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Control Systems: From Mathematical Modelling to PID Control
Rating: 4.2 out of 5(914 ratings)
4,720 students

Control Systems: From Mathematical Modelling to PID Control

Learn the mathematics that will allow you to model and control any engineering system. Make machines do what you want!
Created byEliott Wertheimer
Last updated 7/2018
English
English [Auto],

What you'll learn

  • Understand how systems and signals interact in engineering systems.
  • Model mechanical engineering systems mathematically.
  • Model electrical and electro-mechanical engineering systems mathematically.
  • Apply Laplace Transforms to engineering systems and easily solve differential equations.
  • Fully understand and manipulate transfer functions.
  • Fully understand stability in engineering systems.
  • Manipulate and use block diagrams for engineering systems and control design.
  • Understand and fully grasp control theory including open loop and closed loop control.
  • Design Proportional (P), Proportional Integral (PI), Proportional Derivative (PD), Proportional Derivative Feedback (PDFB) and Proportional Integral Derivative (PID) controllers.
  • Use the Empirical Ziegler Nichols Method to design effective P, PI and PID controllers.

Course content

4 sections • 15 lectures • 2h 56m total length

  • Systems and Signals5:17

    Explore how engineering systems interact with signals to form dynamical machines, model them with differential equations, apply Laplace transforms, and derive transfer functions for control.

  • Mechanical Systems11:05

    Construct mathematical models of mechanical systems with springs, dampers, and lumped masses. Apply Newton's second law to derive motion equations for linear and rotational cases.

  • Electro-mechanical Systems19:21

    Explore mathematical models of electro-mechanical systems, covering resistors, capacitors, inductors, ohm's law, and circuits governed by Kirchhoff's laws and back-emf in brushed dc motors.

  • Laplace Transforms11:40

    Apply Laplace transforms to convert differential equations into algebraic equations, transforming f(t) to f(s) using linearity, derivative rules, and reference tables with initial conditions.

  • Laplace Transforms: Solving Linear Differential Equations11:42

    Apply Laplace transforms to solve a linear differential equation for a mass-damper system, deriving velocity and displacement from a decaying exponential force.

Requirements

  • Basic understanding of physics (force, velocity, acceleration, pressure, etc).
  • High School mathematics level up to differentiation, integration (complex numbers are useful but not mandatory)

Description

ONE OF THE ONLY COMPREHENSIVE, DETAILED AND APPROACHABLE ONLINE COURSES ON CONTROL SYSTEMS ENGINEERING, SPANNING FROM MATHEMATICAL MODELLING TO PID CONTROL DESIGN!

Today, control systems are everywhere: in cars, military aircrafts, interplanetary rockets, computers, fridges, washing machines, etc. As technology advances, control engineering allows us to design systems which make the most complicated machines do exactly what we want them to do with outstanding accuracy and reliabilty. 

This course gives you the opportunity to understand, use and design the following:

- Mathematical Modelling of Engineering Systems.
- Laplace Transforms and Linear Differential Equations.
- Systems' Transfer Functions, Stability and Block Diagrams.
- Open Loop Control, Closed Loop Control and Steady State Performance.
- Proportional (P), Proportional Integral (PI), Proportional Derivative (PD), Proportional Derivative Feedback (PDFB) Controllers.
- Proportional Integral Derivative (PID) Controller Design and Empirical Ziegler-Nichols Method.

I will thoroughly detail and walk you through each of these concepts and techniques and explain down to their fundamental principles, all concepts and subject-specific vocabulary. This course is the ideal beginner, intermediate or advanced learning platform for control systems, the mathematics and the engineering behind them. Whatever your background, whether you are a student, an engineer, a sci-fi addict, an amateur roboticist, a drone builder, a computer scientist or a business or sports person, you will understand the brains behind our most advanced technologies!

If you have questions at any point of your progress along the course, do not hesitate to contact me, it will be my pleasure to answer you within 24 hours!

If this sounds like it might interest you, for your personal growth, career or academic endeavours, I strongly encourage you to join! You won't regret it!

Who this course is for:

  • Anyone interested in fully understanding robotics and control in engineering systems.
  • Anyone interested in learning how to control machines accurately and effectively.

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