PERFORMANCE COMPARISON OF CLASSIC AND FUZZY LOGIC CONTROLLERS FOR COMMUNICATION AIRSHIPS

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1 PERFORMANCE COMPARISON OF CLASSIC AND FUZZY LOGIC CONTROLLERS FOR COMMUNICATION AIRSHIPS Maryam Falahpour, Hassan Moradi, Hazem H. Reai, Mohammed Atiquzzaman, Electrical and Computer Engineering, University o Oklahoma, Tulsa, OK. Robert Rubin, Peter G. LoPresti, Electrical Engineering Department, University o Tulsa, Tulsa, OK. Abstract Communication is vital in order to coordinate rescue and clean up eorts should an event eliminate the most common inrastructure, such a cell tower and phone lines, in a region. One o the most eective ways to set up an alternative communication system without relying on traditional methods would be to attach a temporary system to airships loating above the region. However, an inherent problem with airships is keeping them in the desired area with the correct orientation. This paper compares two dierent airship control methods, namely uzzy logic and classic controllers, to navigate the balloon while hovering over a region in order to reestablish communication. A dynamical model o the airship in the presence o air riction is shown, and simulations are done using MATLAB Simulator. Introduction When a natural catastrophe, e.g. hurricane or earthquake, aects a region, cellular communication may cease and towers can be damaged, causing the loss o vital communication at a time when it is most important. Hence, it is essential to rapidly deploy a replacement system independent o inrastructure to acilitate communication among rescuers, enabling aid to distressed people and expediting recovery eorts. This research considers an airborne communication network that can be rapidly deployed to establish a replacement method o communication. There is immense potential in utilizing robotic airships as low speed, low altitude aerial vehicles in exploration and monitoring tasks. Blimps have several useul properties, including ease in hovering, reduced uel consumption and less noise. Unmanned blimp systems have recently been used or advertisements and atmospheric analysis. Unmanned aerial vehicles (UAVs) play an important role in military reconnaissance and surveillance missions, and agencies such as NASA are employing aerial vehicles as platorms or environmental and climate research. Airships provide some o the most eective platorms or research because they are able to hover over an area and make observations or an extended period o time without disturbing environment. Airships generate little vibration thereby reducing sensor noise and hardware malunction. Also, they can take o and land vertically without runways. Airships can also reach anywhere so that remote or diicult to access regions can be monitored. They have a large payload capacity and have low operation cost []. In light o the aorementioned beneits, controllable balloon studies are o great importance or rapidly deployed airborne communication systems. In this paper we compare the perormance o two methods applicable or controlling the position and direction o communication balloons. The irst is a eedback linearization controller, which is categorized as one o the classic methods in control. The second is a uzzy logic controller, commonly used when the exact conditions o the model are unknown. Related Works Previous research with regard to balloon control exists in the literature. Physical principles o airship operations using nonlinear dynamics to control several light phases rom takeo to landing are described in [, 3]. Also, Zhang and Ostrowski [4] use a vision-guided blimp combined with a classical PID controller. Furthermore [5] discusses imagebased tracking control or an indoor blimp, while Wyeth and Barrons [6] present a low level reactive controller. A learning algorithm has been presented in [7], which does not assume prior knowledge about dynamics or pre-deined controller. Instead, it develops the control policy online and does not /9/$5. 9 IEEE. 4.A.6-

