Design of a Lateral Motion Controller for a Small Unmanned Aerial Vehicle (SUAV)

Transcription

1 Recent advance on Mathematical Model for Engineering Science Deign of a Lateral Motion Controller for a Small Unmanned Aerial Vehicle (SUAV) Ahmed Elayed Ahmed, Electrical Engineering Dept., Shoubra Faculty of Engineering, Benha Univerity, Egypt (Telephone: +797), A. N. Ouda, B. Military technical college, Cairo, Egypt, ahnaroda@yahoo.com Ahraf Hafez, Electrical Engineering Dept., Shoubra Faculty of Engineering, Benha Univerity, Egypt. ahrafhafez@hotmail.com. Hoam Eldin Huein Ahmed, Communication Engineering Dept., Faculty of Electronic Engineering, Menoufia Univerity, Menouf, Egypt (fax: +37), hhoamkh@yahoo.com. Hala Mohamed Abd-Elkader, Electrical Engineering Dept., Shoubra Faculty of Engineering, Benha Univerity, Egypt, hala_manour5@yahoo.com. Abtract the unmanned aircraft ytem (UAS) are playing increaingly prominent role in defene program and trategie around the world. Thi paper preent a deign of lateral autopilot of a Small Unmanned Aerial Vehicle (SUAV). The deigned autopilot i applied to an Ultratick-5e fixed wing UAV depending on lateral linear model and analytic linear model of a coordinated turn derivation with trimmed value of traight and leveling cenario. The lateral motion controller deign i tarted with the deign of mot inner loop (roll rate feedback) of the lateral ytem, then roll tracker deign with a Proportional Integral (PI)- controller. The guidance and control ytem i related with the deign of heading direction controller with P-controller. Yaw damper i deigned with wahout filter to maintain a zero idelip angle. The performance of two claic controller approache for the deign of autopilot are compared and evaluated for both linear and non-linear model. The reult how a good performance in both diturbance rejection and robutne againt enor noie. Keyword autopilot, inner loop, outer loop, roll tracker, yaw damper, heading direction controller. U I. INTRODUCTION AV Automatic Flight Control Sytem (AFCS) preent a very comprehenive treatment of UAV control and related technologie. The inherently untable nature of typical open loop UAV configuration neceitate a rigorou approach to the analyi and deign of UAV control technologie, a well a a thorough undertanding of tability iue. For any dynamic ytem, there may be requirement on certain frequency (to enure the dynamic are fat ) and damping (to enure that the ocillation die out quickly) pecification on the pole location, and minimizing teady tracking error to commanded input. The typical olution to atify thee requirement i to ue linear feedback control to modify the pole location and loop gain []. The complete tate of the UAV comprie it poition, airpeed (V a ), attitude (roll (φφ), pppppppph(θθ), yyyyyy(ψψ)), angle-ofattack (αα), idelip angle (ββ), and rotation (roll (p), pitch (q), and yaw (r)) rate. Poition, airpeed, and attitude are alo known a the navigation tate [].The main purpoe of thi paper i to deign a lateral motion controller for SUAV to completely control lateral tate (vv, pp, rr, φφ, ψψ) by the lateral input control (AAAAAAAAAAAAAAAA (δδ aa ), RRRRRRRRRRRR (δδ rr )). In general term, an autopilot i a ytem ued to guide an aircraft without the aitance of a pilot. For manned aircraft, the autopilot can be a imple a a ingle axi wing-leveling autopilot. a full complete complicated autopilot a a full flight control ytem that control poition (altitude, latitude, longitude) and attitude (roll, pitch, yaw) during the variou phae of flight (e.g., take-off, acent, level flight, decent, landing, and loiter). For SUAV, the autopilot i in complete control of the aircraft during all phae of flight. From beginning, the deign of autopilot i eparated into two eparate deign; longitudinal and lateral motion controller [3]. Thee eparate autopilot are deigned after modeling of ultratick-5e fixed wing UAV [], the longitudinal dynamic (forward peed, pitching, and climbing/decending motion) and the lateral dynamic (rolling, and yawing motion). Thi implifie the development of an accurate autopilot imply. SUAV control and tabilization i more difficult than larger one. Thi i due to everal factor, including the low ma of ISBN:

