Prima di poter impostare il calcolo del conrollore ottimo, `e necessario pro- gettare il sistema di controllo, ossia decidere la posizione e il tipo di sensori e il sistema di attuazione. Inoltre `e necessario impostare il modello matematico del sistema sul quale si baser`a il progetto del controllore.
A.4. Progetto del controllore
Sul modello del velivolo sono stati posti 9 accelerometri, come mostrato in fig. (A.3) 0 5 10 15 20 25 30 35 40 −5 0 5 10 15 20 25 Accelerometer position
Figure A.3 Location of accelerometers.
Oltre alle misure di accelerazione anche le velocit`a e le posizioni derivanti dall’integrazione di queste misure sono state considerate. Si `e supposto di avere a disposizione la completa conoscenza dei movimenti rigidi dell’aereo, si assume quindi che il velivolo `e dotato di un sistema di navigazione inerziale che si suppone essere abbastanza preciso da poterne trascurare la dinamica. Anche le rotazioni delle superfici di controllo vengono misurate, e la dinamica del sensore viene trascurata.
La normativa stabilita dall’European Aviation Safety Agency (EASA) prevede che il velivolo sia in grado di sopportare raffiche della forma 1-cos:
vg = (U gust 2 1 − cos πs H 0 < s ≤ 2H 0 s > 2H (A.8)
dove s `e la distanza di penetrazione nella raffica, H `e il gradiente della raffica, e Ugust `e la velocit`a della raffica, che varia al variare della quota e del gradiente della raffica.
Il progetto del controllore viene effettuato basandosi su una raffica deter- ministica di lunghezza H = 50 m, i risultati ottenuti sono mostratin in fig. (A.4)
Si pu`o notare come una riduzione del picco pari a circa il 18% sia stata raggiunta.
Calcoli eseguiti con diversi valori di lunghezze di raffica e di velocit`a di volo hanno dimostrato la capacit`a del controllore di adattarsi alle varie condizioni di volo.
A.4. Progetto del controllore 0 1 2 3 −1 −0.5 0 0.5 1 1.5x 10 6 time [s] M x [Nm] Open loop LQG SOF
(a) Wing root Bending moment.
0 1 2 3 −6 −4 −2 0 2 4 6 8x 10 4 time [s] M x [Nm]
(b) Horizontal tail plane root Bending moment. −1 −0.5 0 0.5 1 1.5 x 106 −5 0 5 10 x 104 Mx [Nm] M y [Nm] Open loop LQG SOF
(c) Wing root bending and torsion.
−5 0 5 x 104 −2 −1 0 1 2x 10 4 Mx [Nm] M y [Nm] Open loop LQG SOF
(d) Horizontal tail plane bending and torsion. 0 1 2 3 −4 −3 −2 −1 0 1 time [s] δ a [deg] LQG SOF
(e) Aileron deflection angle.
0 1 2 3 −1 −0.5 0 time [s] δ e [deg] LQG SOF
(f ) Elevator deflection angle. Figure A.4 Response to discrete gust. H = 50 m, V∞= 220 m/s.
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