2 require a-priori inormation about the payload, temperature or air pressure. Time delay and disturbance are two challenges when controlling a blimp. State predictive control can be applied to an autonomous blimp in the presence o time delay and disturbance [8]. In that work, model predictive control (MPC) has been applied to an autonomous blimp, and an indoor light experiment has been applied to an autonomous blimp to evaluate its eectiveness. With ocus on position control, a constrained MPC or an autonomous blimp has been discussed in [9]. Image processing and vision-based techniques are common or tracking mobile blimps []. Image-based tracking control o an aerial blimp is proposed or surveillance systems. In this scenario, the controller is designed by back-stepping techniques or under-actuated systems. In this paper, the classic and uzzy controllers are simulated and compared to determine which controller best it to maintain position and orientation or balloon-to-balloon optical communication. This is a work in progress to develop a ast deployable wireless optical/rf hybrid communication system using airships. System Model and Dynamics Once communication in a deined area is disrupted, a group o balloons will be launched to restore communication. The balloons must maintain a speciied distance rom each other. Because the balloons are equipped with optical transceivers enabling higher data rate than RF orientation is vital or sustained communication between balloons. The controllers investigated in this paper simulate a single balloon reaching a certain position and maintaining its orientation in spite o adverse wind condition. The balloon will be equipped with a GPS or position and an electronic compass or direction. Also, the balloon is equipped with a 3-axis accelerometer to measure small changes in position. The propulsion system consists o three propellers assembled at either side o the center o gravity and at the tail. Propellers use three brushless motors and a motor speed controller. Figure shows a model o the balloon used in this paper. As shown, the balloon used in the unmanned airship system has three propellers two assembled at either side o the center o gravity o the balloon and one at the tail. We assume the orces o these propellers operate only the horizontal direction. In Figure, x and y denote the position o the center o gravity o the balloon, and θ denotes the angle rom x axis to the direction o movement o the balloon []. For simplicity we also assume that the balloon is a rigid body and has no rolling, no pitching and no vertical movement. Figure. A Model or the Balloon The parameters shown in Figure are deined as ollows: - u and u and u 3 : [N] thrusts o the propellers - h and l: [m] the distance rom the center o gravity o the balloon to either side o the propellers and rom the center o gravity to the back propeller. The dynamical equations are derived as ollows: mx && = u + u + u3 my && = u + u u3 J && θ = h( u u ) + lu 3 x y () The parameters in the equation () are deined as ollows: - m: mass o the balloon. - J: [kg.m] the moment o inertia around the center o gravity o the balloon. - x and y : the orce o air riction or the x and y axis respectively. A simple air riction is used to using the ollowing model: = CρAv () 4.A.6-

3 where ρ is the density o the luid. (Note that or the earth's atmosphere, the density can be ound using the barometric ormula:.93 kg/m 3 at C and atmosphere). Also, v is the speed o the object relative to the luid; A is the reerence area; and C as a dimensionless parameter is the drag coeicient. The balloon position (i.e. x and y) will be provided by GPS receiver, while the direction θ will be given by the onboard electronic compass. The perormance is evaluated to accomplish two objectives:.) the ability to navigate the balloon to pre-speciied destination.) the ability to maintain balloon orientation in presence o wind disturbance. Feedback Linearization Controller A. The Theory In recent years, eedback linearization to nonlinear control design has attracted the attention o researchers. The goal is to algebraically transorm nonlinear systems dynamics into ull or partial linear systems so that linear control techniques can be applied. This paper does not discuss the concept o this method, as valuable details can easily be ound in related works (e.g. []). This paper deploys a eedback linearization controller or the balloon system as a classic controller. Corresponding results are be presented. The method may be applied to nonlinear systems o the orm: x& = ( + g( u y = h( (3) n p where x R is the state vector, u R is the vector m o inputs, and y R is the vector o outputs. By applying the Lie Derivative [] to the output, we get: h y& = ( ( + g( u) = L h( + Lg h( u (4) x L g and L are Lie derivatives or g and unctions. I h( u then L g ( L h) & y = ( ( + g( u) = L h( + Lg L h( u (5) x But i Lg L h( u, we must continue to apply the Lie Derivative until u appears in the equation: ρ ρ ρ y = L h( + L L h( x u (6) g ) where < ρ < n. Then the control eort signal will be given by u = [ L ρ L L h( g ρ h( + v] (7) where v is a linear PD controller. In our system the inal control eort is deined as ollows: m m m G = m m m h h l J J J x. u = G [ y + Kp. e + Kd. e] where Kp, Kd, e and Kp = =, Kd 5. e are deined as ollow: xd =, e yd θ d (8).. x x d x... y =, e y d y.. θ θ d θ In this equations, x d, yd and θ d are the desired y position and angle o the balloon and x, and θ are the current position and angle. The matrix G is nonsingular or any value o x, y and θ. By calculating the determinant o the matrix G in (8) we have []: h det{ G} = Jm Since h is not equal to zero or any value o x, y and θ, det{g} cannot equal zero. Thus, the matrix G is nonsingular or any value o x, y and θ. B. Simulation A control system based on eedback linearization technique has been developed and applied on the balloon system. The control scheme is shown in 4.A.6-3

4 Figure. In this igure, y r d is a matrix o desired y r signals or our reerence point and p is the current position o balloon. The vector ur is the output o the controller. Disturbance on the balloon is due to only to wind. Its eect on the balloon is simulated as orce with changing magnitude and direction. Simulation results or this controller are presented in Figures 3-6: one showing a block diagram, one the trajectory o the balloon, while others illustrates the angle and control eort signals applied on the propellers u, u, and u 3. Note that the eect o wind simulation took into consideration the act that the wind s direction and orce are not constant. It can be inerred rom Figures 3 and 4 that the balloon is able to achieve the desired point ater approximately minutes. At this interval, a small amount o power still exists a on the propellers. Changes on the control eort signals are within acceptable range and converge. Figure. Control Diagram Figure 5. Angle (θ) Figure 3. Block Diagram o Airship s Sensors/Actuators Figure 6. Control Eorts (u, u, u 3 ) Fuzzy Controller Description Figure 4. X-Y Trajectory A. The Principles Balloon Model has unknown parameters, thus require a sophisticated design. A uzzy logic controller is a good choice or systems with 4.A.6-4

