continuous PID control law

symbols, variables and units

e: setting minus measurement; u: control quantity; K_p, K_i, K_d: defined according to signal unit and time. It is a sufficient condition that

applicable conditions and boundaries

Ideal continuous form; engineering requires derivative filtering, anti-saturation and discretization.

formula source code

The following is a copyable LaTeX expression.

u(t)=K_pe(t)+K_i\int_0^t e(\tau)d\tau+K_d\frac{de}{dt}

Reference and Extended Learning

is organized according to model definition and assumptions. Please check actual conditions and original literature before engineering, research and clinical use.