What is Control Theory?
Control theory is the art and science of making systems behave the way we want. From cruise control in your car to rockets landing themselves, control systems are everywhere.
At its core, we're answering one question: How do we get a system from where it is to where we want it to be?
Where we want to be
Decision maker
What we control
What we measure
Learning Roadmap
We'll build up your understanding step by step, always connecting math to physical intuition.
Part I: Foundations
Mathematical Foundations
Refresher on calculus, linear algebra, and differential equations — focused on what matters for control.
- Derivatives as rates of change
- Integrals as accumulation
- Matrices and eigenvalues
- Solving differential equations
Modeling Dynamic Systems
How to translate physical systems into mathematical models we can analyze.
- Mass-spring-damper systems
- Electrical circuits
- Fluid systems
- State variables
The Laplace Transform
A powerful tool that turns differential equations into algebra.
- Intuition behind transforms
- Common transform pairs
- Solving ODEs with Laplace
- Transfer functions
Part II: Classical Control
Block Diagrams & Transfer Functions
Visual representation of systems and how signals flow through them.
Time Response Analysis
How systems respond to inputs over time — step response, impulse response, and more.
Stability
Will the system settle down or blow up? The most important question in control.
PID Control
The workhorse of industry — understanding and tuning PID controllers.
Frequency Response
Bode plots, Nyquist diagrams, and gain/phase margins.
Root Locus
Visualizing how poles move as we change controller gain.
Part III: Modern Control
State-Space Representation
A more powerful way to describe systems using matrices and vectors.
Controllability & Observability
Can we actually control the system? Can we know what's happening inside?
State Feedback & Observers
Placing poles where we want them and estimating states we can't measure.
Optimal Control (LQR)
Finding the best controller by balancing performance and effort.
How We'll Learn
Intuition First
Every concept starts with the "why" and physical meaning before diving into math.
Visual Learning
Interactive plots and animations to build geometric understanding.
Hands-On
Tweak parameters, see results immediately, develop engineering intuition.
Connected Ideas
See how concepts link together — the big picture always in view.