LPV modeling using PID based pole placement for a small flight system

Abstract

This paper proposes a novel control strategy for Linear Parameter-Varying (LPV) systems by exploiting their capability to represent nonlinear dynamic systems. The proposed approach focuses on the position control of a Quadrotor, where accurate attitude stabilization is essential for achieving the desired position tracking performance. Accordingly, a PID-based tracking controller is developed to regulate the attitude and improve position control performance. Gyroscopic effects are considered to construct an LPV model of the nonlinear Quadrotor dynamics. Moreover, Principal Component Analysis (PCA) is applied to the attitude parameters to obtain a reduced-order multivariable LPV model with fewer dimensions and lower computational complexity. To enhance stability and robustness, a robust state-feedback controller based on a pole placement approach is designed. External disturbances, including wind perturbations, are mitigated using an attenuation-based robust control method formulated through Linear Matrix Inequality (LMI) conditions. In addition, a polar position controller is incorporated to further improve tracking performance and overall control efficiency. The pole locations of the LPV multimodal closed-loop system are assigned by defining an appropriate LMI region corresponding to a conic sector in the complex plane, with an inner angle of approximately 139° and an apex at (-2β,0). Simulation results indicate that β = 10 and an attenuation level of γ = 2.5 provide the desired control performance. The obtained results verify the effectiveness of the proposed strategy in achieving robust attitude and position control of the Quadrotor system under external disturbances. This framework balances tracking accuracy, robustness, model simplicity, and computational efficiency for Quadrotor control.

Keywords

• Position control
• Attitude control
• PCA
• Pole placement
• LMI

References

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