Aerospace and Electronic Systems Magazine September 2016 - 46
An Advanced Sense and Collision Avoidance Strategy for Unmanned Aerial Vehicles in Landing Phase
Figure 6.
The structure of the energy-based controller.
The elevator plays a central role in the pitch angle change.
Assuming that a = 0, qm = qd, and
can be simplified as:
(30)
, the first step for de,max is to deSimilar to the calculation of
rive the time when the maximal de will take place. Using the time
derivative of (30),
is expressed as:
sign consists of 1) designing an inner-loop control to minimize the
tracking error of pitch angle q and pitch rate ; 2) developing an
energy-loop to meet the performance criteria for energy tracking in
the slow dynamics; and 3) implementing an outer-loop to eliminate
the altitude tracking error. The structure of the energy-based controller is illustrated in Figure 6.
INNER-LOOP CONTROL
The objective of inner-loop control design is to eliminate the tracking error of pitch angle q, which can be modeled as:
(31)
(35)
where
where
The inner-loop controller is given as:
(32)
By setting t = 0, one can obtain the extrema elevator deflection de,max when
(36)
Comparing the value of
elevator deflection de at t = 0, t = ts, and t = text, the maximal deflection can be found at t = 0. The elevator deflection at t = 0 is:
(33)
From (33) and to ensure
, inequality (34) holds:
,
(37)
where z, Kd Î R+, K5, K6 Î R. Combining (35), (36), (37) and (1),
ϒi = 0 can guarantee that q → qd,
. On the basis of (1), the
desired energy function for the inner-loop is:
(38)
(34)
After examining (29) and (34), ts should satisfy
to keep UAV's stability during collision avoidance process.
For the convergence of tracking error, it is required that the
time derivative of energy function is no greater than zero. In order
to prove that the desired pitch angle qd and desired pitch rate are
achieved by following the proposed inner-loop controller, the time
derivative of (38) is:
PATH FOLLOWING CONTROLLER DESIGN
(39)
The energy-based control design is adopted to modify energy function of the UAV to track the reference trajectory. Similar to the
methodology developed in [25], the procedure of controller de46
By substituting (35) into (39),
requirement of energy objective.
IEEE A&E SYSTEMS MAGAZINE
is derived to satisfy the
SEPTEMBER 2016
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