Abstract
ABSTRACTThe main aim of this paper is to present stability region analysis for a closed-loop system with the second-order model with a time delay and continuous-time fractional-order proportional-derivative (PD) controller. The model of the plant used in the paper approximates the dynamics of a simplified motor–rotor model of multirotor's propulsion system. The controller tuning method is based on Hermite–Biehler and Pontryagin theorems. The tracking performance is also analysed in the paper by observing the integral of absolute error and integral of squared error indices. The presented results are expected to be useful in future when comparing simulation with experimental results.
Highlights
Fractional-order systems, can be considered as a generalization of integer-order ones [1]
The main aim of this paper is to present stability region analysis for a closed-loop system with the second-order model with a time delay and continuous-time fractional-order proportionalderivative (PD) controller
The step response of the real propulsion unit has been presented in Figure 4 together with a proposition of a simplified model, namely the second-order inertia model with a time delay, where the unity gain corresponds to maximum useful rotational speed of the propulsion unit, namely approx. 9550 rotations per minute (RPM)
Summary
Fractional-order systems, can be considered as a generalization of integer-order ones [1]. Due to the characteristics of controlling a UAV, every additional correction of its position or orientation, resulting from lack of balance between the forces, is connected with an additional energy expense, limited by the battery capacity, and may result in reducing the time of flight This is the reason the authors propose to introduce an additional feedback loop to track the rotational speed in a multirotor UAV control loop, to ensure the control system can reserve a set of rotational speed and thrust force values of the output of the driving units [21]. It is expected to propose an efficient control algorithm that is tuned to an adequate dynamics model (adequate model of the motor)
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