Advanced Materials Research Vol. 903 (2014) pp 309-314 Online

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Advanced Materials Research Vol. 903 (2014) pp 309-314 Online available since 2014/Feb/27 at www.scientific.net © (2014) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.903.309

Altitude and Attitude Control of a Trirotor UAV Ismail M. Khairuddin1, a, Anwar P.P. A. Majeed1, b, ANN. Lim2, c, MOHD. Azraai M. Razman1, d, and Abdul Aziz. Jaafar1, e. 1

Faculty of Manufacturing Engineering, Universiti Malaysia Pahang, 26600 Pekan, Pahang Malaysia 2

Department of Aerospace Engineering, Faculty of Engineering, University Putra Malaysia 43400 Serdang, Selangor, Malaysia

a

[email protected], [email protected], [email protected], d [email protected], [email protected]

Keywords: Trirotor, Unmanned Aerial Vehicle (UAV), Vertical Take-Off and Landing (VTOL), Proportional-Integral-Derivative (PID), MATLAB/Simulink

Abstract. This paper outlines the dynamic modelling as well as the attitude and altitude control of a rotary based unmanned aerial vehicle (UAV). A multirotor vertical take-off and landing (VTOL) UAVs, namely Trirotor aircraft is investigated. In essence the the trirotor model consists of three DC motors equipped with three fixed pitch angle rotors without the aid of a swashplate. The mathematical modelling of this multirotor is governed by the Newton-Euler formulation. A classical control algorithm viz. heuristic (Proportional-Integral-Derivative) PID tuning was adopted in the attitude and altitude control of this particular multirotor configuration. It was established from the Simulink simulations that, a PD controller was suffice to control the attitude whilst PID was apt for controlling the altitude of this form of multirotor. Introduction Unmanned Aerial Vehicles, frequently known as UAVs, are basically aircrafts without the existence of an onboard human crew [1]. These vehicles are remotely controlled or pre-programmed with a flight plan for a certain designated task. Primarily focused on military operations, the application of UAVs has been extended to cater civilian tasks which includes area mapping, traffic and air pollution monitoring [2,3]. Its unparalleled attributes facilitate assignments where the risk is high or beyond human endurance, or human intervention is unnecessary [3]. UAVs may be categorized either as fixed wing aircrafts or rotary based aerial vehicles with the former’s contribution is on long flight ranges whilst the latter on its hovering ability as well as its agility to take off and land in limited space. Further maneuverability characteristics are exhibited by vertical take-off and landing (VTOL) type of multirotor UAVs such as quadrotor and trirotor aircrafts [4,5]. The study of UAVs are of great interest among research community since last two decades. A number research groups in the past few years have looked into the thesis of trirotors, for instance the University Technology of Compiegne scrutinizes on single trirotor type [6] while Draganfly Innovations Inc. initiates Draganflyer X6, a coaxial trirotor system. The development of the mathematical models for trirotor aircrafts have been studied extensively. The equation of motion of the rotorcrafts may be derived using either the Newton-Euler or the Euler-Lagrange formulation [6, 7]. The control input describing the motion of such rotorcrafts are primarily due to the thrust generated by the varying velocities of the rotors in which a tilt angle is considered on the tail rotor. The actuator dynamics are taken into account by means of obtaining it either by using system identification or via torque-voltage relationship [8], however others opined that the effect of the actuator dynamics may be ignored [6]. Both modern as well as classical control schemes have been used to control the altitude, position and the attitude of multirotors. Nested saturation control technique was instigated on the roll-y and pitch-x subsystems of a trirotor aircraft and was found to be positive [9]. PID control algorithm were employed and showed desirable results in controlling the attitude and altitude of a trirotor [10]. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 103.6.236.38, Universiti Teknologi Mara (UiTM), Shah Alam, Malaysia-13/01/15,08:00:05)

