equations - The SPAARO model response can be approximated...

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The SPAARO model response can be approximated in theory by a second order system equation. Since we know that the stability of the system is dependent upon the necessity that the coefficients of the characteristic equation must both be positive. Since our model feedback is dependent upon gain, only one of the coefficients is affected. Shown below are the steps to determine the sign of the gain such that no matter how large of a value is used for gain, the system will never go unstable. Therefore, the gain must be negative for all values if the system is never to go unstable. To account for actuator dynamics in the model, the system must be approximated by a third order model. This is done by taking the derivative of the second order model and combining the result with the equation for a first order actuator model, shown below. Once this is done, the change in elevator deflection for the model can be substituted in. For third order systems, no matter what the sign of the gain is chosen to be, the system
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equations - The SPAARO model response can be approximated...

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