# Applied Control Systems 1: autonomous cars: Math + PID + MPC

## What you'll learn

- mathematical modelling of systems
- reformulating models into state-space equations
- applying a PID controller to systems (simple magnetic train catching objects)
- applying Model Predictive Control (MPC) to systems (autonomous car: lane changing maneuvers)

## Requirements

- Basic Calculus: Functions, Derivatives, Integrals
- Vector-Matrix multiplication

## Description

The world is changing! The technology is changing! The advent of automation in our societies is spreading faster than anyone could have anticipated. At the forefront of our technological progress is autonomy in systems. Self driving cars and other autonomous vehicles are likely to be part of our every day lives. How would you like to understand and be able design these autonomous vehicles? How would you like to understand Mathematics behind it?

Welcome! In this course, you will be exposed to one of the most POWERFUL techniques there are, that are able to guide and control systems precisely and reliably.

You are going to DESIGN, MASTER and APPLY:

mathematical models in the form of state-space systems and equations of motion

a PID controller to a simple magnetic train that needs to catch objects that randomly fall from the sky

a Model Predictive Controller (MPC) to an autonomous car in a simple lane changing maneuver on a straight road at a constant forward speed.

You will LEARN the fundamentals and the logic of Modelling, PID and MPC that will allow you to apply it to other systems you might encounter in the future.

You need 3 things when solving an Engineering problem: INTUITION, MATHEMATICS, CODING! You can't choose - you really need them all. After this course, you will master Modelling, PID and MPC in all these 3 ways. That's a promise!

I'm very excited to have you in my course and I can't wait to teach you what I know.

Let's get started!

## Who this course is for:

- Science and Engineering students
- Working Scientists and Engineers
- Control Engineering enthusiasts

## Course content

- Preview03:58
- Preview06:52
- Preview06:34
- Preview06:36
- Preview02:52
- 04:44Intro to a proportional controller
- 01:45Modelling the water tank 1
- 12:13Modelling the water tank 2
- 09:52Numerical integration applied to the water tank model
- 07:07Combining math with the control structure
- 02:28Water tank simulation - proportional controller
- 02:26Intro to a PID simulation
- 00:58Follow up!
- 06:27PID: Modelling the train with forces 1
- 09:36PID: Modelling the train with forces 2
- 10:00PID: Going from system input to system output using numerical integration
- 01:59PID: Magnetic train simulation - proportional controller
- 04:39PID: Proportional controller overshoot explanation 1
- 06:28PID: Proportional controller overshoot explanation 2
- 03:40PID: Proportional controller overshoot explanation 3
- 10:24PID: Intro to Derivative Control
- 06:11PID: Tuning the controller
- 09:01PID: Proportional & Derivative controller & magnetic train simulation in Python
- 04:35PID: Intro to Integral Control
- 01:49PID: Python magnetic train simulation at an inclination angle
- 03:43PID: Mathematical modelling of the train with the inclination angle 1
- 05:39PID: Mathematical modelling of the train with the inclination angle 2
- 15:15PID: Proportional, Derivative, Integral Control combined
- 02:26PID: Magnetic train simulation (inclination angle & PID)
- 1 questionTest your PID fundamental understanding
- Preview12:54
- Preview06:45
- Preview06:34
- Preview08:04
- Preview17:56
- 11:15PID train code explanation 2
- 11:18PID train code explanation 3
- 12:24Short intro to Python animation tools
- 28:29Quick code & animation explanation (water tanks)
- 00:06Codes for the P & PID controllers (Python 3, Numpy & Matplotlib needed)

## Instructor

The Mission: to elevate humanity's knowledge, skills and love for science & engineering

I think that online education is the future because of one single fact - it is easily scalable. One course of a single great teacher can reach millions of people and potentially transform their lives. If education is more scalable, it will be more affordable. More affordable and accessible education will give more people an opportunity to stay out of poverty and create a great life for themselves.

I am here to contribute to this movement.