Fuzzy Controller for Small Size Unmanned Aerial Vehicles

Fuzzy Controller for Small Size Unmanned Aerial Vehicles

Dániel Stojcsics

Óbuda University, John von Neumann Faculty of Informatics, Budapest, Hungary stojcsics.daniel@nik.uni-obuda.hu

Abstract—The AERObot autopilot for small and medium size unmanned aerial vehicles (UAVs) developed at Óbuda Universtiy has multiple control systems. It is possible to switch between the control systems even during in flight.

The purpose of the current research was to examine the applicability of full fuzzy flight control (takeoff, cruise and land) in unmanned aerial vehicles instead of partial or hybrid control [1, 2, 3]. The easy tuning of the parameters and features is quite important because one autopilot should control different sized and designed planes.

Since the safety of the flight, life and value is the most important, real test flights should always be performed after many hours of computer simulation. For this purpose Hardware In the Loop simulation was used. The advantage of this simulation is that the very same environment can be created as in real flights (e.g. atmospheric, aerodynamic, propulsion model, different weather conditions). After successful simulations the real test flights can be started.

I. CONTROL SYSTEMS OF AN UNMANNED AERIAL V^EHICLES

Selecting the proper control method is not trivial since there are many things to consider. The classic PID controller has many benefits, several autopilots are using it. The setup process of these autopilots is pretty difficult or they can be used with strong limitations, due to the non-linear aircraft characteristics [4, 5].

At least three controller channels and a few compensators are needed to control an unmanned airplane and achieve the appropriate flight characteristics.

The basic three controller channels are the airspeed, altitude and heading (navigation) controllers. The implementation can be different based on the available flight data. The AERObot autopilot controls the altitude with the engine throttle and the airspeed with the elevator.

In case of electric propulsion (continuously decreasing

performance because of the electric battery characteristics), this implementation provides adequate airspeed control.

On top of these channels a roll and pitch axis stabilization controller is needed which keeps the UAV on a straight level flight and protects it from the effects of the wind.

Additional turn compensators are needed for the precise turning maneuvers. These are the rudder-aileron and rudder-elevator compensators. Most of the UAVs cannot turn with rudder alone because of its structural design (zero dihedral wings). The turn must be assisted with the ailerons like in the case of manned planes.

During the turning maneuver without any elevator action the UAV losses altitude and accelerates because the lift on the wings is decreased. To compensate this a rudder-elevator compensator must be used.

A special non-linear third order controller function has been applied in the AERObot autopilot. The advantage of this is the capability to control non-linear systems like UAVs without linearization. Furthermore several years of practical experience are available for this kind of controller.

The transfer functions used in the controllers can be interpreted as seen on fig. 1. The target value (i.e. Xc=150 m - altitude controller) and the neutral output for that (Z0=0, trim condition) has been marked. If the target altitude is higher than the current measured altitude, the output will be higher than the neutral value.

If the target altitude is lower than the current measured altitude, the output will be lower than the neutral value.

The function outputs must be limited between predefined values (e.g. ±255) for practical use.

Figure 1. Airspeed and altitude plot of two turns (third order controller)

Figure 1. Third order altitude controller characteristics -255

-204 -153 -102 -51 0 51 102 153 204 255

0 100 200 300

Control signal

Altitude [m]

target altitude

Z₀

min max

This control method can be used for control surfaces with symmetrical deflection, e.g. the rudder, aileron, elevator or the engine (both electric and glow) throttle.

The central “flat” part of the function should be the trim output value (Z0) e.g. the throttle control signal at level flight. This controller is capable of controlling the airspeed, altitude and heading directly (fig. 2).

The independent controller channels should be inspected separately then joint tests must be done under various conditions (e.g. wind). For this the complete mathematical model of the UAV is needed.

II. NAVIGATION

The AERObot autopilot has several different navigation and control systems. The selected navigation method calculates the actual desired heading for each calculated positions. This process is based on waypoints, GPS data and sensor fusion. The UAV should always fly towards the selected destination waypoint from the previous one (fig. 3).

The advantage of this navigation is the ease of use and the visual controllability (Matlab vector plot) of the internal parameter changes. The output of the navigation function is a single value, the desired heading (1). Because of this many controller types can be applied for heading control.

After the UAV reaches the destination waypoint it selects the next waypoint as destination. The vector navigation basis is:

1,

(1) where:

: Cross track error, : Desired heading,

: Target waypoint heading (from UAV), : Route constant,

: Cross track error constant.

Figure 3. Vector navigation

III. HIL SIMULATION

The Hardware In the Loop (HIL) simulation is able to create the same environment as the real flight. The autopilot is acting the same as real; it has no information about the source of the measured signals which are generated with PC simulation software.

A mathematical model created in Matlab/Simulink (fig.

4.) processes the states of the UAV using the actuator signals captured from the autopilot. The autopilot is using the simulated signals instead of its own internal sensors for the filter, navigation and control algorithms [6].

The simulator sends the output of the simulation (position, orientation, airspeed and altitude etc.) to the autopilot via serial port with a desired control frequency (e.g. 100Hz) which is the same as the update frequency of the control functions (discrete time simulation with a real time model). The autopilot is not using its internal timer but the timestamp from the simulator.

The simulated outputs can be ideal or noisy (generated).

Using ideal values the internal filters can be bypassed.

Otherwise the HIL simulation is capable of testing the onboard software filters in different situations.

The autopilot calculates and sends back the actuator signals based on the received values while also refreshing the physical actuator. These signals are the inputs of the simulation model.

