Example invoices and editable projects

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An engineering invoice, with the equations

See how technical explanations can remain part of a readable business document.

This one-page English example invoices the development and verification of an analogue PID controller and a digital PI controller. The editable project lets you inspect the input fields and reuse the structure for your own work.

• Analogue PID: integral and derivative terms, with a filtered derivative stage using Tf = 35 ms.
• Digital PI: a backward-Euler recurrence with a sampling period of Ts = 10 ms.
• 86 hours; EUR 8,650.00 net; 19% VAT (EUR 1,643.50); EUR 10,293.50 total.
• EPC/SEPA QR captioned “Pay with Code”, with a 35 mm sample stamp over the signature.

\(\displaystyle u(t)=K_p e(t)+K_i\int_0^t e(\tau)\,d\tau-K_d\frac{dy(t)}{dt}\)

\[u[k]=u[k-1]+K_p(e[k]-e[k-1])+K_i T_s e[k]\]

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The same seven examples are included in the installer: editable .luabill projects, .bill sources and ready-made PDFs. The ZIP also includes the demo signature and stamp images. Extract it before opening a project. SHA-256