Applied Mathematics

Learn Control Theory

Feedback, built on state space rather than transfer functions: what a state is, when a system is stable, and how to make it so. Stability from the eigenvalues of A and from Routh-Hurwitz without finding them, step-response specifications as regions of the s-plane, damping ratio and natural frequency, steady-state error, proportional and PID control. Then the structural questions: controllability, observability, pole placement, state observers, linear quadratic regulation and the Kalman filter, closing with Bode plots, gain and phase margins, and what sampling does to a loop. Scoped against diff-eq, fourier, linear algebra and dynamics, which own the Laplace transform, the z-transform and sampling theorem, the matrix exponential, and phase portraits and Lyapunov theory respectively.

Free to start · adaptive placement finds your level · reviews timed so it stays learned.

What you'll learn

18 lessons in Control Theory

Open loop & closed loopThe state-space modelStability from the eigenvaluesThe Routh-Hurwitz criterionStep response specificationsDamping ratio & natural frequencySteady-state errorProportional controlPID controlControllabilityObservabilityPole placementState observersLinear quadratic regulationThe Kalman filterBode plotsGain & phase marginsDigital control & sampling
How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the moment just before you'd forget it. A short placement check finds what you already know, so you start Control Theory exactly where it's useful.

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