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[ u[n] = u[n-1] + K_p(e[n]-e[n-1]) + K_i T_s e[n] + \fracK_dT_s(e[n] - 2e[n-1] + e[n-2]) ]

| Controller | Rise time (s) | Overshoot (%) | Steady-state error (%) | |------------|---------------|---------------|-------------------------| | P-only | 0.45 | 42 | 15 | | PI | 0.50 | 20 | 0 | | PID (tuned)| 0.38 | 8 | 0 |

[ G(s) = \fracK\tau s + 1 ]

Is discretized (Tustin method, sampling time ( T_s = 0.05 ) s):

[ u(t) = K_p e(t) + K_i \int e(t)dt + K_d \fracde(t)dt ]