1. Figs. 24-28 illustrate a sample performance of the multi-axis landing controller amidst velocity and altitude noise shown in Fig.23, filtered by the first-order filter with 8 = 0.8.This value of 6 is selected according to an optimization study of stochastic response of the filter to noiseanditsrisetime.Whilethe initial altitudeinthe noisefree results in Fig.21 is 300 m, that in Figs. 24-28 is based on the realism that the longitudinal controller will be triggered within one 20 ms sampleperiod after the altimeter detects crossing the reference altitude of 350 m. The true
2. a, b.
3. 5-1 Vertical Velocity
4. vertical velocitycomponents altitude, then, is 348.84 m,considering the 1.66 percent 10 bias error in altitude measurements. The actual and reference vertical velocity profiles confirm the earlier conclusion that, becauseofanegativealtitudebiaserror of-2.14 m, and a positive vertical velocity bias error of 0.48 m/s, the actual touchdown takes longer than the reference touchdown (nearly 19 s against 15.85 s). The vertical touchdown velocity is about 1.2 m/s -the constant velocity of the final descent and within the requirement of 1-3 m/s (Table 2). Also, since the horizontal velocity bias error is positive (0.8 m/s), the actual touchdown horizontal velocity vxis negative, 1.32 m/s, exceeding the requirement of+ 1 m/s, Table 2. Fig. 24 shows the measured, noisy horizontal and vertical velocity components. Because the IRU navigation system takes over below h = 45 m, and because the IRU is essentially noise-free, the velocities are seen to be such after t = 8 sec when the lander crosses 45 meter altitude (Fig.26). Next, Fig. 25 illustrates filtered velocity components for 6 = 0.8,much smoother than the measured values in Fig. 24. Fig. 26 compares reference altitude with actual altitudes and, asstated earlier, thelander descends slower than expected. Fig. 26 shows, in addition, the measured altitude, always shorter than the true altitude because of the negative hbias. The h-vzguidance trajectory and actual trajectory are portrayed inFig. 27 and weobserve that thelongitudinal controller trackstheguidancetrajectory easily during both the constant acceleration phase and the constant velocity phase, the latter starting at a true altitude of 5+2.14=7.14 minstead of 5mdueto- 2.14 mofhbiaserror. Fig. 28 shows picturesquely the poignant descent of the lander in the trajectory plane x-h. A slight horizontal, backward motion before touchdown is apparent in the figure. Thethree-axis attitudecontrol, notshown heredueto spaceconstraints, performs exactly asdesired.