Avoiding Switching Upon Failure of a Sensor in the Lateral Control System of a Quadcopter
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International Applied Mechanics, Vol. 56, No. 2, March, 2020
AVOIDING SWITCHING UPON FAILURE OF A SENSOR IN THE LATERAL CONTROL SYSTEM OF A QUADCOPTER* V. B. Larin1 and À. À. Tunik2
An algorithm of designing a controller of the lateral movement of a quadcopter is offered. This algorithm guarantees the stability of the system in the case of failure of the roll angle sensor. The controller does not require changing the configuration of the feedback circuit after failure of the sensor. All procedures used to design the controller can be implemented using standard MATLAB routines. Keywords: quadrocopter, failure, feedback Introduction. Mathematical problems related to the control of mechanical systems are of special importance for engineering [1, 3, 6, 8]. They include some operating reliability problems [4, 12, 13]. For example, the following problem of improving the reliability of the lateral control system of a quadcopter was addressed in [9]: in the case of failure of the roll sensor, the signal from a dynamic observer can be used as a source of corresponding information (i.e., the configuration of the feedback circuit is changed). We will address the problem of improving the reliability of the lateral control system of a quadcopter in which the configuration of the feedback circuit is not changed. Assuming that the signal from the failed roll sensor is equal to zero, we will solve the problem of ensuring the stability of a closed-loop system (without change in its configuration) in the case of either regular functioning or failure of the corresponding sensor. Thus, the controller is subject to additional constraints. We will describe an algorithm of designing a lateral motion controller that ensures the stability of a quadcopter in the case of failure of the roll sensor. It is assumed that the whole phase vector is observable and that the system has one input. The procedure of designing such a controller can be implemented using standard MATLAB routines [5]. 1. General Relation. Let x = [ x y z ]¢ be the position vector of the quadcopter center; y , q, j be the yaw, pitch, and bank angles, respectively; f1 be the lift of the ith motor M i ( i = 1, 4 ); the prime denotes transposition. According to [3], the equations of motion of the system are mx&& = -u sin q,
(1.1)
&& = u cos q sin j , my
(1.2)
mz&& = u cos q cos j - mg,
(1.3)
&& = ~ y ty ,
(1.4)
1
S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova Str., Kyiv, Ukraine 03057; e-mail: [email protected]. 2National Aviation University, 1 Komarova Av., Kyiv, Ukraine; [email protected]. Translated from Prikladnaya Mekhanika, Vol. 56, No. 2, pp. 53–59, March–April 2020. Original article submitted January 16, 2019.
*
170
This study was sponsored by the budget program “Support for Priority Areas of Scientific Research” (KPKVK 6541230).
1063-7095/20/5602-0170 ©2020 Springer Science+Business Media, LLC
&&q = ~ tq ,
(1.5)
&& = ~ j tj ,
(1.6)
where mis the mass of the vehicle; g = 9.8 m/sec2 is the accelerat
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