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In this paper the mathematical modeling derived for the single trirotor platform is governed by the Newton-Euler formulation. The control architecture is based on the classical PID controller tuned heuristically to obtain thorough altitude and attitude control. Rigid Body Dynamics Trirotor aircraft is considered to be a rigid body due to its dimension relative to its surroundings. The nonlinear equations of motion (EoM) developed are susceptible to up to 6-degree of freedom (DoF). The trirotor is allowed to rotate and translate freely in three-dimensional space. The ensuing rigid body dynamics are derived by the aforementioned formulation. Trirotor. A single trirotor comprises three rotors, in which the tail-rotor is tilted. The tilting action is accomplished by the employment of a servomotor. Apart from cancelling the influence of the system’s torque reaction, the tilt rotor also generates pitch torque, yaw and rapid motion. Hence, an accurate tilt angle is essential to stabilize the system as it controls the hovering and 3 DoF motion.

Figure 1: The Free Body Diagram of a Trirotor aircraft The configuration of a single trirotor is depicted in Fig. 1. The distances of each rotors from the center of gravity are identical and denoted as l1, l2 and l3. The two front rotors, rotors 1 and 2, which rotates in the opposite directions provides the main thrust as well as the roll torque. As the tilt rotor, rotor 3, rotates in the same direction as rotor 2, the system have a tendency to yaw in the counterclockwise direction. The yawing moment of the system is cancelled by the moment created by the thrust produced by tilt rotor as it is tilted in the manner illustrated in the figure above. The tilt angle, α may be expressed as  −ψ I z  α = sin −1  (1)   M3  where ψ, I z , M 3 are the yaw angular acceleration, mass moment of inertia about z-axis and the moment created by the thrust produced by rotor 3. The equation of motion governing the altitude and the rotational motion of the trirotor are as follows: Altitude Motion cos θ cos φ  (2) z = −g + ( F1 + F2 + F3 cos α ) m Rotational Motion

φ = θ =

l1 ( F2 − F1 ) Ix

l1 ( F2 + F1 ) − l3 F3 cos α Iy

(3) (4)

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−l3 F3 sin α (5) Iz The gyroscopic effect is neglected in this model as its influence in near hovering mode is considered as a small disturbance.

ψ =

Control Inputs The altitude and attitude inputs are designated as U1 , U 2 , U 3 and U 4 respectively where U i is a function of the square of motor voltage, V 2i . The thrust generated by the individual rotor, Fi are described by the following expression [8]. (6) Fi = K mVi 2 where K m is the motor constant. Therefore, equations (2,3,4,5) describing the altitude as well as attitude of the trirotor expressed in the preceding section may be rewritten as U 1 U U  (7) z = − g + ( cos θ cos φ ) U1 , φ = 2 , θ = 3 , ψ = 4 Iy m Ix Iz

Control Algorithm The classical PID control algorithm was chosen to investigate the altitude and attitude response of the trirotor aircraft. Simulink model was developed by taking into account the delay time in generating thrust from voltage as well as servo communication. The sampling time used was 0.4s under the pretext of linearized model as well as low noise and disturbance. The model depicted is as per in Fig. 2, whilst the parameters considered is tabulated in Table 1.

Figure 2: Simulink Model of a Trirotor System

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Table 1: Parameters of the Model Parameters Value Mass 1.10 kg Mass Moment of Inertia in the X-axis, Ix 0.02306 kgm2 Mass Moment of Inertia in the Y-axis, Iy 0.02306 kgm2 Mass Moment of Inertia in the Z-axis, Iz 0.04612 kgm2 Arm length of tail rotor, l3 0.3 m Length, l2 0.3 cos 60° m Length, l1 0.3 sin 60° m Motor constant, C 1619.237 N/V2

Results and Discussion Table 2 tabulates the fine-tuned gain parameters obtained heuristically as well as the transient response characteristics obtained.

