1. Introduction

Nowadays, the unmanned aerial vehicles (UAVs) represent a big boom in the electronic industry, thanks to their versatility and largely due to the falling cost of the electronic parts and the UAV by itself. UAV is a kind of an aerial vehicle that is able to take off vertically, such as helicopters and some special airplanes, and it is represented by the planar vertical take-off landing (PVTOL) aircraft model. Note that PVTOL aircraft models represent more than only UAV systems. Reliability requirements in aerial vehicles bring the necessity of a fault detection and isolation schema. In general, they are non-linear systems, and so a non-linear inspired strategy for the detection and

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isolation of faults could also be used. An idea consists in taking advantage of the structure given by the Lagrangian model of a PVTOL in order to develop an algorithm for the detection, isolation and identification of faults.

Many research studies dealing with the fault detection and isolation (FDI) problem have been already published, most of them deals with linear systems, see for instance Refs. [1–3]. On the other hand, for non-linear systems, some solutions exist, based on the inherited characteristics, see Refs. [4, 5] for more details. The most common approach used for FDI is the hardware redundancy; however, this approach normally represents an increment in weight and economical cost of the aircraft. In order to avoid this problem, somemathematical relations could be used, the simplest way is to compare two or more internal signals, having as goal to create a residue, which, in fact will be zero if the system is working normally and different from zero if not. In order to create such relations it is common to exploit some intrinsic characteristics of the systems. See for instance Ref. [6]. Diagnosis for the PVTOL system has been considered previously using a Hamiltonian formalism [7].

A Lagrangian formalism is used to model a PVTOL in order to obtain an aircraft model. The Euler-Lagrange model of the PVTOL is used to develop an algorithm for fault diagnosis. Diagnosis implies the detection, isolation and identification of a fault. The considered approach is based on the knowledge of a system model as well as the model of the possible faults. The idea is to use non-linear decoupling approach to derivate a set of subsystems, each related to a specific fault or a set of faults. An observer-based residual generation is designed for each subsystem. Detection and isolation of faults can be reached at this stage, for fault identification a kind of approximated inversion algorithm to meet the different diagnostic levels. The results are obtained taking advantage of the structure given by the Euler-Lagrange modelling of the PVTOL as well as from recent results related to observer design and fault identification.

Fault diagnosis algorithms can be developed for a more or less general Euler-Lagrange model of a system, which, in fact, also include a PVTOL system. Fault diagnosis includes detection, isolation and identification of faults. In order to meet a diagnosis task, an observer-based residual generator is designed in order to determine whether a fault is present. A decoupling approach is used in order to guarantee also a fault isolation task. As discussed, both steps could be systematically developed for the considered system model. Further, fault isolation is approached using a kind of approximated system inversion to develop approximated fault estimation through dynamic inversion of the corresponding residual equation. The schema is shown using a specific example of a PVTOL. As presented in the results, the proposed approach can be used effectively for the diagnosis of a PVTOL system.
