Flight Control Simulators for Unmanned Fixed-Wing and VTOL Aircraft

Flight Control Simulators for Unmanned Fixed-Wing and VTOL Aircraft Naoharu Yoshitani 1, Shin-ichi Hashimoto 2, Takehiro Kimura 3, Kazuki Motohashi 2 and Shoh Ueno 4 1 Dept. of Aerospace Engineering, Teikyo University, Utsunomiya, Japan (Tel: +81-28-627-7135; E-mail: n-yoshi@koala.mse.teikyo-u.ac.jp) 2 Tokyo Keiki Inc., Japan 3 JATCO Ltd., Japan 4 East Japan Railway Company, Japan Abstract: Flight control simulators for fixed-wing aircraft and VTOL (Vertical Take-off and Landing) aircraft have been developed for understanding flight control dynamics and for improving control strategies and performances. They simulate automatic control of a flight path of the aircraft, using six-degree-of-freedom nonlinear equations to represent aircraft dynamics. The control system is multi-layered. For fixed-wing aircraft, it consists of flight-path controller, heading and flight-path angle controller, acceleration controller and attitude controller. The control strategy is based on required acceleration, proposed by the first author. On the other hand, the VTOL aircraft is of ducted-fan type. It has a propeller at the top of the duct, fixed vanes below it to cancel the counter torque of the propeller, and control vanes to control the attitude. The simulators have proved effective in testing and improving aircraft control strategies. Keywords: simulation, flight control, flight dynamics, VTOL, ducted-fan NOMENCLATURE m : aircraft mass g : gravity acceleration ρ a : atmosphere density (dependent on altitude) F : external force vector acting on the aircraft M t : external moment vector acting on the aircraft V a : velocity vector of the aircraft H : angular momentum vector of the aircraft F x, F y, F z : aerodynamic force components in the body axes of the aircraft L, M, N : aerodynamic moment components in the body axes U, V, W : velocity components in the body axes P, Q, R : roll rate, pitch rate, yaw rate φ, θ, ψ : roll, pitch and yaw angles α, β : angle of attack, side-slip angle I x, I y, I z, J xz : moment of inertia and product of inertia of the aircraft T h, T h : thrust vector and its magnitude I th : moment of inertia of the thrust system (consisting of, such as, engine, motor and propeller) about the thrust vector ω th, ω th : angular rate vector of the thrust system with respect to I th, and its magnitude ([ ω th and T h have the same direction.) h : altitude (height) F dx, F dy, F dz : drag force components in the body axes acting on the VTOL aircraft F mx, F my : momentum drag components by the incoming air into the duct acting on the VTOL aircraft { } c : command of any variable { } v : constant or variable related to a control vane of VTOL aircraft { } T : transposed vector or matrix 1. INTRODUCTION In recent years, large technological advancements have been achieved in UAV(unmanned aerial vehicle)- related fields such as micro-computers, sensors, electric motors and batteries, turning them smaller in size, higher in performances and lower in manufacturing costs. This enables to develop a UAV, especially an electricallypowered UAV, that is lighter in weight, lower in manufacturing and operational costs, and capable of flying for a longer time. Various types of UAVs are being researched and developed for both military and civilian uses in universities, research institutes and private companies all over the world. For the development of UAVs, flight control simulators are helpful in understanding flight dynamics and for improving control strategies and performances. We have developed flight control simulators for conventional fixed-wing aircraft [1] and VTOL (Vertical Take-Off and Landing) aircraft [2]. The fixed-wing aircraft has control surfaces of ailerons, elevator and rudder for flight control. On the other hand, the VTOL aircraft is of a cylindrical ducted-fan type. It has been developed in a joint project of Teikyo University and Fuji Aerospace Technology, Co., Ltd. It has a vertical duct, a propeller at the