Designing 3-DOF Hardware-In-The-Loop Test Platform Controlling Multirotor Vehicles

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1 WeAT3.5 Designing 3-DOF Hardware-In-The-Loop Test Platfor Controlling Multirotor Vehicles Muhsin Hancer Rahan Bitirgen Isail Bayezit Faculty of Aeronautical and Space Sciences, Necettin Erbakan University, Konya, Turkey (e-ail: Faculty of Aeronautics and Astronautics, Istanbul Technical University, Istanbul, Turkey (e-ail: Abstract: Main idea of this paper is the developent of Hardware-in-the-Loop test platfor in order to flight echanical odeling and better stabilization of ultirotor vehicles via different feedback control structures, including PID controllers. First, nonlinear atheatical odel of the quadrotor platfor is built and validated via Matlab/Siulink based siulation environent.then, Hardware-in-the-Loop (HIL) test scenario is developed to analyze and tune controller paraeters with the help of in-house designed testbed echanis. Next step is observing the quadrotor attitude aneuvers via ebedded hardware over the gyroscopic giballed testbed. The HIL testbed enables us validate and calibrate odel and control paraeters within real-tie environent including inertial and echanical sensors for ultirotor systes. In this study, the particular platfor is IRIS cross-type quadrotor vehicle PID based control for stable hover flight. Keywords: Hardware-in-the-Loop siulation, Model Based Design, Flight Mechanical Modeling, Engine Test Platfor, Pixhawk Processor, Rotary Wing Aerial Vehicles, Multirotor Systes, Real-tie PID Control. 1. INTRODUCTION Recent developents on the sensor and electronics technology triggered increasing attention on the quadrotor airvehicles. The usage of ultirotor vehicles are increased very rapidly within civilian and ilitary applications nowadays. Especially specific issions, which are dangerous for and over the capacity of huans, such as security and surveillance operations, detection and follow-up of eneies and targets, border patrolling, road traffic control, daage detection after natural disasters, investigation of crie scene, and agricultural applications. In the literature, a lot of topics are studied for odeling and control of quadrotor vehicles. Before starting our HIL platfor design task, our bencharking is focused on testbench designs specifically for high fidelity and ultiphysical odeling and control of quadrotor vehicles. Many researchers design various type of testbeds for experiental duties on the real-tie stabilization of quadrotor vehicles. Prach et al. (216) studies an experiental evaluation of the forward-propagating Riccati Equation control. The paper includes nonlinear dynaics of Quanser 3 Degrees of Freedo (3-DOF) Hover experiental testbench to update real-tie feedback gains coparing with conventional linear quadratic regulator. Alexis et al. (21) gives the background of design and verification of a constrained finite tie optial controller for attitude stabilization of a quadrotor ebedded on the testbench. Experiental set-up consists of a fan for wind-gust disturbances and Dragonfly quadrotor on-board Inertial Measureent Unit (IMU). Yu and Ding (212) tests and validates 6-DOF flight controller on a quadrotor testbed. Quadrotor vehicle is ounted both 6-axes force/torque sensor (3-axes assigned to forces and 3-axes assigned to torques) and a sphere joint to let vehicle rotate in 3-axes. On-board IMU sensor is used for sensor fusion in order to experientally control the vehicle via nonlinear trajectory linearization control technique. An et al. (213) handles the control of a quadrotor vehicle using second order geoetric sliding ode attitude observer on a testbench coparing traditional quaternion based sliding ode observer. The paper includes the design of an experiental testbed which coposed of wireless reviver, on-board controller, and the IMU to stabilize of attitude states. In this paper, a new 3-DOF HIL testbed is designed and anufactured at ITU Model Based Design Lab to test and validate different ultirotor attitude aneuvers via tuning PID coefficients. Organization of this paper is as follows: Section 1 is the Introduction, includes the literature review and bencharking of different HiL test platfors for ultirotor operations. Section 2 presents atheatical odeling of cross-frae type quadrotor vehicle with Newton-Euler ethods. Section 3 elaborates the identification of the quadrotor vehicle paraeters considering frae type configuration with diensions, otor and propeller thrust and drag coefficients, and experiental calculation of oents of inertia of quadrotor vehicle. Designing and anufacturing of HIL Aerospace testbed steps are also 218 International Federation of Autoatic Control 119

