Control Systems

A plain-language field guide to Design and Process FMEA. Imagine how a design or process can fail, decide which failures matter, and fix the worst before a customer ever meets t...

How a vehicle decides something is wrong, writes it down, lights a lamp, protects itself, and how that same machinery becomes the foundation for predicting failures before they ...

Post 6 of the VHM statistical-methods series — and the one that ties the previous five together. Bayes' rule as the diagnostic framework. The Kalman filter and particle filter a...

Post 5 of the VHM statistical-methods series. Real machines don't fail in one signal — they fail across a joint distribution of dozens or hundreds. The classical multivariate to...

Post 4 of the VHM statistical-methods series. A fault often shows up not in a single signal but in the relationship between two. The toolkit for measuring relationships is broad...

Post 3 of the VHM statistical-methods series. A fault announces itself as a change in time. The skill is deciding, from noisy data, that a change is real and not just scatter, a...

Post 2 of the VHM statistical-methods series. The residual — what the model predicted minus what actually happened — is the workhorse signal of model-based diagnosis. This monog...

The classical bedrock of vibration-based condition monitoring. RMS, kurtosis, crest factor in the time domain. The FFT, the power spectral density, order analysis in the frequen...

Case 5 of 5 — and the case that almost everyone gets wrong on the first pass. Brake noise and reduced initial bite in a subpopulation of EVs. The Pareto says it's a rotor lot; t...

Case 4 of 5. An intermittent HV isolation warning, clustered geographically (coastal climates) and temporally (dawn hours). The Pareto points at a connector lot; the truth is an...

Case 3 of 5. Elevated tab-to-busbar weld resistance is creating thermal hotspots in finished battery modules. The Pareto chart points straight at one supplier lot — and is wrong...

Case 2 of 5. A tonal whine during battery preconditioning, reported by drivers in cold-climate fleets. The investigation traces three independent design choices — d-axis current...

Case 1 of a five-part series on root-cause analysis in vehicle health monitoring. We follow a single anomaly — a cohort of electric vehicles losing battery health faster than th...

The simplest powerful idea in engineering is the feedback loop: measure what the system is doing, compare it with what you want, push back against the difference, repeat. The sa...

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...

The unglamorous foundation under the fleet posts. Those posts assumed a clean 'one row per car' table — build attributes, telemetry summary, warranty outcome — and went straight...

The whole diagnosis series, until now, has been offline — an analyst with logs. But the first diagnostician is the car itself. This post drops down to the edge, where an ECU dec...

The diagnosis series found a cause by watching: a charging code (P0AE0) concentrated in cars on firmware ≥ v5.1, pointing to a cold-throttle bug, and a v5.2 patch was proposed. ...

The closing note in the diagnosis series. The earlier posts found the cause; this one asks the harder question — how do you make sure it never happens again? Fixing the affected...

The rigorous companion to Fleet-Scale Root-Cause Analysis. That post showed the logic; this one puts numbers under the figures and closes the gaps. We make 'is this cohort split...

The capstone of the diagnosis set. A single car gives you one observation; a fleet gives you a distribution — and a hypothesis must now explain not just that the code fired, but...

The third post in the diagnosis set. The sufficiency method assumed away three hard realities, and this post tackles them head-on, in plain words. Multiple simultaneous faults: ...

The companion to Root-Cause Analysis Under Uncertain, Heterogeneous Evidence. That post showed how to weigh messy evidence into a cause; this one answers the question it left op...

The methodological companion to the five-case RCA series. Real investigations don't begin with clean synthetic data — they begin with a heap of evidence of unequal trust: a DTC ...

An index and reading map for the nine-part diagnosis series. It is one long argument: turn untrustworthy evidence into a cause, know when you have enough to conclude, handle the...

A plain-English reference for the whole diagnosis series. Around two hundred terms, grouped into thirteen themes and defined in one sentence each: faults and symptoms; the diagn...

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...