Control, from first principles.
The equations are useful when you can connect them to a moving system. Follow this path, check your intuition, then test each idea in the lab.
Foundations → models → time response → root-based design → frequency response → controllers → state-space.
Why feedback?
A controller compares what you wanted with what happened, then acts on the difference.
From hardware to equations
A model keeps the mechanisms that matter for your question and leaves the rest out.
Why use the Laplace transform?
It turns differential equations into algebra while preserving the story of transients and stability.
Transfer functions, poles and zeros
Poles describe the system's natural modes; zeros reshape how inputs excite them.
Read a step response
A single target change reveals speed, overshoot, settling and residual error.
Stability and steady-state error
A response can be bounded yet inaccurate, or accurate in theory but unreachable with real actuator limits.
Root locus: follow the poles
Root locus shows where closed-loop poles move as a gain changes.
Lead and lag compensation
Shape the loop across frequency instead of increasing one gain everywhere.
Why analyze frequency and phase?
A complex system can be probed one sine wave at a time.
Bode plots: gain and phase
Two aligned plots show how a loop responds across slow and fast inputs.
Why −180° matters: Nyquist and margins
Negative feedback can become reinforcing feedback when the returning signal is inverted and strong enough.
PID, saturation and windup
P reacts to error now, I remembers error, D anticipates measured motion.
States, cart-pole and LQR
When one output hides too much, track the system's internal state.
The broad progression follows the publicly listed topics of Katsuhiko Ogata’s Modern Control Engineering (5th ed.), adapted and independently written for this lab. This is not a reproduction of the textbook. Publisher's table of contents ↗