El controlador PID combina tres acciones:
Función de transferencia:
[
G_c(s) = K_p + \fracK_is + K_d s = \fracK_d s^2 + K_p s + K_is
]
Problem:
The step response of a process shows an inflection point with ( L = 2 ) s (delay) and ( T = 10 ) s (time constant). Gain ( K = 1 ). Find PID parameters using Ziegler-Nichols.
Solution:
Ziegler-Nichols table for step response (process model ( G(s) = \fracK e^-LsTs+1 )):
| Controller | ( K_p ) | ( T_i ) | ( T_d ) | |------------|---------------|-----------|-------------| | P | ( T/(KL) ) | – | – | | PI | ( 0.9T/(KL) ) | ( L/0.3 ) | – | | PID | ( 1.2T/(KL) ) | ( 2L ) | ( 0.5L ) |
Answer:
[
K_p = 6,\quad K_i = 1.5,\quad K_d = 6
] control pid ejercicios resueltos
Problem:
Same system ( G(s) = \frac5s+2 ). Design a PI controller ( K_p + \fracK_is ) so that the closed-loop system has zero steady-state error to a step and a dominant pole at ( s = -3 ).
Solution:
Answer: ( K_p = 0.8,\ K_i = 1.8 ). Error = 0. El controlador PID combina tres acciones:
[ G_lc(s) = \fracs^2 + 6s + 3s^3 + 3s^2 + 7s + 3 ] ess = 0, menor sobreoscilación que PI (gracias al término derivativo).
Conclusión: PID da mejor equilibrio entre rapidez y sobreoscilación.
**Paso