top of the duct, four fixed vanes below it to cancel the counter torque of the propeller, and four control vanes to control the attitude. This structure was chosen as it is relatively safe and easy to operate in a limited space. The simulators have been developed under MAT- LAB/SIMULINK environment. They simulate automatic control of a flight path of the aircraft, using six-degreeof-freedom nonlinear equations to represent aircraft dynamics. The control system consists of a cascade of controllers, actuator dynamics, aircraft dynamics and sensor dynamics. For fixed-wing aircraft, the control strategy is based on required acceleration, proposed by the first

M Rω th I th = QI y + PR(I x I z )+(P 2 R 2 )J xz (7) N + Qω th I th = ṘI z PJ xz + PQ(I y I x )+QRJ xz (8) where the angular momentum vector of the thrust system, I th ω th, is assumed to be parallel to the body x axis. The aerodynamic forces and moments are expressed by Fig. 1 body axes, angles and angular rates author [1]. For VTOL aircraft, the simulator takes into account aerodynamic forces and moments acting on control vanes and those caused by incoming airflow. 2. FLIGHT CONTROL SIMULATOR FOR FIXED-WING AIRCRAFT 2.1 Mathematical model of aircraft dynamics Fig. 1 shows a fixed-wing aircraft with the body coordinates frame and angles and angular rates about the axes. A mathematical model of fixed-wing aircraft dynamics is typically presented by such as [3], [4], etc. The simulator presented here is based on a model described here, which is similar to those in the literature. In order to derive a mathematical model of the aircraft, it is common to put the following assumptions: A1 : The aircraft body is rigid. A2 : The aircraft is symmetrical about the vertical plane that contains the CG (Center of Gravity). A3 : The aircraft mass is constant during flight. A4 : A coordinates frame on the surface of the earth is an inertial frame. The movement and the roundness of the earth are ignored. The aircraft dynamics is described by the following equations of forces and moments. F = m d dt V a (1) M t = d H (2) dt where the vectors are expressed in the inertial frame. Considering the relative motion of the body frame against the inertial frame, the above equations can be transformed and expanded into the following six-degreesof-freedom equations in the body frame: F x = m( U + QW RV + g sin θ) T h (3) F y = m( V + RU PW g cos θ sin φ) (4) F z = m(ẇ + PV QU g cos θ cos φ) (5) L ω th I th = PI x ṘJ xz + QR(I z I y ) PQJ xz (6) F x =[C x (α, δ e )+0.5C xq (α) cq/v a ] qs (9) F y =[C y (β,δ a,δ r ) +0.5(C yr R + C yp P )b/v a ] qs (10) F z =[C z (α, β, δ e )+0.5C zq (α) cq/v a ] qs (11) L =[C L(α, β)+c Lδa (α, β)δ a + C Lδr (α, β)δ r +0.5(C Lr (α)r + C Lp (α)p )b/v a ]b qs (12) M =[C M (α, δ e )+0.5C Mq (α) cq/v a + C z (α, β, δ e )(x cgr x cg )] c qs (13) N =[C N (α, β)+c Nδa (α, β)δ a + C Nδr (α, β)δ r +0.5(C Nr (α)r + C Np (α)p )b/v a C y (β,δ a,δ r )(x cgr x cg ) c/b]b qs (14) where q =0.5ρ a Va 2 (15) Here, C x, C y, C z, C xq, C yr, C yp, C zq, C L, C M, C N, C Lδa, C Lδr, C Lr, C Lp, C Mq, C Nδa, C Nδr, C Nr and C Np are aerodynamic coefficients dependant upon α, β, δ a, δ e or δ r. Their values are calculated using linear equations or look-up tables, where parameters or table values can be determined through wind-tunnel tests or flight tests [4]. Euler angles φ, θ and ψ are related to P, Q and R as φ = P + tan θ(q sin φ + R cos φ) (16) θ = Q cos φ R sin φ (17) ψ =(Qsin φ + R cos φ)/ cos θ (18) The derivatives of aircraft position, (p N p E h)intheneu (North-East-Up) inertial frame, are given by ṗ N = U cos θ cos ψ + V ( cos φ sin ψ +sinφsin θ cos ψ) + W (sin φ sin ψ +cosφsin θ cos ψ) (19) ṗ E = U cos θ sin ψ + V (cos φ cos ψ +sinφsin θ sin ψ) + W ( sin φ cos ψ +cosφsin θ sin ψ) (20) ḣ = U sin θ V sin φ cos θ W cos φ cos θ (21) In the simulator, the aircraft movements are obtained by integrating the derivatives of state variables X,given by X =[UVWφθψPQRp N p E ph] T (22) The derivatives, X, can be calculated from (3) to (21).