5 parametric perturbation. However, the system requires substantial knowledge and experience rom a skilled operator. The controller must have the capability to immediately correct any errors detected in the system. (Interested readers may ind useul inormation about uzzy logic control in [3, 4].) In the control system researched in this paper, the control procedure is divided to two parts or subcontrollers, such that the controller may use one in a given time. The irst is or navigation and is used rom the place o origin until the desired point is achieved. The corresponding sub-controller attempts to direct the balloon to the destination at the desired point. The second is designed or orientation purposes, which denotes the direction o the balloon ater reaching the desired point. Since the balloon should maintain a directional wireless communication system, this latter task is an extremely important actor in the design. Data received rom sensors attached to the balloon goes to the controller, where it converted into uzzy variables. This unction is called the uzziication process. The uzziied data then goes through a set o i-then rules in an inerence engine, which results in uzzy outputs that are converted back to a crisp value through a process called deuziication by the weighted average method [5]. Deining the membership unctions or input/output variables is the irst step or uzziication. A membership unction is a graphical representation o the magnitude o participation or each input. It associates a weighting with each o the inputs that are processed, deines unctional overlap between inputs, and ultimately determines an output response. Some control rules are required to use the input membership values as weighting actors to determine their inluence on the uzzy output sets o the inal output conclusion. Once the unctions are inerred, scaled, and combined, they are deuzziied into a crisp output, which drives the system. Dierent membership unctions may be associated with each input and output response [4]. In this paper, three and ive membership unctions with triangular shapes are considered or each input and output variable, respectively. They are illustrated in Figures 7 and 8. Dierent states are assigned to controlled variables to represent the state o each variable. The values o states might be Small (S), Normal (N), Big (B) and or the control eorts might be Negative Big (NB), Negative Small (NS), Normal (N), Positive Small (PS) and Positive Big (PB). The instructions which determine the relation between controlled variables and control eorts are denoted above as control rules. The input errors or navigation system are x d x, y d y, θ d θ and & θ & d θ ; which θ d is the angle between the current position o the balloon and the desired point, and or the orientation system the. inputs are θd θ and θ d θ. Rules are generated based on the number o inputs or navigation controller 3 4 = 8 rules and or the orientation controller 3 = 9 rules. The rules deined or the orientation control are listed in Table. Table. Control Rules or Orientation Rule # θ d θ & θ & d θ u u Rule S S NS PB Rule S N S B Rule3 S B N N Rule4 N S S B Rule5 N N N N Rule6 N B B S Rule7 B S N N Rule8 B N B S Rule9 B B PB NS Figure 7. Membership Function o Input Variables. 4.A.6-5

6 Figure 8. Membership Function o Output Variables Finally, the control eorts can be ormulated by: Figure 9. XY Trajectory u i = n j= n j= x μ j μ j j ; i =,,3 (8) By applying control eort signals in (8) to the balloon, the simulation results or this controller can be shown as in Figures 9, and. The simulation has been done in the presence o wind. The wind s direction and magnitude is not constant. As shown in Figure 9, balloon is able to achieve the desired point. The oscillation o the control eorts in Figure at the beginning are less than the classic controller in previous section. It can be concluded that this controller can work best i there is any limitation in the real control eorts; however, its total perormance is not as good as the classic controller in the presence o the wind disturbance. Figure. Angle (θ) Figure. Control Eorts (u,u ) 4.A.6-6

