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Abstract

In a linear regulator problem with a quadratic cost function, there are two weighting matrices which determine the feedback gain matrix, and thereby the closed loop eigenvalues and eigenvectors of the system. To find the weighting matrices leading to a desired eigenstructure, trial and error is a common approach. In spite of its simplicity, trial and error is too time-consuming and does not guarantee achieving expected results. In this regard, this paper presents a step-by-step algorithm for calculation of state and control weighting matrices in such a way that the pre-specified eigenstructure is generated with acceptable accuracy. Accordingly, once the designer chooses preferred eigenvalues and eigenvectors, the feedback gain matrix will be available uniquely. In design procedure, tracking of flight path and pitch attitude commands for an F-16 aircraft will be provided. To achieve this aim completely, the feedforward gain matrix necessary for getting a zero steady state error is calculated based on the mathematical model of the aircraft as well as the pseudoinverse matrix concept. Various simulations demonstrate that the resulted controller has good performance, gives the desired eigenstructure satisfactorily and also shows the expected robustness of a linear quadratic regulator.

Keywords

Linear quadratic regulator (LQR)eigenstructure assignment (EA)weighting matrix tracking pseudoinverse matrix

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Pitch and flight path controller design for F-16 aircraft using combination of LQR and EA techniques

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