Bienvenido: Ingresar
location: Diferencias para "LabElectronica/ProyectoQuadricoptero/QA3Fase1EstModYConArqRobMoviles/Balancin"
Diferencias entre las revisiones 1 y 32 (abarca 31 versiones)
Versión 1 con fecha 2010-09-20 23:19:32
Tamaño: 231
Editor: Jaarac
Comentario:
Versión 32 con fecha 2010-10-04 13:06:01
Tamaño: 1861
Editor: Jaarac
Comentario:
Los textos eliminados se marcan así. Los textos añadidos se marcan así.
Línea 6: Línea 6:
== Modelo Balancín ==
=== Continuo ===
 
== Modelo Balancín con Compensador PID ==
=== Modelo Continuo ===

{{attachment:planta_lc_continuo.png}}

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

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

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

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

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

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

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

==== Archivos para Simulaciones ====
{{attachment:PID_LA_continuo.m}}

=== Modelo Discreto ===

{{attachment:planta_lc_discreto.png}}

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

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

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

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

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

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

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

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

Modelo Balancín con Compensador PID

Modelo Continuo

planta_lc_continuo.png

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

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

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

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

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

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

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

Archivos para Simulaciones

   1 J = 0.0086556;
   2 Kp = 1;
   3 Kt = 90.63e-6;
   4 Ti = 0;
   5 Td = 0;
   6 
   7 desicion = 1;
   8 
   9 while( desicion == 1)
  10 
  11 	%Kp = input('Ingrese Kp : ');
  12 	Ti = input('Ingrese Ti : ');
  13 	Td = input('Ingrese Td : ');
  14 
  15 	num = Kp*Kt/(Ti*J)*[Ti*Td, Ti, 1];
  16 	den = [1, 0, 0, 0];
  17 
  18 	sistema = tf(num,den);
  19 
  20     K_inc = input('Ingrese el incremento de K del rlocus: ');
  21 	K_max = input('Ingrese el K_max del rlocus: ');
  22 	
  23 	%rlocus(sistema,K_inc,0,K_max);
  24     rlocus(sistema);
  25 
  26     pause;
  27 	desicion = input('Ingrese 1 para hacer otro rlocus: ');
  28 
  29 end

PID_LA_continuo.m

Modelo Discreto

planta_lc_discreto.png

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

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

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

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

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

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

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

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

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