Control Pid: Ejercicios Resueltos
El controlador PID, correctamente sintonizado y con medidas prácticas (anti-windup, filtrado derivativo, discretización adecuada), ofrece una solución flexible y efectiva para una amplia gama de sistemas. La resolución de ejercicios típicos sigue un flujo: modelado de la planta, selección de criterios de desempeño, elección de método de sintonía, simulación y ajustes prácticos.
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The story of PID control is one of mathematical elegance solving industrial chaos. While a single "story" doesn't exist, the narrative of a student or engineer solving "control pid ejercicios resueltos"
(solved PID control exercises) follows a classic progression: from the struggle of an unstable system to the balance of a perfectly tuned loop. The Narrative of Tuning: From Chaos to Control
Imagine an industrial plant where a chemical reactor's temperature must stay at exactly 80 raised to the composed with power cap C
. Without a controller, the temperature swings wildly. The engineer turns to solved exercises to implement a PID strategy. The Proportional (P) Struggle : The engineer first increases the gain ( cap K sub p
). In solved exercises, this often shows the system reacting faster, but as cap K sub p control pid ejercicios resueltos
gets too high, the system begins to oscillate. The "story" here is finding the Critical Gain cap K sub u
)—the point where the system vibrates at a constant amplitude without stopping. The Integral (I) Solution : The system is stable but stuck at 78 raised to the composed with power cap C
. This is the "steady-state error." By applying the Integral action ( cap K sub i
) learned in exercises, the controller "remembers" the past error and slowly pushes the temperature to the exact 80 raised to the composed with power cap C The Derivative (D) Foresight
: Now, every time a cold liquid enters the tank, the temperature drops sharply. The Derivative term ( cap K sub d
) acts as a "prophet," calculating the trend of the error to dampen the response and prevent overshooting the target. Classic "Ejercicios Resueltos" (Solved Examples) El controlador PID, correctamente sintonizado y con medidas
Most educational stories for PID revolve around these standard problems: 9.6: PID Downsides and Solutions - Engineering LibreTexts
Paso 1: Calcular la señal de error El error se define como la Referencia menos la Salida del Proceso.
$$e(t) = \textReferencia - \textSalida$$ $$e(t) = 50^\circ C - 45^\circ C = 5^\circ C$$
Paso 2: Analizar cada componente del PID
Paso 3: Sumar las acciones (Salida Total) Suponiendo un valor de integral acumulada estándar para este ejemplo (o ignorando el cálculo exacto de la integral por falta de datos históricos y centrándonos en la estructura):
$$u(t) = P + I + D$$ $$u(t) = 20 + (\texttérmino integral) - 0.5$$ Paso 1: Calcular la señal de error El
Conclusión: Vemos cómo la parte Proporcional domina la respuesta, mientras que la Derivativa actúa como un amortiguador.
[ 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.
[ G_c(s) = \fracK_d s^2 + K_p s + K_is ] Elegimos un cero doble o dos ceros reales. Probamos: ceros en ( s = -1 ) y ( s = -3 ).
Entonces: [ K_p = K_d (1+3) = 4K_d, \quad K_i = K_d \cdot 1 \cdot 3 = 3K_d ] Escribimos ( K_d = K ), entonces ( G_c(s) = K \frac(s+1)(s+3)s ).