The 6-dof model of the Tiger60 AERObot UAV (developed at Obuda University) was created in Matlab/Simulink using the AeroSim block set for the validation of the HIL simulation. A lot of conclusion and test data are available for the control functions and navigation from real flights in the past, so the simulated results could be compared to real measured ones. The selected block set has an interface to FlightGear flight simulator so the HIL test flights can be observed in such a graphical way. This way new control methods can be easily developed and compared to the previous ones.

Figure 4. Matlab/Simulink HIL model

IV. FUZZY CONTROL

The fuzzy control box was created with the Matlab fuzzy toolbox. The inputs of the controller box are the same as in the third order controller (target speed, target altitude, actual airspeed, actual altitude, bank angle, pitch angle, heading error). The outputs are the same too (control surface deflection and engine throttle commands).

The fuzzy controller box contains five simple fuzzy controller channels and two linear compensators (fig 5.).

There are two stabilization channels (bank and pitch angle) in addition to the three classic controllers (airspeed, altitude, heading). In the case of the third order controller, they were embedded into the three classic channels.

Figure 5. UAV Fuzzy controller box in Simulink Every controller is a simple Mamdani controller with two (bank angle, pitch angle, heading) or three (airspeed, altitude) triangular input and output membership functions (fig. 6).

The minimum and maximum input values of the channels are the same as in third order controllers (e.g.

airspeed error: ± 45 km/h). The output values are between

± 100%.

Figure 6. The three triangular input and output membership functions (airspeed controller)

Figure 7. The transfer diagrams of the Mamdani controllers with two and three membership functions

The used Mamdani controllers with two or three triangular input and output membership functions has a quite similar transfer diagram as the third order controller (fig. 7). The initial values of the controller therefore should be the same as the third order controller.

If the target value is higher than the current measured one, the output will be higher than the neutral value. If the target value is lower than the current measured one the output will be lower than the neutral value. When the controller gain is weak the input region must be reduced.

Otherwise, when the gain is too strong the region must be increased (reducing the gain) or the output values decreased.

The two linear turn compensators are between the controllers and the box outputs (fig. 8, 9). In some cases, non-linear compensators must be used which correlates with airspeed or bank angle [7]. Using both pitch and bank angle controllers there is no need for this.

Figure 8. Effect of rudder – elevator compensator with different parameters

Figure 9. Effect of rudder - aileron compensator with different parameters

Figure 10. Effect of rudder – aileron compensator with different parameters on the flight route with three waypoints

The rudder – aileron compensator is needed for the precise navigation. Without this the UAV cannot perform banked turns. The turn radius can be way more than 100 meters instead of the desired 10-20 meters (fig. 10). The proper value can be specified with HIL simulation flight tests.

V. COMPARISON

Many flight tests have been made with HIL simulation under similar conditions with the old third order and the new fuzzy controllers.

The interesting thing in the fuzzy controller is the similarity to the third order one. Because of this feature the initial parameters gave satisfactory simulation results.

The UAV with the new fuzzy controller with turn compensators is more stable, has better performance, less overshoot and less bank angle in the turning maneuvers (fig. 11, 12).

In the case of the navigation (heading control) the flight route is stable, oscillation free but the course track error is higher (fig 13.). This can be corrected a bit with increasing the rudder-aileron compensator value or the heading gain.

Although the transfer diagram of the fuzzy controller is similar to the third order controller, the fuzzy has better performance (has less overshot and better heading control). Further fine tuning can make it even better and the cross track error can be eliminated.

VI. S^UMMARY

The analysis of the HIL simulation flight test results showed that the simple Mamdani fuzzy controller described in the paper is capable of controlling small and medium size unmanned aerial vehicles with better performance quality than the classic third order controller.

The simulation studies demonstrated the usability of this method.

The next step will be the real flight tests of the AERObot autopilot in the UAVs of the Obuda University

Figure 11. UAV roll and pitch angle plot of two turns (blue: fuzzy, red: third order)

Figure 12. Airspeed and altitude plot of two turns (blue: fuzzy, red:

third order)

Figure 13. Flight route with four waypoints. Each side is 300m long (blue: fuzzy, red: third order)

R^EFERENCES

[1] K. Bickraj, T. Pamphile, A. Yenilmez, M. Li, I.N. Tansel: Fuzzy Logic Based Integrated Controller for Unmanned Aerial Vehicles, Florida Conference on Recent Advances in Robotics, FCRAR 2006

[2] S. Kurnaz, O. Çetin: Autonomous Navigation and Landing Tasks for Fixed Wing Small Unmanned Aerial Vehicles, Acta Polytechnica Hungarica Vol. 7, No. 1, 2010, pp. 87-102

[3] Y. Shengyi, L. Kunqin, S. Jiao: Optimal tuning method of PID controller based on gain margin and phase margin, International Conference on Computational Intelligence and Security, 2009, pp.

634 - 638, ISBN: 978-1-4244-5411-2

[4] R. Beard et al: Autonomous Vehicle Technologies for Small Fixed-Wing UAVs, Journal Of Aerospace Computing Information and Communication (2005) Volume: 2, Issue: 1, pp: 92-108, ISSN: 19403151.

[5] H. Chao, Y. Luo, L. Di and Y. Chen: FRACTIONAL ORDER FLIGHT CONTROL OF A SMALL FIXED-WING UAV:

CONTROLLER DESIGN AND SIMULATION STUDY, Proceedings of the ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, 2009, pp. 621-628, ISBN: 978-0-7918- 4900-2

[6] Stojcsics, D.; Molnar, A.: Fixed-wing small-size UAV navigation methods with HIL simulation for AERObot autopilot, Proceedings of 9th International Symposium on Intelligent Systems and Informatics, 2011, ISBN: 978-1-4577-1975-2, pp. 241 - 245 [7] S. Leven, J. Zufferey, and D. Floreano: A minimalist control

strategy for small UAVs, in Proc. IROS, 2009, pp. 2873-2878.