LabElectronica/ProyectoQuadricoptero/QA3Fase1EstModYConArqRobMoviles/Balancin

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})$

$$ 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}]$

$$ Z[\frac{1 - e^{-TS}}{S} * \frac{1}{J*S^2}] = (1-z^-1) * Z[\frac{2}{2*J*S^3}] = \frac{1-z^{-1}}{2*J}*\frac{T^2*z^{-1}*(1+z^{-1})}{(1-z^{-1})^3}$

$$ Z[G_p, G_r] = \frac{T^2}{2*J} * \frac{z^{-1}*(1+z^{-1})}{(1-z^{-1})^{2}}$

$$ F(z) = G_p(z)*G_r(z)*G_c(z) = \frac{T^2}{2*J} * \frac{z^{-1}*(1+z^{-1})}{(1-z^{-1})^{2}} * Kp * [1 + \frac{1}{T_i*(1-z^{-1})} + T_d*(1-z^{-1})]$

$$ F(z) = \frac{T^2 * K_p}{2*J} * [\frac{z^{-2} + z^{-1}}{(1-z^{-1})^2} + \frac{z^{-2} + z^{-1}}{T_i*(1-z^{-1})^3} + \frac{T_d*z^ {-2} + T_d*z^{-1}}{(1-z^{-1})}]$

$$ F(z) = \frac{T^2 * K_p}{2*J} * \frac{T_i*T_d+(-T_i-T_i*T_d)*z+(1-T_i*T_d)*z^2+(1+T_i+T_i*T_d)*z^3}{z^4-3*z^3+3*z^2-z}$

None: LabElectronica/ProyectoQuadricoptero/QA3Fase1EstModYConArqRobMoviles/Balancin (última edición 2010-10-01 23:01:50 efectuada por Jaarac)