Tutorials

Full derivation of the cart-pole equations of motion, linearization at upright, state-feedback design (pole placement), the transfer-function form (Ex 9.6), and how to map PID gains between the Ex 2.2 and Ex 9.6 presets on 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.