2 expressed in this section. Siulation and ipleentation results are given in Section 4 related to the design of the quadrotor flight controller and the evaluation of siulations and experiental test results. Section 5 provides the conclusion discussing the potential future roadap. ψ ω b = R φ + R φ R θ θ + R φ R θ R ψ φ [ [ ωbx 1 sθ φ ω b = ω by = cφ cθsφ ω bz 1 sφ cθcφ θ ψ (2) 2. MATHEMATICAL MODEL OF CROSS TYPE QUADROTOR Matheatical odeling of quadrotor is the proinent part in order to better design and tune controller gains. In this work, cross frae type IRIS quadrotor vehicle is used for siulation and experiental studies. Inertial, vehicle, and body fraes can be considered as coordinate fraes of quadrotor vehicle. The inertial frae is earth centered at the vehicle otion starting point and has orthogonal three axes ξ i =(X i, Y i, Z i ). Vehicle frae is centered at center of gravity of the quadrotor ξ v =(X v, Y v, Z v ). This frae is used for translational otion of the vehicle with respect to inertial frae. The origin of the body coordinate frae, ξ b =(X b, Y b, Z b ) is related with rotational otion with respect to vehicle frae at the center of the gravity of the quadrotor. X axis points out to the front of the quadrotor with roll otion phi (φ) angle, Y axis always points out fro right of the quadrotor with pitch otion theta (θ) angle and Z axis always points down fro center of the gravity of the quadrotor with yaw otion psi (ψ) angle. Quadrotor has two types of otion: linear translational and rotational otion. Quadrotor can also be represented as a point ass during translational otion for the sake of siplicity to obtain PID control gains. Linear and angular velocities are as follows: V b = [u v w T η b = [p q r T Cobination of three atrix to Direction Cosine Matrix to transfor angular otion fro body frae to inertial frae is obtained as (s refers to sine and c refers to cosine); Xb R b i = Y b = Z b [ sθcψ cψsθsφ sψcφ cψsθcφ + sψsφ sθsψ sψsθsφ + cψcφ sψsθcφ cψsφ sθ cθsφ cθcφ R b = R b i R i [ sθcψ cψsθsφ sψcφ cψsθcφ + sψsφ sθsψ sψsθsφ + cψcφ sψsθcφ cψsφ sθ cθsφ cθcφ Xi Y i Z i (1) Rotational otion atrix for angular velocities in body frae; Therefore, transforation of angular velocities fro body frae to inertial frae is as follows; φ 1 sφtθ cφtθ = cφ sφ θ ψ 1 sφ 1 cθ cφ 1 cθ [ ωbx ω by ω bz (3) T = K t (ω ω ω ω 2 4) T = K t U 1 (4) T is total trust of four otor and K t is thrust coefficient of the propellers. U 1 is thrust control input. τ ψ = K d (ω ω 2 2 ω 2 3 ω 2 4) τ ψ = K d U 4 (5) K d is drag coefficient of the propellers. U 4 is yaw control input. τ θ = K t (L xf (ω ω 2 3) L xb (ω ω 2 4)) τ θ = K t U 3 (6) τ φ = K t (L yf (ω 2 3 ω 2 1) + L yb (ω 2 2 ω 3 4)) τ φ = K t U 2 (7) U 2 and U 3 are roll and pitch control inputs. The following atrix shows relationship between control input and angular velocities of each otors with propeller coefficients. T K t K t K t K t ω1 2 τ φ K τθ = t L yf K t L yb K t L yf K t L yb K t L xf K t L xb K t L xf K t L ω 2 xb ω 2 (8) 3 τ ψ K d K d K d K d ω4 2 Eq. (8) includes L yb, L yf, L xb, and L xb oent ars syetric axis of X and Y as shown in Fig. 1. The Gravity effect on the quadrotor direction is along to z axis into earth center. The vector notations of Gravity can be given as follows: F G = [ g The gravitational force acting on the quadrotors center of gravity in the body frae, it needs to be converted by ultiplying the rotation atrix with the gravitational force vector in the inertia coordinate frae; (9) 12