2.2 Actuator dynamics The aircraft in the simulator has four command inputs: the commands to control surfaces aileron, elevator and rudder and to the engine. Control surfaces are driven by hydraulic systems and, in small UAVs, by electric servo motors. In both cases, the actuator dynamics, the dynamics from the commands to the control surface movements, can be expressed by first-order lag models. In some aircraft, the engine dynamics can be expressed similarly. On the other hand, many actual aircraft such as F-16 [4] have more complicated engine dynamics. 2.3 Control configuration Fig. 2 shows the control system of the simulator for fixed-wing aircraft. A desired flight-path (flight-path command) are determined beforehand and fed into the flight-path controller. The controller takes into account the direction to the forward point on the desired path and calculates the commands of the heading angle and the flight-path angle. Then the controller of these calculates the required acceleration vector, which is vertical to the velocity vector. The acceleration controller calculates the attitude and velocity commands. The attitude and velocity controller uses PID control scheme to calculate the commands to elevator, aileron, rudder and engine throttle or motor. It also controls the side-slip angle β to zero and includes the roll damper and the yaw damper. 2.4 Simulation The simulator described so far has been tested for F-16 fighter plane. The specifications and aerodynamic characteristics of the plane were taken from [4]. Figs. 3 to 4 show an example of simulation, where a desired flight path consists of 5 steps as follows: Step 1 : straight horizontal flight of 122 m at the altitude of 0 m (sea level) with the heading of 0 degree (north) Step 2 : a quarter upward circle with the radius of 518 m without heading change Step 3 : vertical upward flight of 244 m Step 4 : a quarter upward circle with the radius of 518 m and with the heading of 90 degrees (east) Step 5 : straight horizontal flight with the heading of 90 degrees (east) and, after 20 seconds in simulation time, with the stepwise wind disturbance of 30 m/s from the north The velocity command was set constant at 156 m/s. In Fig. 3, the flight path of the airplane well follows its command. In Fig. 4, x, y and z represent the aircraft position in the inertial frame and x c, y c and z c represent its command. In the figure, the velocity V a decreases when the aircraft flies upward, but increases to its command after the upward flight. When a stepwise wind disturbance was added at 20 seconds, the flight path showed little fluctuation and the yaw angle ψ settled to 78 degrees. This indicates that the aircraft moved its x axis 12 degrees toward the windward to keep its flight path. Various simulations have been performed with different flight conditions and flight paths to give reasonable results. Thus, the simulator and the control strategy described here have proved effective. 3. FLIGHT CONTROL SIMULATOR FOR VTOL AIRCRAFT 3.1 The aircraft structure Fig. 5 is a photo of the VTOL aircraft developed at Teikyo University with the body coordinate frame. It has a container box above the propeller and the duct. It contains the autopilot main board and related materials such as a GPS antenna and a battery for them. Under the propeller, there are four fixed vanes to cancel the countertorque generated by the propeller. Further below, four vertical control vanes are equipped for attitude control. The body coordinates frame is defined as in Fig. 5. Fig. 6 shows a sectional front view of the VTOL aircraft. Next, Fig. 7 shows looking-down views of control vane movements. Arrows in the figure show the directions of forces acting on the vanes. Let δ i and δ ic (i =1, 2, 3, 4) denote actual # i vane deflection and its command, respectively, where the subscript c represents a command. Let a clockwise rotation in the figure be a positive one. δ ic is given by δ 1c = δ rc δ ec, δ 2c = δ rc δ ac (23) δ 3c = δ rc + δ ec, δ 4c = δ rc + δ ac (24) 3.2 Mathematical model of the VTOL aircraft The modeling and control of a similar ducted-fan VTOL aircraft were presented by Johnson and Turbe [5]. Their aircraft has six control vanes. The vanes are located below and out of the duct. The number of vanes and their locations are different from the VTOL aircraft presented here. The equations of forces and moments are almost the same as (3) to (8), except that the direction of the thrust vector [ T h is different here. The equations are given by F x = m( U + QW RV + g sin θ) (25) F y = m( V + RU PW g cos θ sin φ) (26) F z = m(ẇ + PV QU g cos θ cos φ)+t h(27) L Qω th I th = PI x ṘJ xz + QR(I z I y ) PQJ xz (28) M + Pω th I th = QI y + PR(I x I z )+(P 2 R 2 )J xz (29) N ω th I th = ṘI z PJ xz + PQ(I y I x )+QRJ xz (30) where J xz =0due to the simmetry of the body. The aerodynamic forces and moments are expressed differently from (9) to (14). They are also different from those in [5]. First, let F Lvi and F dvi (i =1,, 4) denote the lift and the drag acting on # i control vane. They are given by F Lvi = 1 2 ρ ac Lvδ δ i v 2 ads v (31)