Table 2: Summary of the Tuning Gains and Response Characteristics Roll angle Pitch angle Yaw angle Altitude Z Proportional gain, Kp -1.5 2 -0.11 10 Integral gain, Ki 4 Derivative gain. Kd -0.7 1 -0.1 9 Rise time (s) 1.065 1.163 1.6725 4.372 Settling time (s) 1.472 1.543 2.001 5.345 The initial conditions for the Euler angles, φ ,θ ,ψ and altitude, z were set to 0.3 rad, 0.3 rad, 0.3 rad and 1m, respectively. The simulation was carried out for over 20 seconds. The results obtained are illustrated in Fig. 3. The low frequency and low amplitude oscillations of the aircraft for roll and pitch angles depicted in Fig. 3 illustrates the response of the aircraft maintaining the same 0.3 rad heading. The oscillations mentioned are most likely caused by the action of the rear motor to provide the torque reaction to sustain the heading of the aircraft.

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Pitch angle vs. Time / θ vs. t

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Figure 3: Altitude and Attitude Response Conclusion and Future Works This paper presents the modelling of a trirotor system using the Newton-Euler formulation. The control of the attitude as well as altitude of the aircraft was modelled using the classical PID controller. The controller was tuned heuristically to obtain the optimum response of the aforementioned system. Based on the result obtained, it may be concluded that the classical PID controller is sufficient to maintain the heading of the aircraft as well as its altitude in indoor environment. The study also shows that the roll and pitch motion are sensitive to the response of the tilt motor. Future works will look into the implementation of modern control schemes apart from bench test/experimental works on the model with respect to the tail rotor to improve the roll and pitch oscillations observed. The study on the remaining translation motion will also be carried out.

References [1] G McCall, J CORDER. New world vistas: Air and space power for the 21 st century, (1996). [2] P Castillo, R Lozano, A Dzul. Stabilization of a mini rotorcraft with four rotors, Control Systems, IEEE. 25 (2005) 45-55. [3] L Derafa, A Ouldali, T Madani, A Benallegue, Four Rotors Helicopter Yaw and Altitude Stabilization, 1 (2007). [4] A L Salih, M Moghavvemi, H A Mohamed, K S Gaeid. Flight PID controller design for a UAV quadrotor, Scientific Research and Essays. 5 (2010) 3660-3667.

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[5] N Guenard, T Hamel, V Moreau, Dynamic modeling and intuitive control strategy for an "X4flyer", Control and Automation, 2005. ICCA '05. International Conference on. 1 (2005) 141-146 Vol. 1. [6] Z Li, S S Sastry, R Murray. A mathematical introduction to robotic manipulation, (1994). [7] E Altug, J P Ostrowski, C J Taylor, Quadrotor control using dual camera visual feedback, Robotics and Automation, 2003. Proceedings. ICRA '03. IEEE International Conference on. 3 (2003) 4294-4299 vol.3. [8] G M Hoffmann, H Huang, S L Wasl, E C J Tomlin, Quadrotor helicopter flight dynamics and control: Theory and experiment, (2007). [9] P Castillo, R Lozano, A Dzul, Stabilization of a mini-rotorcraft having four rotors, Intelligent Robots and Systems, 2004. (IROS 2004). Proceedings. 2004 IEEE/RSJ International Conference on. 3 (2004) 2693-2698 vol.3. [10] Dong-Wan Yoo, Hyon-Dong Oh, Dae-Yeon Won, Min-Jea Tahk, Dynamic modeling and control system design for Tri-Rotor UAV, Systems and Control in Aeronautics and Astronautics (ISSCAA), 2010 3rd International Symposium on. (2010) 762-767.

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Altitude and Attitude Control of a Trirotor UAV 10.4028/www.scientific.net/AMR.903.309 DOI References [7] E Altug, J P Ostrowski, C J Taylor, Quadrotor control using dual camera visual feedback, Robotics and Automation, 2003. Proceedings. ICRA '03. IEEE International Conference on. 3 (2003) 4294-4299 vol. 3. http://dx.doi.org/10.1109/ROBOT.2003.1242264