3 ẍ = (sφsψ + cψsθcφ) K tu 1 ÿ = ( cψsφ + sψsθcφ) K tu 1 z = g + (cθcφ) K tu 1 φ = I yy I zz qr + K tu 2 I xx I xx θ = I zz I xx I yy pr + K tu 3 I yy ψ = I xx I yy I zz qp + K du 4 I zz (14) 3. PHYSICAL PARAMETER IDENTIFICATION OF QUADROTOR AND HIL TEST PLATFORM Fig. 1. Moentar lengh and angles between ar groups of quadrotor. F b G = P b i F i G [ gsθ F b G = gcθsφ gcθcφ (1) Force and Moent dynaic equations acting on the quadrotor are expressed as in Eq. (4 6) and Eq. (1). The basic principle of the Newton-Euler Method is given as: [ F b = τ b [ [ I I V b η b [ + ηb (V b ) η b (Iη b ) (11) Rotational equations with Newton-Euler ethod are as follows: [ Kt U 2 I xx φ K t U 3 = I yy φ + K d U 4 I zz φ [ qizz r ri zz q ri xx p pi xx r pi yy r ri yy p Translational equations with Newton-Euler ethod; [ẍ ÿ z = Xb [ Y b Z b K t U 1 + [ g (12) (13) Nonlinear atheatical odel of quadrotor with rotational and translational equations: Quadrotor physical paraeter identification is divided into two phases in this section. First, otor and propeller thrust and drag coefficients are obtained for the calculation of thrusts and drag forces of the propelling echanis with the help of in-house designed engine testbench as illustrated in Fig. 2. Next, oents of inertias (I xx, I yy, and I zz ) are calculated as the second of the experiental identification study. 3.1 Motor And Propeller Perforance Testbed Deterining the physical paraeters of the quadrotor vehicle needs special testbeds. This paraeters are oents of inertia atrix, and propeller drag and thrust coefficients. Propeller coefficients are needed to calculate thrust, yaw, pitch and roll otion as seen in Eqs. (4 7). Therefore, obtaining K t and K d thrust and drag coefficients are pretty iportant. Measureent of the trust and drag are generated by the propeller. Thrust force is perpendicular to the rotation direction of the otor. The drag force generates oents around the rotation axis as seen in Figure 2. Basic forulations are T = S (13/235) and D = S (13/235). S is refer to scale reaction force. The trust coefficient K t and drag coefficient K d forula are K t = T/ρn 2 d 4 and K d = D/ρn 2 d 5. n is refer to revolution persecond (RPS), d is diaeter of the propeller. So revolution per inutes (RPM) values is converted to RPS values to calculate K t and K d. The otor-propeller perforance testbed was designed on the CAD, produced with 3D printer assebled with T- otor MN Kv and propellers. The otor were connected to Lipo Battery via a 2 Ap Electronic Speed Controller (ESC) unit and controlled by Arduino UNO with Pulse-Width odulation (PWM) signals. There was soe bottleneck when experiental works was going. Upstrea flow is in front of the propeller that air flow encounters it. Downstrea flow is back of the propeller that air flow passes it. First experient, there was a blockage for downstrea flow that acting as a ground effect that reducing the thrust nearly fifty percent and generated irritating sounds. Second experient, the blockage was reoved but when the gathering data in front of the propeller, thrust value was changing so upstrea flow affects the thrust relatively. This aerodynaic experienced 121

Table 1. Moents of Inertia of Quadrotor Experiental Analytical Unit I xx.218.238 kg 2 I yy.11.88 kg 2 I zz.31.33 kg 2 Fig. 2. A- Thrust Force, B- Drag Force Calculations. Fig. 4.

Whenever it is felt enough then the period of the oscillation calculate with tie (t) and turn counter (N), T = t/n. The eq. 15 is used to calculate oent of inertia. D refers to distance between ropes.