Fig. 2 Control system for fixed-wing aircraft Fig. 3 Control simulation : aircraft movements Fig. 5 VTOL aircraft Fig. 4 Control simulation : position, velocity and yaw F dvi = 1 2 ρ ac dvδ δ i v 2 ads v (32) where c Lvδ, c dvδ : gradient of lift and drag, respectively, with respect to δ i v ad : air velocity inside the duct (proportional to ω th when the aircraft is hovering) : area of a control vane S v The lift F Lvi acts parallel to the xy plane, having the same sign as δ i, and the drag F dvi acts parallel to the z axis. When the aircraft moves in the air, the drag acts on the aircraft. Let F dx, F dy and F dz denote the drag components. Considering that the Reynolds number of the Fig. 6 VTOL aircraft Fig. 7 Control vane movements VTOL aircraft is roughly up to 10 3 in normal operations, the drag is assumed to be proportional to Va 1.3 [6]. When the aircraft moves toward x or y direction, the

Fig. 8 Control system for VTOL aircraft momentum of the incoming air into the duct causes a momentum drag, denoted by F mx and F my. Using these notations, forces and moments are expressed by F x = F dx + F Lv1 F Lv3 + F mx (33) F y = F dy F Lv2 + F Lv4 + F my (34) F z = F dz + F dv1 + F dv2 + F dv3 + F dv4 (35) L = F dy z d +(F Lv2 F Lv4 )z v F my z m +(F dv1 F dv3 )d v (36) M = F dx z d +(F Lv1 F Lv3 )z v + F mx z m (F dv2 F dv4 )d v (37) N = (F Lv1 + F Lv2 + F Lv3 + F Lv4 )d v (38) where F dx = ρ a c dx sign(u) U 1.3 S x (39) F dy = ρ a c dy sign(v ) V 1.3 S y (40) F dz = ρ a c dz sign(w ) W 1.3 S z (41) F mx = ρ a S d v ad U (42) F my = ρ a S d v ad V (43) and where c dx, c dy, c dz : drag coefficient of the aircraft in the x, y and z axis, respectively S x, S y, S z : projected area of the body on yz, zx and xy plane, respectively S d : sectional area of the duct z d, z v, z m : z coordinates of the acting point of (F dx, F dy ), F Lvi and (F mx, F my ), respectively, with the CG at the origin d v : distance from the center axis of the fuselage to the acting points of lift and drag on a control vane The actuator dynamics of the VTOL aircraft can be modeled in the same way as for the fixed-wing aircraft. 3.3 Control configuration Fig. 8 shows the control system for the VTOL aircraft. A time-series of flight commands is determined beforehand. It consists of commands of altitude, velocity, yaw angle, waypoints, and hovering time. The flight-path and velocity controller calculates the commands of pitch, roll, yaw and altitude. The attitude and altitude controller, which is being developed and has not been completed yet, first calculates just the same commands as the attitude and velocity controller in Fig. 2. Then it converts the commands to elevator, aileron and rudder into the commands to four control vanes. All the control laws are based on well-matured PID control. 3.4 Simulation Fig. 9 and Fig. 10 show an example of attitude and altitude control simulation of the VTOL aircraft for 15 Fig. 9 Control simulation : pitch and roll Fig. 10 Control simulation : aircraft movements seconds. Here, the pitch command was set at 5 degrees from 0 to 5 seconds, while the roll command was set similarly from 5 to 9 seconds. They were set at zero in other periods. The altitude and the yaw command were kept constant at 0 m and at the north (the x direction in the surface-of-the-earth frame), respectively. The aircraft was controlled reasonably and the control performance was satisfactory. The simulators have proved effective in testing and improving aircraft control strategies. 4. CONCLUSIONS Flight control simulators for unmanned fixed-wing aircraft and for ducted-fan VTOL aircraft were presented. For fixed-wing aircraft, the control strategy is based on required acceleration, proposed by the first author, while the aircraft dynamics is modeled as described in a reference book [4]. For VTOL aircraft, the aircraft is modeled after the one developed by the authors, et al., while the control strategy is based on conventional PID control. Both simulators have proved effective through various simulations. In the VTOL simulator, aerodynamic coefficients have not been well adjusted to actual values and flight path control algorithm has not been fully implemented. They remain for future work.

ACKNOWLEDGEMENTS The authors would like to thank Mr. Kamiyoshihara, Mr. Hirose, Mr. Satoh, Mr. Itoh, Mr. Izumikawa and other members of Fuji Aerospace Technology Co., Ltd. for their cooperation in developing ducted-fan VTOL aircraft. The authors would also like to thank those graduates from Teikyo University who contributed to the development of the simulators and the VTOL aircraft. REFERENCES [1] N. Yoshitani, A Flight-Path Control of Aircraft Based on Required Acceleration Vector, Journal of Japan Society of Aeronautics and Space Sciences, 55-638, pp. 111 116, 2007 (in Japanese). [2] N. Yoshitani, M. Aragaki, R. Koyanagi, J. Matsuwaki, Y. Kamiyoshihara, H. Hirose and T. Satoh, Development of Small Unmanned VTOL Aircraft and Its Flight Control Simulator, Preprints of #46 Aircraft Symposium, 1B11, October 22-24, 2008, at Ohta-ku Industrial Plaza, Tokyo, Japan (in Japanese). [3] K. Kanai, Flight Control Basics and Applications of CCV Technology, Maki Shoten, Tokyo, 1985 (in Japanese). [4] B. L. Stevens and F. L. Lewis, Aircraft Control and Simulation, John Wiley & Sons, New York, 1992. [5] E. L. Johnson and N. A. Turbe, Modeling, Control, and Flight Testing of a Small Ducted-Fan Aircraft, Journal of Guidance, Control, and Dynamics, 29-4, pp. 769 779, 2006. [6] R. Ishiwata, Introduction to Fluid Dynamics, Morikita Publishing, Tokyo, 2000 (in Japanese)