7 Result Discussion The results shown in the balloon trajectory, controller eorts, and response timings per tested controller scheme are discussed in this section. When the classical controller with eedback linearization is used, aster response time is achieved comparing to when a uzzy controller is used. A ast response makes the system aster to reach its steady state in the presence o disturbance, as shown in Figures 4-6. Using classical controller, the balloon light time to destination located at 36 meters (3m,m) away is simulated to be 3 seconds. It is observed that the balloon is not able to arrive at the exact destination due to wind disturbance. The position error is limited to between 3 and 4 meters. No position error is observed with no wind disturbance. The controller is able to place the balloon on the destination. On the other hand, the uzzy controller arrives at destination in approximately 4 seconds. The models used in the simulation are selected to be simple: nd order balloon dynamic model, velocity-squared riction model, and non-constant orce or wind disturbances. Hence, the classical controller out perormed the uzzy controller. However, the uncertainties in a practical balloon navigation and deployment may make the classical controller under perorm, while uzzy controller may perorm better with the uncertainties. Both controllers use the same hardware or collecting attitude data and navigation the balloon. In terms o the MATLAB simulation time, the uzzy controller requires more time to compute control eorts, while the classic controller does the computation much aster. Conclusion This paper considers a controllable airborne platorm to employ a wireless communication network that can be rapidly deployed to establish communication service in a distressed area. The perormance o two alternative controllers (classic and uzzy) or balloon navigation is analyzed and simulated using MATLAB. The simulation results indicate that the classical controller out perorms the uzzy controller in achieving destination with approximately seconds less. Reerences [] A. Eles, S. S. Bueno, M. Bergerman, J. J. G. Ramos, May 998, A Semi-Autonomous Robotic Airship or Environmental monitoring Missions, Proceedings o the IEEE International Conerence on Robotics & Automation, pp , Belgium. [] S. Varella Gomes and J. Ramos, 998, Airship dynamic modeling or autonomous operation, In Proc. o the IEEE Int. Con. on Robotics & Automation (ICRA), pp [3] E. Hygounenc, I-K. Jung, P. Soueres, and S. Lacroix, 4, The autonomous blimp project at LAAS/CNRS: Achievements in light control and terrain mapping, In International Journal o Robotics Research., pp [4] H. Zhang and J. Ostrowski, 999, Visual servoing with dynamics: Control o an unmanned blimp, In Proc. o the IEEE Int. Con. on Robotics & Automation (ICRA), pp [5] T. Fukao, K. Fujitani, T. Kanade, 3, Imagebased Tracking Control o a Blimp, the 4nd IEEE Conerence on Decision and Control, pp [6] G. Wyeth and I. Barron,, 997, An autonomous blimp, In Proc. o the IEEE Int. Con. on Field and Service Robotics (FSR), pp [7] A. Rottmann, C. Plagemann, P. Hilgers, 7, W. Burgard, Autonomous Blimp Control using Modelree Reinorcement Learning in a Continuous State and Action Space, IEEE/RSJ International Conerence on Intelligent Robots and Systems, pp [8] H. Fukushima, K. Kon, Y. Hada, F. Matsuno, K. Kawabata, H. Asama, 7, State-Predictive Control o an Autonomous Blimp in the Presence o Time Delay and Disturbance, 6th IEEE International Conerence on Control Applications Part o IEEE Multi-conerence on Systems and Control, pp [9] H. Fukushimal, K. Kon, F. Matsunol, Y. Hada, K. Kawabata, H. Asama, 6, Constrained Model Predictive Control: Applications to Multi-Vehicle Formation and an Autonomous Blimp, SICE-ICASE International Joint Conerence, pp [] L. D. S. COELHO, M. F. M. CAMPOS, V. KUMAR, 998, Computer Vision-Based Navigation or Autonomous Blimps, International Symposium 4.A.6-7

8 on Computer Graphics, Image Processing, and Vision (SIBGRAPI), pp [] Yasunori Kawai, Satoshi Kitagawa, Shintaro Izoel and Masayuki Fujita, August 4-6 3, An Unmanned Planar Blimp on Visual Feedback Control : Experimental Results. SICE Annual Conerence in Fukui, Fukui University, Japan. pp. 7- [] Hassan K. Khalil,, Nonlinear Systems, Third edition, prentice Hall. [3] D. Driankov, H. Hellendoorn, M.. Reinrank, L. Ljung, R. Palm, 996, An Introduction to Fuzzy Control, Springer, nd edition. [4] S.D. Kaehler, Fuzzy Logic-An Introduction, available at: lindex.html [5] Guo Jian-guo, Zhou Jun, Dec. 8, Altitude Control System o Autonomous Airship Based on Fuzzy Logic, nd International Symposium on Systems and Control in Aerospace and Astronautics, 8. ISSCAA 8. pp:-5. Acknowledgement This work is unded by NSF grant number NSF- ECCS Addresses Maryam Falahpour: maryam@ou.edu Hassan Moradi: hmoradi@ou.edu Hazem H. Reai: hazem@ou.edu Mohammed Atiquzzaman: atiq@ou.edu Peter G. LoPresti: pgl@ohm.ee.utulsa.edu 8th Digital Avionics Systems Conerence October 5-9, 9 4.A.6-8