Control Systems

A seven-act visual walkthrough of multi-agent control — from the simplest consensus problem (six agents averaging with their neighbors) to fully-heterogeneous containment, where...

Nearly every dynamical system worth controlling is nonlinear. Nearly every tool we have — stability proofs, frequency analysis, MPC — is built for linear systems. Bernard Koopma...

Continuous-time control theory is taught in s-domain. Real control runs at a fixed sample rate on a microcontroller, in z-domain, with finite numerical precision and a one-sampl...

A fixed-gain controller is a promise that the plant you tuned against is the plant you'll meet in the field. When that promise breaks — drift, wear, operating-point change, unit...

Optimal control gets taught as proofs and Riccati equations; in practice it lives or dies on tuning, discretization, conditioning, and whether your solver finishes in the sample...

A field manual on twelve practical techniques most control textbooks under-treat: Smith predictors, 2-DOF PID, anti-windup, feedforward, derivative filtering, cascade, gain sche...

An interactive notebook on the structural properties of linear state-space systems — controllability, observability, the Kalman decomposition, Luenberger observers, and Kalman f...

An interactive tour of classical compensator design. Pick a controller (P / PI / PD / PID / lead / lag / lead-lag), pick a plant, drag the parameters, and watch the Bode plot an...

An interactive primer on system identification — the practical art of getting a working model of a real plant. Step tests, PRBS, transfer-function and state-space fitting, valid...

Ten ideas that turn up almost every time a real controller meets a real plant — feedforward, time delay, Padé approximants, non-minimum phase, gain scheduling, the step response...

A field guide to filters — what they are, why classical electrical engineering spent decades designing them, and the seven chapters that take you from RC pairs through the bilin...

An interactive primer on automotive diagnostics — UDS, the DTC structure, OBD, sessions and security, and what changes for the electrified powertrain. The protocol underneath ev...

Monograph No. 4 of the diagnostics series. The gap between textbook FDI and deployed FDI — domain shift, certification, edge-deployment, fleet-scale digital twins, unlabeled ano...

Monograph No. 3 of the diagnostics series. Remaining Useful Life, degradation modeling, health indicators, the uncertainty question, and the maintenance scheduling that uses all...

Monograph No. 2 of the diagnostics series. Passive vs active fault-tolerant control, reference governors, graceful degradation, and the stability question during the transition ...

Monograph No. 1 of a four-part series on diagnostics and fault-handling. The classical model-based methods (observers, parity, Kalman), the data-driven methods (residuals, class...

An interactive primer on RUL prediction — four algorithm families compared on the same problem. Similarity matching against historical trajectories, ML regression on time-window...

An interactive primer on the three classical tools of diagnostic reasoning — fault tree analysis, Bayesian network inference, and ranked hypotheses with priors. Three live figur...