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== Modelo Balancín con Compensador PID ==
=== Modelo Continuo ===


{{attachment:planta_lc_continuo.png}}

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

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

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

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

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

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

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

=== Modelo Continuo ===