Abstract
In this note, the problem of tracking random references and rejecting random perturbations in a quadrotor, both generated by an auxiliary system named exosystem, is solved by extending the deterministic tracking problem to the area of stochastic processes. Besides, it is considered that only a part of the state vector of the quadrotor is available through measurements. As a consequence, the state vector of the plant must be estimated in order to close the control loop. On this basis, a controller to track random references and to reject random perturbations is developed by combining a Kalman filter to estimate the references and perturbations of an exosystem and an observer to estimate the states of a quadrotor. Besides, to obtain a more practical controller, the analysis is carried out in discrete time. Numerical simulations are used in a quadrotor to confirm the validity and effectiveness of the proposed control.
Highlights
In the control field, the problem of imposing random references on some outputs of unmanned aerial vehicles is a very recurrent problem. is is because such scenarios appear in many disciplines of science and technology, and among them, aeronautics is one of those areas
To estimate the random references and random perturbations by means of the Kalman filter, it must be recalled that both matrices Cexo and P can be viewed as output matrices for the exosystem, and because of their dimension, they can be used to construct an overall output matrix for the exosystem, namely, CTot [CTexoPT]T, with CTot ∈ R15×5
Remark 3. e design of the controller has been performed on the linear model of the quadrotor, the results presented correspond to the response of the nonlinear system under the action of the designed controller
Summary
The problem of imposing random references on some outputs of unmanned aerial vehicles is a very recurrent problem. is is because such scenarios appear in many disciplines of science and technology, and among them, aeronautics is one of those areas. The flight of butterflies, the behavior of the heart, brain, human march, among others, include a little bit of randomness, to say the least To estimate these kinds of references and perturbations, the Kalman filter [25] has been and still is a very good alternative. E novelty of the proposed approach is the combination of the Kalman filtering and the regulation theory to solve the references tracking and perturbations rejection; this problem cannot be solved by the Kalman filter or the regulation theory by themselves In this sense, the desired controller must achieve two goals which are very similar to those considered in the tracking problem: (1) to stabilize the quadrotor around an operation point when the exosystem is affecting it and (2) to minimize the tracking error when the quadrotor is influenced by external perturbations.
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