Bowde - Interactive control-theory plotter

This is V2, a ground-up rebuild. V1 was built back in 2021 as a self-teaching project.

Bowde is a browser-based control-systems workbench: type a transfer function, get Bode, Nyquist, Nichols, pole-zero, and time-domain response plots — all recomputed live, with stability metrics (gain/phase margin, settling time) derived alongside them. Everything runs client-side; there is no backend.

Live demo →

What it does

• LaTeX equation input. Enter a transfer function G(p) in the Laplace variable p (e.g. 1 / (1+ap)). Any other letter becomes a free variable, exposed as a slider (linear or logarithmic) so you can sweep a parameter and watch every diagram update in real time.
• Five synchronized views. Bode (gain + phase), Nyquist, Nichols, pole-zero map, and time-domain step/impulse response, plus an all-in-one layout — all driven off the same computed data.
• Closed-form-free numerics. No symbolic Laplace inversion: poles and zeros come from an eigenvalue decomposition of the rationalized numerator/denominator's companion matrix (arbitrary polynomial degree, not just the cubics mathjs's built-in solver handles), and the time response comes from a numerical inverse Laplace transform (Gaver–Stehfest). See computation.utils.ts.
• Derived stability metrics. Gain/phase crossover frequencies, gain margin, phase margin, and 5%-band settling time, read directly off the sampled curves.
• Adjustable precision. Draft / Standard / High presets trade sample density (frequency decades and time-domain points) against recompute cost — useful since every parameter tweak recomputes every visible curve.

Formula syntax

Formulas are algebraic expressions in p (the Laplace variable), evaluated by mathjs:

1 / (1 + ap)              first-order lag, with slider variable `a`
(p + 2) / (p^2 + p + 5)   arbitrary rational function

• p is reserved for the Laplace variable — for frequency-domain plots it's substituted with jω at each swept frequency; for the time-domain solve it's substituted with the real Gaver–Stehfest abscissae.
• Any other letter (a–o, q–z) used in a formula is treated as a free variable. Adding a slider for that letter under Variables binds it; referencing an unbound letter clears that equation's curves rather than throwing.
• The time-domain response convolves the transfer function with whatever input signal is configured in the Time Response panel (step, impulse, etc.) — internally (input) * (G(p)), inverted once.

Tech stack

Layer	Choice
Framework	Angular 21 (standalone components, signals)
Math input	MathLive
Computation	mathjs — complex arithmetic, polynomial rationalization, eigenvalues
Rendering	p5.js (canvas-based diagram rendering)
Layout	angular-split
Export	html-to-image
Testing	Vitest
Deployment	GitHub Actions → GitHub Pages (deploy-pages.yml)

Getting started

Requires Node.js and npm (the repo pins npm@10.9.3 via packageManager).

cd bowde
npm install
npm start          # ng serve — http://localhost:4200

Other scripts (run from bowde/):

npm run build       # production build → dist/bowde/browser
npm run watch       # dev-mode build, rebuilds on change
npm test            # unit tests via Vitest

License

No license file is currently published in this repository — treat the code as all-rights-reserved unless a LICENSE is added.