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Enhancing aircraft handling with stability augmentation using LQR

Posted 2 years ago

POSTED BY: Maher Kuzbari
3 Replies

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POSTED BY: Moderation Team

Maher,

Another excellent example! Can you also show how to design the controller when there is measurement noise? I was always confused by whether to use KalmanEstimator[] or LQGRegulator[] and how to use the result in Mathematica to make a complete controller. (I always seem to use the "long way" -- manually doing many of the steps that Mathematica does automatically).

Regards,

Neil

EDITED: To clarify my question, let's say you have measurement noise on the states you can measure and you can't measure some of the states so you need to estimate them from the noisy inputs.

POSTED BY: Neil Singer

Thanks for your feedback! With regards to your question, I had addressed that topic in my previous post. Briefly put, an LQG controller is an estimator based-controller where the regulator is an optimal controller and the estimator is a Kalman filter (hence the name, Kalman estimator). The Symbol KalmanEstimator[] gives you the estimator gains for the Kalman estimator, similar to how in this example, EstimatorGains was used to calculate the gains of the estimator for the estimator-regulator with the difference being that you use estimator gains when the information regarding your states is incomplete (unobservable), while the Kalman estimator also takes in to account the noise to from your sensors. This all comes down to the conclusion that if you have your process and noise covariance inputs, then you can obtain an LQG directly using the symbol LQGRegulatorGains!

POSTED BY: Maher Kuzbari
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