Tham khảo tài liệu 'advances in flight control systems part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Adaptive Backstepping Flight Control for Modern Fighter Aircraft 27 Inertial position control We start the outer-loop feedback control design by transforming the tracking control problem into a regulation problem 0 0 1 sin X cos X 0 0 - Yref 9 where we introduce a vehicle carried vertical reference frame with origin in the center of gravity and X-axis aligned with the horizontal component of the velocity vector Ren and Beard 2004 Proud et al. 1999 . Differentiating Eq. 9 now gives Zo V Z2X - V cos x- Xrei -Z01X V refsin x-Xref zref - V sin Y 10 We want to control the position errors Zo through the flight-path angles X and Y and the total airspeed V. However from Eq. 10 it is clear that it is not yet possible to do something about z02 in this design step. Now we select the virtual controls Vdes 0 Vrefcos x- Xref - c z 11 _ -ref c03zo3 - V Y 12 n n where c01 0 and c03 0 are the control gains. The actual implementable virtual control signals Vdes and ydes as well as their derivatives Vdes and Ydes are obtained by filtering the virtual signals with a second-order low-pass filter. In this way tedious calculation of the virtual control derivatives is avoided Swaroop et al. 1997 . An additional advantage is that the filters can be used to enforce magnitude or rate limits on the states Farrell et al. 2003 2007 . As an example the state-space representation of such a filter for Vdes 0 is given by r 1 1 t m Ì . f _ V-V SR 2 X V -q1 J- J 13 V des 1 V des 14 where SM and SR represent the magnitude and rate limit functions as given in Farrell et al. 2007 . These functions enforce the state V to stay within the defined limits. Note that if 28 Advances in Flight Control Systems the signal Vdes 0 is bounded then Vdes and Vdes are also bounded and continuous signals. When the magnitude and rate limits are not in effect the transfer function from V des 0to Vdes is given by ydes 2 m. V deS 0 g2 2ZVmV m2 15 and the error Vdes 0 - Vdes can be made arbitrarily small by selecting the
