Thesis - Beaver simulation

Chapter 5

77

f

[s]

f

[s]

i

f

[radls]

f

[radls]

phugoid

i

-0.01614 +

i

23.8

i

42.94

0.0612

:

0.2631

i

0.2636

i

0 26311 i

.......................

;...........................................

........................

........................

....................

..........................

short

i

-2.1606 *

i

2.606

i

0.32

i

0.6673

i

2.4112

i

3.2374

period

i

2.4112i j

Asymm

roll subsi-	1	-5.1351	j	-		0.135	i
dence	i
.....................................................................................................................................................................
spiral	!	-0.04573	i	-	i	15.15	f

Table 5-3. Basic open-loopproperties of the linear 'Beaver' model, derived from the nonlinear SIMULINKmodel with ACLIN.

Figure 5-12, which has been included a t the end of this chapter, shows some Bode plots for the longitudinal open-loop system." The amplitude-ratios and phase-angles have all been determined for an input signal upon the elevator. The resulting plots have been compared with 'typical control-input Bode plots for conventional airplanes', given in ref.[23] (fig.5-2), and the results match remarkably well. Hence, the SIMULINKlinearization tool, applied with default linearization options (perturbation level, etc., see ref.[4]) gives good results, both in time and in frequency domain.

5.6 Conclusions.

The SIMULINKmodels, presented in this report, yield the same results as the flightsimulator software, presented in refs.[6], [18], and [30],so the most critical parts of the models, i.e., the aerodynamic model, engine model, atmosphere and airdata model, and the state equations themselves, have been implemented correctly. The open-loop responses to atmospheric turbulence, given in this chapter, are not exactly equal to the results from ref.[24], but the aircraft model used here differs a lot from the small perturbation models in ref.[24]. For instance, the cross-coupling of longitudinal and lateral motion variables, which is really significant for the 'Beaver', has been neglected totally in ref.[24]. The turbulence models seem to be good enough for most AACS research purposes.

The definition of the phase-angle, used in the MATLABcommand BODE has been maintained, to make sure that the user can reproduce figure 5-12 easily. However, often other definitions for the initial value of the phase-angles are used!

Figure 5-2.Open-loopresponses of the 'Beaver' to a block-shaped elevator input A6, = 3O during 2 seconds. Vo = 45 mls, Ho = 6000 ft.

Chapter 5

79

[Zap] emrue%

Figure 5-2 (continued).

Figure 5-3.Open-loopresponses of the 'Beaver'to a block-shaped aileron input A6, = 3O dud'ng 2 seconds. Vo = 45 m/s, Ho = 6000 ft.

Figure 5-3 (continued).

Figure 5-4.Open-loopresponses of the 'Beaver' to a rudder input A6, = 3O during 2 seconds. Vo = 45 m/s ,

block-shaped

H, = 6000 ft.

Chapter 5

83

Figure 5-4 (continued).

Figure 5-5. Open-loop responses of the 'Beaver' to a flap deflection Asf = 3O in 3 seconds. V, = 45 m/s,H, = 6000 ft.

Chapter 5

85

Figxire 5-5 (continued).

Figure 5-6.Open-loopresponses of the 'Beaver'to a change in engine speed A n = 200 RPM in 4 seconds. Vo= 45 m/s, Ho = 6000 ft.