Abstract
This paper presents the application of the model predictive approach to design a flight control system (FCS) for longitudinal dynamics of a fixed wing aircraft. Longitudinal dynamics is derived for a conventional aircraft. Open loop aircraft response analysis is carried out. Simulation studies are illustrated to prove the efficacy of the proposed model predictive controller using H∞ state observer. The estimation criterion used in the \({\text{H}}_{\infty }\) observer design is to minimize the worst possible effects of the modelling errors and additive noise on the parameter estimation.
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Abbreviations
- \({\text{A}}, {\text{B}}, {\text{C}}, {\text{D}}\) :
-
Matrices with appropriate dimensions defining system dynamics
- \({\grave{\text{A,}}} {\grave{\text{B,}}} {\grave{\text{C}}}\) :
-
Augmented system matrices
- \({\updelta }_{\text{e}} ,\;{\updelta }_{\text{t}} ,\;{\updelta }_{\text{a}} ,\;{\updelta }_{\text{r}}\) :
-
Elevator, thrust, aileron and rudder deflections respectively, degree
- \({\text{F}}_{\text{X}} , {\text{F}}_{\text{Y}} , {\text{F}}_{\text{Z}}\) :
-
Aerodynamic forces along x, y and z axes, respectively, N
- \({\text{g}}\) :
-
Gravity, m/s2
- \(\upgamma\) :
-
Performance bound on \({\text{H}}_{\infty }\) filter/observer
- \({\text{I}}_{\text{x}} , {\text{I}}_{\text{y}} , {\text{I}}_{\text{z}}\) :
-
Mass moment of inertia about x, y and z axes, respectively, kg/m2
- \({\text{I}}_{\text{xz}}\) :
-
Product of inertia in x–z plane, kg/m2
- \({\text{J}}\) :
-
Cost function for \({\text{H}}_{\infty }\) filter/observer
- \({\text{J}}_{\text{MPC}}\) :
-
Cost function for model predictive controller
- \({\text{K}}_{\text{k}}\) :
-
\({\text{H}}_{\infty }\) filter/observer gain
- \({\text{L}}, {\text{M}}, {\text{N}}\) :
-
Aerodynamic moments about x, y and z axes, respectively, N/m
- \({\text{m}}\) :
-
Mass, kg
- \({\text{p}}, {\text{q}}, {\text{r}}\) :
-
Body axis angular rates about x, y and z axes, respectively, rad/s
- \({\text{p}_{0}} ,\;{\text{S}}_{\text{k}} ,\;{\text{Q}}_{\text{k}} ,\;{\text{R}}_{\text{k}}\) :
-
Weighting matrices
- \({\upphi },\;{\uptheta },\;{\Uppsi }\) :
-
Angles of roll, pitch and yaw, degree
- \({\text{u}}_{\text{e}}\) :
-
Forward equilibrium velocity, m/s
- \({\text{u}}, {\text{v}}, {\text{w}}\) :
-
Body axis velocities along x, y and z axes, respectively, m/s
- \({\mathbb{u}}\) :
-
Input vector
- \({\mathbb{u}}_{\text{e}} , {\text{x}}_{\text{e}}\) :
-
Equilibrium/trim input and state vectors, respectively
- \({\Updelta} {\mathbb{u}}\) :
-
Change in input vector
- \({\Updelta} {\mathbb{U}}\) :
-
Augmented input vector
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Sanwale, J., Singh, D.J. Model Predictive Flight Control System with Full State Observer using H∞ Method. J. Inst. Eng. India Ser. C 100, 323–332 (2019). https://doi.org/10.1007/s40032-018-0443-9
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DOI: https://doi.org/10.1007/s40032-018-0443-9