want to automate this process

that is we want the car to drive without

a person determining the inputs where do

we go from here

and the first question is can an

algorithm determine the necessary

control inputs without constantly having

to know the current state of the system

or maybe a better way of putting it is

do you need to measure where the car is

and how fast it's going in order to

successfully drive the car with good

control inputs and the answer is

actually no we can control a system with

an open loop controller also known as a

feed forward controller

a feed forward controller takes in what

you want the system to do called the

reference R and it generates the control

signal without ever needing to measure

the actual state

in this way the signal from the

reference is fed forward through the

controller and then forward through the

system never looping back hence the name

feed forward

for example let's say that we want the

car to autonomously drive in a straight

line and at some arbitrary constant

speed if the car is controllable which

means that we have the ability to

actually affect the speed and direction

of the car then we could design a feed

forward controller that accomplishes

this

the reference drive straight means that

the steering wheel should be held at a

fixed zero degrees and drive at a

constant speed means that we depress the

accelerator pedal some non-zero amount

the car would then accelerate to a

constant speed and drive straight

exactly as we want

however let's say that we want the car

to reach a specific speed like 30 miles

an hour we can actually still do it with

a feed forward controller but now the

controller needs to know how much to

depress the accelerator pedal in order

to reach that specific speed and this

requires knowledge about the Dynamics of

the system and this knowledge can be

captured in the form of a mathematical

model

now developing a model can be done using

physics and first principles where the

mathematical equations are written out

based on your understanding of the

System Dynamics

or it can be done by using data and

fitting a model to that data with a

process called system identification

both of these modeling techniques are

important Concepts to understand because

as we'll get into models are required

for almost all aspects of control theory

now as an example of system

identification we could test the real

car and record the speed it reaches

given different pedal positions and then

we could just fit a mathematical model

to that data basically speed is some

function of the pedal position

now for the feed forward controller

itself we could just use the inverse of

that model to get pedal position as a

function of speed

so given a reference speed the feed

forward controller would be able to

calculate the necessary control input

so feed forward controllers are a pretty

straightforward way to control a system

however as we can see it requires a

really good understanding of the System

Dynamics since you have to invert them

in the controller and any error in that

inversion process will result in error

in the system state

also even if you know your system really

well the environment the system is

operating in should have predictable

Behavior as well you know so that

there's not a lot of unknown

disturbances entering the system that

you're not accounting for in the

controller

of course it doesn't take much

imagination to see that feed forward

control breaks down for systems that

aren't robust to disturbances and

uncertainty I mean imagine wanting to

autonomously drive a car across the city

with feed forward control

theoretically you could map the city

well enough and know your car well

enough that you could essentially

pre-program in all of the steering wheel

and pedal commands and just let it go

and if you had perfect knowledge ahead

of time then the car would execute those

commands and then make its way across

the city unharmed

obviously though this is unrealistic I

mean not only are other cars and

pedestrians impossible to predict

perfectly but even the smallest errors

in the position and speed of your car

will build over time and eventually

deviate much too far from the intended

path

so this is where feed back control or

closed loop control comes to the rescue

in feedback control the controller uses

both the reference and the current state

of the system to determine the

appropriate control inputs that is the

output is fed back making a closed loop

hence the name

and in this way if the system state

starts to deviate from the reference

either because of disturbances or

because of errors in our understanding

of the system then the controller can

recognize those deviations those errors

and adjust the control inputs

accordingly so feedback control is a

self-correcting mechanism and I like to

think of feedback as a hack that we have

to employ due to our inability to

perfectly understand the system and its

environment we don't want to use

feedback control but we have to

all right so feedback control is

powerful but it's also a lot more

dangerous than feed forward control and

the reason for this is that feed forward

changes the way we operate a system but

feedback changes the Dynamics of the

system it changes its underlying

behavior and this is because with

feedback the controller changes the

system State as a function of the

current state and that relationship is

producing new Dynamics

and changing Dynamics means that we have

the ability to change the stability of

the system and on the plus side we can

take an unstable or marginally stable

system and make it more stable with

feedback control but on the negative

side we can also make a system less

stable and even unstable and this is why

a lot of control theory is focused on

designing and importantly analyzing

feedback controllers because if you do

it wrong you can cause more harm than

good and since feedback control exists

in many different types of systems the

control community over the years have

developed many different types of

feedback controllers

there are linear controllers like PID

and full State feedback that assume the

general behavior of the system being

controlled is linear in nature

and if that's not the case there are

non-linear controllers like on off

controllers and sliding mode controllers

and gain scheduling

now often thinking in terms of linear

versus non-linear isn't the best way to

choose a controller so we Define them in

other ways as well for example there are

robust controllers like mu synthesis an

active disturbance rejection control

which focus on meeting requirements even

in the face of uncertainty in the plant

and in the environment so we can

