Tutorials

Example 4.2 of Mathematics for Machine Learning states that |det A| is the volume of the parallelepiped spanned by the columns of A, but gives no proof. Here are three rigorous proofs: column operations, QR factorization, and the wedge-product (volume form) argument.

How a microcontroller with only two digital outputs and one digital input measures temperature — charge a capacitor through a thermistor, time how long it takes to reach the logic-1 threshold, discharge it, and repeat. Full derivation of both charge and discharge phases plus a working block-simulation model with automatic charge/discharge cycling.

A practical guide to USB-to-serial converter internals: USB-serial chips, TTL voltage levels (3.3V/5V), RS485 differential signaling, transceivers, and when to use each interface. Includes signal-chain diagrams for adapters and industrial gateways like the Moxa mGate 3270.

A small nudge to the input direction can flip the sign of an output. This is not a bug — it is the geometry of the 2×2 static gain matrix. We walk through the Bequette Module 13 LV distillation model, the SVD picture, and what it means for control pairing.

Full derivation of the cart-pole equations of motion, linearization at the upright equilibrium, and state-feedback design via pole placement and LQR for the Inverted Pendulum Simulator.

A derivation of Lyapunov-based model reference adaptive control for first-order SISO systems. Learn how to design controllers that adapt to unknown or changing plant parameters in real time.

Learn relay feedback auto-tuning to measure ultimate gain and period directly from a closed-loop experiment, then convert to PID gains using Ziegler–Nichols frequency-domain rules.

A hands-on walkthrough of PID controller tuning using the Ziegler-Nichols, Cohen-Coon, and IMC methods. Learn how to adapt gain parameters for first-order lag plus deadtime (FOLPD) processes.

How frequency-domain thinking guides PID tuning in practice — bandwidth, phase margin, and low-frequency gain explained through a worked FOLPD example.