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It was confirmed through software-in-the-loop SIL verifications using blade element theory BET that the autopilot is capable of performing navigation and landing under high parametric variations and strong winds. Currently work is in progress for establishing hardware-in-the-loop HIL and flight test platforms to validate the outlined design strategy [ 58 — 67 ].

Future research directions also include studying alternative methods for the controllers and investigating the possibility of reducing controller size. Conceptualization: CK. Data curation: CK. Formal analysis: CK. Funding acquisition: CK. Investigation: CK. Methodology: CK. Project administration: CK.

Resources: CK. Software: CK. Supervision: CK. Validation: CK. Visualization: CK. Writing — original draft: CK. Browse Subject Areas? Click through the PLOS taxonomy to find articles in your field. Abstract Some level of uncertainty is unavoidable in acquiring the mass, geometry parameters and stability derivatives of an aerial vehicle.

Introduction Quite a few applications require automatic flight control techniques that help or even replace the human pilot [ 1 , 2 ]. These traditional approaches are presently embedded in many of the existing autopilot systems used in civilian and military aircraft.

Systematic construction of autopilots to remedy the risks associated with parameter variations : It is demonstrated that MIMO robust control approaches can endure large parametric variations and at the same time maintain good performance for aircrafts. Separation of design-models and verification-models : A clear separation between the aircraft model used in design and that used for verification is made for this study. The autopilot designs utilize a mathematical model based on the theory of aircraft dynamics.

This model consists of nonlinear differential equations for which the forces and moments are computed using coefficients called stability derivatives. Once the controllers are established, the final closed-loop verifications are done with SIL tests which are based on different and much more accurate models of the aircraft. These models use BET in which all surfaces of the aircraft are subdivided into small regions called blade elements for force and moment calculations.

BET flight simulations are widely regarded to produce the most realistic results. Moreover, they are not based on ordinary differential equation models of the aircraft such as the one we use here for designing the controllers. Avoiding the same type of model in the testing phase is advantageous to increase the validity of the proposed methods. Methodology Mathematical Model The first step is the derivation of the mathematical model on which numerical analysis and controller design will be carried out.

I is the inertia tensor of the rigid body defined as The coefficients of the matrix I are the moments and products of inertia of the rigid body and they are constant for a frame of reference fixed to the aircraft. A rearrangement of Eqs 1 and 2 yields 3 4 After some manipulations the following non-linear state space system is obtained 5 with 6 7 These equations can be written compactly as 8 with state vector x , input vector u , disturbance vector v , and time t. Download: PPT. Fig 1. Trimming and Linearization Trimming describes the procedure for identifying an operating point for a provided flight condition.

The nonlinear aircraft model could then be linearized around the operating conditions x 0 , u 0 , which produces a linear state-space system G of the form to be utilized in controller design 18 where and 19 20 The vectors fields f x , u and h x , u consist of respectively the equations for derivatives of the states and the outputs to be controlled.

The objective of the robust controller design is to stabilize by a controller K , not only the nominal plant but also the family of perturbed plants defined as 34 For robust stability, internal stability must be achieved for the nominal and perturbed plant. Fig 2. Blade Element Simulation After nonlinear dynamical simulations, the final test for the control system is software-in-the-loop SIL verifications based on blade element theory BET.

Fig 3.

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During flight simulation, the aircraft is split into a number of surfaces and the forces on each are computed by BET. Fig 4. Illustration of the main idea of blade element theory BET on a propeller blade. Results In this part first the issues linked to the conventional independent SISO control strategy is highlighted on the attitude control inner loop of a popular general aviation aircraft, namely the Cessna Table 1. Mass, geometry parameters and performance specifications for Cessna Fig 5. Fig 7. States of perturbed aircrafts under combined SISO control.

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Fig 9. States of the nominal aircraft under loop-shaping control. Fig Inputs to the nominal aircraft under loop-shaping control.

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States of perturbed aircrafts under loop-shaping control. Inputs of perturbed aircrafts under loop-shaping control. States of the nominal aircraft with loop-shaped inner and outer controllers. Inputs to the nominal aircraft with loop-shaped inner and outer controllers.

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Outputs of perturbed aircrafts with loop-shaped inner and outer controllers. Inputs to perturbed aircrafts with loop-shaped inner and outer controllers. Conclusions Two multi-input multi-output MIMO control design approaches were investigated to handle parametric uncertainties in autopilot design for aircrafts. Supporting Information.

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S1 File. Author Contributions Conceptualization: CK. References 1. Etkin B, Reid LD. Dynamics of flight: stability and control, 3rd edition. New York: Wiley; Nelson RC. Flight stability and automatic control. McGraw Hill; Aircraft Control and Simulation, 2nd edition. Wiley-Interscience; Blakelock JH. Automatic control of aircraft and missiles, John Wiley and Sons; Autopilots for small unmanned aerial vehicles: a survey. International Journal of Control, Automation and Systems.

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Roll-pitch-yaw integrated robust autopilot design for a high angle-of-attack missile. Journal of guidance, control, and dynamics. Dynamic inversion for missile lateral velocity control via polynomial eigenstructure assignment. Tsay TS. Decoupling the flight control system of a supersonic vehicle. Intelligent adaptive backstepping control for MIMO uncertain non-linear quadrotor helicopter systems.

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Nonlinear H-infinity decoupling hover control of helicopter with parameter uncertainties. American Control Conference; Longitudinal and lateral adaptive flight control design for an unmanned helicopter with coaxial rotor and ducted fan. Feedback control strategies for quadrotor-type aerial robots: a survey.