guarantee that they are robust to a

certain amount of uncertainty there are

adaptive controllers like extremum

seeking and model reference adaptive

control that adapt to changes in the

system over time there are optimal

controllers like lqr where a cost

function is created and then the

controller tries to balance performance

and effort by minimizing the total cost

there are predictive controllers like

model predictive control that use a

model of the system inside the

controller to simulate what the future

state will be and therefore what the

optimal control input should be in order

to have that future State match the

reference

there are intelligent controllers like

fuzzy controllers or reinforcement

learning that rely on data to learn the

best controller and there are many

others and the point here isn't to list

every control method I just wanted to

highlight the fact that feedback control

isn't just a single algorithm but it's a

family of algorithms and choosing which

controller to use and how to set it up

depends largely on what system you are

controlling and what you want it to do

so what do you want your system to do

what state do you want the system to be

in what is the reference that you want

it to follow

and this might seem like a simple

question if we're balancing an inverted

pendulum or designing a simple Cruise

controller for a car the reference for

the pendulum is vertical and for the car

it's the speed that the driver sets

however for many systems understanding

what it should do takes some effort and

this is where planning comes in

the control system can't follow a

reference if one doesn't exist and so

planning is a very important aspect of

Designing a control system

with a self-driving car for example

planning has to figure out a path to the

destination while avoiding obstacles and

it has to follow the rules of the road

plus it has to come up with a plan that

the car is physically able to follow you

know it doesn't accelerate too fast or

it doesn't turn too quickly and if there

are passengers then planning has to

account for their comfort and safety as

well and only after the plan has been

created can the controller then generate

the commands to follow it an example of

two different graph-based planning

methods are rapidly expanding random

trees rrt and a star

once again there are too many different

algorithms to name but the important

thing is that you understand that you

have to develop a plan that your

controller will then try to follow

all right so once you know what you want

the system to do and you have a feedback

controller to do it now you need to

actually execute this plan and as we

know for feedback controllers this

requires knowledge of the state of the

system that is after all what we are

feeding back and the problem is that we

don't actually know the state unless we

measure it and measuring it with a

sensor introduces noise so for our car

example we're not feeding back the true

speed of the car we're feeding back a

noisy measurement of the speed

and our controller is going to react to

that noise so in this way noise in a

feedback system actually affects the

true state of the system and so this is

one additional problem that we're going

to have to tackle with feedback control

a second problem is that of

observability in order to feedback the

state of the system we have to be able

to observe the state of the system and

this requires sensors in enough places

that every state that is fed back can be

observed

now it's important to note that we don't

have to measure every state directly we

just need to be able to observe every

state for example if our car only has a

speedometer we can still observe

acceleration by taking the derivative of

the speed

so there are two things here we need to

reduce measurement noise and we need to

manipulate the measurements in such a

way that allows us to accurately

estimate the state of the system

State estimation is therefore another

important area of control theory and for

this we can use algorithms like the

column and filter the particle filter or

even just run a simple running average

and choosing an algorithm depends on

which states you are directly measuring

and how much noise and what type of

noise is present in those measurements

now the last major part of control

theory is responsible for ensuring the

system that we just designed works that

it meets the requirements that we set

for it and this comes down to analysis

simulation and test for this we can plot

data in different formats like with a

body diagram a nickels chart or a

Nyquist diagram

we could check for stability and

performance margins we could simulate

the system using Matlab and simulink and

all of these tools can be used to ensure

that the system will function as

intended

and so this full diagram here I think

represents everything you need to know

about control theory you have to know

about different control methods both

feed forward and feedback depending on

the system you're controlling you have

to know about State estimation so that

you can take all of those noisy

measurements and be able to feed back an

estimate of System state

you have to know about planning so that

you can create the reference that you

want your controller to follow

you have to know how to analyze your

system to ensure that it's meeting

requirements and finally and possibly

most importantly you have to know about

building mathematical models of your

system because models are often used for

every part we just covered they are used

for controller design they're used for

State estimation they're used for

planning and they are used for analysis

all right I always leave links below to

other resources and references and this

video is no exception and there are a

bunch for this video since I mentioned

so many different topics and something I

think is nice is that we already have

Matlab Tech talks for almost every topic

I mentioned we have feed forward and PID

and gain scheduling and fuzzy logic and

Coleman filters and particle filters and

planning algorithms and system

identification and more so if there's an

area of control theory that you want to

learn more about I hope you check out

the links below

and to make it easier to browse through

all of them I put together a journey at

resourcium.org that organizes all of the

references in this video again link to

that is below as well

so this is where I'm going to leave this

video if you don't want to miss any

other future Tech talk videos don't

forget to subscribe to this Channel and

if you want to check out my channel

control system lectures I cover more

control theory topics there as well

thanks for watching and I'll see you

next time