4 Table 1. Moents of Inertia of Quadrotor Experiental Analytical Unit I xx kg 2 I yy kg 2 I zz kg 2 Fig. 2. A- Thrust Force, B- Drag Force Calculations. Fig. 4. The support part production and quadrotor assebly via support on the testbed. are started sae tie, one coing and one going is counted one turn. Whenever it is felt enough then the period of the oscillation calculate with tie (t) and turn counter (N), T = t/n. The eq. 15 is used to calculate oent of inertia. D refers to distance between ropes. L refers to length of ropes. g refers to gravity. is ass of the quadrotor. I = g D2 T 2 16 π 2 (15) L The experient result is shown at the Table 1 with analytically results DOF Multirotor Test Platfor Fig. 3. Measureent thrust and drag values respect to RPM values. was gained during the otor and propeller coefficients were experiented. Experient data consists of PWM, RPM, RPS and thrust or drag values as illustrated in Fig. 3. Trust and drag experients are done to get K t and K d coefficients. 3.2 Moents of inertia The oent of inertia of the quadrotor is iportant for designing the controller and siulation. I xx, I yy and I zz are calculated analytically and obtained experientally. With assuption of syetric geoetry of the quadrotor, I xy, I xz, I yx, I yz, I zx and I zy are zero. Analytically calculations for sae quadrotor odel are used fro Fu (215), I xx =.238kg. 2, I yy =.882kg. 2, and I zz =.33kg. 2. The obtaining the oents of inertias with experiental is a ethodology that chronoeter, ruler, scale and soe rope are the basic needs. To preparing for the experiental set up, the quadrotor lash down along the desired oent of inertia axis. The ropes have to be lashed down perpendicular to the flat and parallel each others. To find I xx and I yy two rope is enough but for I zz one ore rope needs. Firstly, quadrotor is turned sall angle enough to initiate oscillation on the center of ass along the desired axis. After oscillation and chronoeter Validation of the siulation outputs is iportant before ready to flight. So experiental works are needed to verify how the control signal is reliability and stability. PID controller perforance has to be tested on the testbench. Therefore, a new testbench is designed to ipleent control ethods on the quadrotor vehicle with 3-DOF referring to attitude otions thats are pitch, roll, and yaw. 3-DOF testbed having gyroscope working principle as ain idea as in literature?. Main frae, outer circle, inner circle and beas aterials were chosen as iron because of cheap, reachable and easily shaping and welding factors. Coputer nuerical control and iron bending achines were used at production process. Last step of producing was printing all the part with white color. Mounting the quadrotor odel on the test platfor is needed one part design and production. This parts should be at the center of ass of the quadrotor and the testbench and ade fro light aterial because of little affects on the quadrotor otion. The support part connecting the quadrotor on testbed was designed as CAD part then produced on the 3D (three diensional) printer as seen in Fig SIMULATION AND EXPERIMENTAL RESULTS Quadrotor vehicle is dynaically odeled and HIL testbed is produced up to this section. The experiental identification of the quadrotor is done to run siulations and 122

