Diferencias para "LabElectronica/ProyectoQuadricoptero/QA3Fase1EstModYConArqRobMoviles/Balancin"

Diferencias entre las revisiones 7 y 24 (abarca 17 versiones)

Tabla de Contenidos

Modelo Balancín con Compensador PID
1. Modelo Continuo
2. Modelo Discreto

Modelo Balancín con Compensador PID

Modelo Continuo

$$ \sum{\tau_x} = \tau_2 - \tau_1 = J\frac{d^2\theta}{dt^2}$

$$ s^2\theta_{(s)}= \frac{\tau_{(s)}}{J}$

$$ G_{bal(s)} = \frac{1}{Js^2}$

$$ G_{torque(s)} = k_\tau$

$$ G_{PID(s)} = k_p\cdot(1 + \frac{1}{T_is} + T_ds})$

$$ G_{LA(s)} = G_{bal(s)}G_{torque(s)}G_{PID(s)} = \frac{k_pk_\tau}{T_iJ}\frac{T_iT_ds^2 + T_is + 1}{s^3}$

$$ G_{LC(s)} = \frac{G_{LA(s)}}{1+G_{LA(s)}} = k_pk_\tau\frac{T_iT_ds^2 + T_is + 1}{T_iJs^3 + k_pk_\tauT_iT_ds^2 + k_pk_\tauT_is + k_pk_\tau}$

Modelo Discreto

$$ G_{bal(s)} = \frac{1}{Js^2}$

$$ G_{ROC(s)}=\frac{1-e^{-TS}}{S}$

$$ G_{torque(s)} = k_\tau$

$$ G_{PID(s)} = k_p\cdot(1 + \frac{1}{T_is} + T_ds})$

$$ G_{planta(Z)} = Z[G_{ROC(s)}G_{bal(s)}G_{torque(s)}] = Z[\frac{1 - e^{-TS}}{S}\frac{k_\tau}{JS^2}] = (1-z^-1)Z[\frac{2k_\tau}{2JS^3}] = \frac{T^2k_\tau}{2J}\frac{z+1}{z^2-2z+1}$

$$ G_{PID(Z)} = K_P + \frac{K_I}{1-z^-1} + K_D(1-z^-1) = \frac{(K_P + K_I + K_D)z^2 + ( -2K_D - K_P )z + K_D }{ z^2 - z }$

$$ G_{LA(Z)} = G_{PID(Z)}G_{planta(Z)} = \frac{T^2k_\tau}{2J}\frac{(K_P + K_I + K_D)z^3 + (K_I - K_D)z^2 + (-K_P - K_D)z + K_D}{z^4-3z^3+3z^2-z}$

$$ G_{LC(Z)} = \frac{G_{LA(Z)}}{1+G_{LA(Z)}} = k_\tauT^2\frac{(K_P + K_I + K_D)z^3 + (K_I - K_D)z^2 + (-K_P - K_D)z + K_D}{1}$

{2Jz^{4 + ((K_P + K_I + K_D)k_\tauT}2 -6 )z^{3 + ((K_I - K_D)k_\tauT}2 +6 )z^{2 + ((-K_P - K_D)k_\tauT}2 -2)z + K_Dk_\tauT^2} $$

None: LabElectronica/ProyectoQuadricoptero/QA3Fase1EstModYConArqRobMoviles/Balancin (última edición 2010-10-04 16:04:32 efectuada por Jaarac)

-  ⇤ ← Versión 7 con fecha 2010-10-01 21:46:02 → 
  Tamaño: 743
  Editor: Jaarac
  Comentario:
+   ← Versión 24 con fecha 2010-10-01 23:37:26 → ⇥
  Tamaño: 1770
  Editor: Jaarac
  Comentario:
-Los textos eliminados se marcan así.
+Los textos añadidos se marcan así.
 Línea 9:
+{{attachment:planta_lc_continuo.png}}
-Línea 15:
+Línea 17:
+$$$ G_{torque(s)} = k_\tau $$
-Línea 17:
+Línea 21:
-$$$ G_{LA(s)} = G_{bal(s)}G_{PID(s)} = \frac{k_p}{T_iJ}\frac{T_iT_ds^2 + T_is + 1}{s^3}$$
+$$$ G_{LA(s)} = G_{bal(s)}G_{torque(s)}G_{PID(s)} = \frac{k_pk_\tau}{T_iJ}\frac{T_iT_ds^2 + T_is + 1}{s^3} $$
-Línea 19:
+Línea 23:
-$$$ G_{LC(s)} = \frac{G_{LA(s)}}{1+G_{LA(s)}} = k_p\frac{T_iT_ds^2 + T_is + 1}{T_iJs^3 + k_pT_iT_ds^2 + k_pT_is + k_p}$$
+$$$ G_{LC(s)} = \frac{G_{LA(s)}}{1+G_{LA(s)}} = k_pk_\tau\frac{T_iT_ds^2 + T_is + 1}{T_iJs^3 + k_pk_\tauT_iT_ds^2 + k_pk_\tauT_is + k_pk_\tau}$$
-Línea 21:
+Línea 25:
-{{attachment:use4651.png}}
+=== Modelo Discreto ===
-Línea 23:
+Línea 27:
-=== Modelo Continuo ===
+{{attachment:planta_lc_discreto.png}} 

$$$ G_{bal(s)} = \frac{1}{Js^2} $$

$$$ G_{ROC(s)}=\frac{1-e^{-TS}}{S}$$

$$$ G_{torque(s)} = k_\tau $$

$$$ G_{PID(s)} = k_p\cdot(1 + \frac{1}{T_is} + T_ds}) $$

$$$ G_{planta(Z)} = Z[G_{ROC(s)}G_{bal(s)}G_{torque(s)}] = Z[\frac{1 - e^{-TS}}{S}\frac{k_\tau}{JS^2}] = (1-z^-1)Z[\frac{2k_\tau}{2JS^3}] = \frac{T^2k_\tau}{2J}\frac{z+1}{z^2-2z+1}$$

$$$ G_{PID(Z)} = K_P + \frac{K_I}{1-z^-1} + K_D(1-z^-1) = \frac{(K_P + K_I + K_D)z^2 + ( -2K_D - K_P )z + K_D }{ z^2 - z } $$

$$$ G_{LA(Z)} = G_{PID(Z)}G_{planta(Z)} = \frac{T^2k_\tau}{2J}\frac{(K_P + K_I + K_D)z^3 + (K_I - K_D)z^2 + (-K_P - K_D)z + K_D}{z^4-3z^3+3z^2-z} $$

$$$ G_{LC(Z)} =  \frac{G_{LA(Z)}}{1+G_{LA(Z)}} = k_\tauT^2\frac{(K_P + K_I + K_D)z^3 + (K_I - K_D)z^2 + (-K_P - K_D)z + K_D}{1}$${2Jz^4 + ((K_P + K_I + K_D)k_\tauT^2 -6 )z^3 + ((K_I - K_D)k_\tauT^2 +6 )z^2 + ((-K_P - K_D)k_\tauT^2 -2)z + K_Dk_\tauT^2} $$

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Modelo Balancín con Compensador PID

Modelo Continuo

Modelo Discreto