embedded_PID

Embedded systems programming tutorial. The example in question is that of a DC Motor:

Phisical Parameters

(J) moment of inertia of the rotor 0.01 kg.m^2
(b) motor viscous friction constant 0.1 N.m.s
(Ke) electromotive force constant 0.01 V/rad/sec
(Kt) motor torque constant 0.01 N.m/Amp
(R) electric resistance 1 Ohm
(L) electric inductance 0.5 H

Constitutive Equations

$$ J\ddot{\theta} + b\dot{\theta} = Ki $$

$$ L \frac{d i}{dt} + Ri = V - K\theta $$

The Transfer Function Description $$P(s) = \frac{\dot{\Theta}(s)}{V(s)} = \frac{K}{(Js+b)(Ls+R) + K^2} $$ where $K = K_e = K_t$