5 ipleent on the HIL testbench via apply PID controller. Main ai of this section is PID controller responses both siulation and real tie response of the quadrotor otions in the HIL testbed. This section coposes of two ain part. First is related with Matlab Siulink environent to run the nonlinear syste odels. Second is about to ipleentation of the designed PID controller real tie C++ codes on the Pixhawk autopilot on the testbed and gathering the logged real flight data with anual tunning gains of the controllers. The ain control architecture of this work is based on angle control via easured or siulated feedback signals. For attitude control of the quadrotor, HIL testbed was designed and siulations are run due to this perspective. In this work, Pixhawk, controller of the syste as hardware on board different types of sensors, controls the quadrotor syste via designed control algorith and sensors data to siulate HIL and validation. The Pixhawk runs the NuttX Shell real tie operating syste with Ardupilot open-source algoriths as software. On the HIL testbed, PID controller coefficients are anually set to reach optial outputs.pid (Proportional-Integral- Derivative) controller is currently ost used closed-loop (feedback) controller in industrial applications. Besides, siple structure and easily tunning the paraeters and enabling efficiently and relatively robust control capabilities with regard to Modern Control Methods are attracting ways to be ost in usage. It is currently been used to design autopilot for UAVs as a beginning for private sector copanies and research institutes. Control architecture of quadrotor vehicle is in siulation environent is PID controller block and nonlinear odel of quadrotor. There is an input to attitude controller block which includes both desired φ, θ, and ψ angles and outputs of feedback which are easured angles φ, θ, and ψ. In ipleentation, Pixhawk autopilot is used for real tie tests. Fig. 5. Siulation results of PID controller on the nonlinear quadrotor odel. 4.1 PID Controller Siulation Result In this work, Matlab Control Syste Toolbox is used for K p, K i, and K d paraeter of PID tuning for siulation of nonlinear odel of quadrotor. During tuning each coefficient, others paraeters values are get zero values to eliinate their effect on the tunned paraeter. Inputs of the siulation are set 2 for φ and θ angles but ψ is set 1 degree as seen in Figure 5. Both of the graphics have saller than one second of rise tie and 3% percent overshoot and 4 second settling tie and have ignorable steady state errors. The nonlinearities of the syste causes terination of siulation in short tie. In shortly, the results shows that controlling of the quadrotor via PID controller is possible. 4.2 Experiental Real-Tie Test Results Two experients are done on the HIL testbed with PID controller via different coefficients as seen in Tables 2 and 3. The response of the roll angle generally has soe overshoots but rise and settling tie is so sall. About roll otions, there are ignorable overshoots and no tie delay, so its so fast and robust. The pitch otions have no overshoots but soe tie delays and oscillations related Fig. 6. Tie responses of Pitch and Roll angles with respect to Table 2. with oents of inertia. The yaw otions has high tie delays and overshoots generated fro high total oent of inertia fro outer and inner circle of the testbench. Differences between first and second experients are caused by P coefficient of PID controller. It is clearly seen that second experient easured values of pitch angle is well tracking the reference signal than first experient values. However, increentation of P coefficient values on the roll angle causes soe overshoot respected to first experient. In addition, increentation of P coefficient values on the yaw 123

6 Fig. 7. Tie response of Yaw angle with respect to Table 2. angle decreases tie delays on signal tracking respected to first experient. Table 2. PID Gains for First Experient Roll Rate Pitch Rate Yaw Rate K p K i K d Fig. 9. Tie Response of Roll and Yaw angles with respect to Table 3. focusing on itigating the inertial effects of outer rings and working on designing novel carbon-fiber based rings in order to provide iniu disturbance ipact fro giballed platfor. Fig. 8. Tie response of Pitch angle with respect to Table 3. Table 3. PID Gains for Second Experient Roll Rate Pitch Rate Yaw Rate K p K i K d CONCLUSION Testing aircraft controller perforance is generally expensive and tie consuing process due to hardship of flight operations. In this work, HIL testbed provides us easy solution in order to set optiu PID coefficients for quadrotor test platfor. In the potential future roadap, this platfor enables us testing various nonlinear and robust controller structures, besides we are capable of testing the perforance of tilt-rotor ulticopter systes in the real-tie test environent including inertial sensor inforation via Pixhawk controller. Especially feedback linearization, backstepping, and different nonlinear control approaches are still in progress. Additionally, we are still REFERENCES Alexis, K., Nikolakopoulos, G., and Tzes, A. (21). Design and experiental verification of a constrained finite tie optial control schee for the attitude control of a quadrotor helicopter subject to wind gusts. In Proceedings of IEEE ICRA 1 Robotics and Autoation, An, H., Li, J., Wang, J., Wang, J., and Ma, H. (213). Second-order geoetric sliding ode attitude observer with application to quadrotor on a test bench. Matheatical Probles in Engineering, 213. Fu, W.Z. (215). Ipleentation of Siulink controller design on Iris+ quadrotor. Ph.D. thesis, Monterey, California: Naval Postgraduate School. Prach, A., Kayacan, E., and Bernstein, D.S. (216). An experiental evaluation of the forward propagating riccati equation to nonlinear control of the quanser 3 dof hover testbed. In Proceedings of IEEE Aerican Control Conference, Yu, Y. and Ding, X. (212). A quadrotor test bench for six degree of freedo flight. Journal of Intelligent and Robotic Systes,

A Simulation Study for Practical Control of a Quadrotor

A Simulation Study for Practical Control of a Quadrotor A Siulation Study for Practical Control of a Quadrotor Jeongho Noh* and Yongkyu Song** *Graduate student, Ph.D. progra, ** Ph.D., Professor Departent of Aerospace and Mechanical Engineering, Korea Aerospace