2 Recent advance on Mathematical Model for Engineering Science the vehicle, lower Reynold number, and light wing loading. Thee factor make it more difficult to deign a flight control ytem [5]. In order to fly an aircraft, low-level inner loop mut tabilize the airframe uing available enor and actuator, higher-level outer loop control will implement path following (guidance), while the inner loop keep the aircraft flying (tabilization). Detailed deign procedure of a flight control ytem to adequately tabilize and control SUAV are utilized by deigning autopilot inner loop, and outer loop. The two derived linearized model (tate pace and analytical linearized model) for Ultratick-5e (thor) aircraft were ued in the deign of autopilot []. The behavior of the aircraft due to the deired cenario reult were compared between (the tate pace linearized model and the analytical linearized model) and (the nonlinear aircraft dynamic), the reult i too matched between all of the three. The outer-loop wa deigned to achieve the tracking command requirement in (ground track angle). The inner loop are deigned to track roll attitude reference ignal required for the outer loop. Several deign goal were introduced againt the inner loop performance that the cloed loop rie time hould be le than econd, and the overhoot ha to be maller than 5% in ome cae. Root locu technique and PI-controller were tuned uing the two linearized model of the aircraft []. If the controller caue overhoot and degrade the controller performance when coming out of aturation. In order to prevent thi, an anti-windup cheme i implemented which check if the actuator would aturate on the current time tep and doe not perform the integration if thi cae i happened [7].Roll angle reference i contrained at 5. Thi paper i organized a follow; t ection i the introduction, nd ection invetigate the deign procedure of a lateral motion controller, 3 rd ection i the deign of the inner loop of lateral motion controller, th ection how the inner loop deign reult, 5 th ection i the deign of the heading direction controller, th ection i the deign of the yaw damper, 7 th ection how the performance of the whole lateral motion controller in the cenario of rectangular motion command to the aircraft, and th i the lat ection which i the concluion. II. LATERAL MOTION CONTROLLER DESIGN PROCEDURES The lateral motion controller ue the rudder and aileron to keep the aircraft flying in a coordinated turn and following a commanded turn rate (including a zero turn rate for traight flight), it conit of inner loop and outer loop to manage the navigation of the aircraft in the lateral motion and zero ide lip angle control, the dynamic affected the lateral motion begin with the body axi roll rate which i fed back to the aileron to modify the damping of the roll mode. Yaw rate feedback i deigned to modify the damping of the dutch roll mode, but yaw rate feedback only i not ufficient due to coupling between yaw and roll which reult a teady tate yaw rate component during turn, a imple olution i ue a wahout filter on the output of the yaw rate enor. The high pa filter action of the wahout filter i to remove thi teady tate component. The output of the wahout approximate a differentiated yaw rate which i uitable feedback for the dutch roll mode []. For large angle of attack another problem can be appeared which i that the roll pole coupled with the piral pole to form a complex pair, the olution of thi i to deal with the ytem a multi input multi output ytem due to the coupling between the input and the output at high angle of attack, or we can aume that the maximum angle of attack i degree. The lat aumption i good and uitable for laminar condition becaue great value of angle of attack can caue turbulent o the tolen condition will be happened to fail the flight of the aircraft [9]. After that the controller of roll attitude (bank angle hold controller) will be deigned from the inner loop of roll rate by PI-controller. The lat controller i the outer loop and ued for UAV guidance; the heading direction of aircraft with P-controller only which atifie the deigned purpoe. The whole lateral motion controller block diagram a hown in Fig. Fig. : Lateral motion controller block diagram. III. INNER LOOPS OF LATERAL MOTION CONTROLLER (ROLL ATTITUDE TRACKER) DESIGN. Roll rate feedback i deigned to increae the damping of roll rate and i the mot inner loop of the roll attitude (bank angle) hold controller. The analytical open loop linearized tranfer function of roll rate from aileron i ued to deign the roll damper then bank angle tracker. After that the main tet reult. Roll rate (p) from aileron tranfer function can be approximately implified to a reduced linear tranfer function (roll mode) [, ] conidered a eqn. (). pp() 5.5 (+.9) δδ aa() () The choen pole will move from -.9 to the left to be -. with k d_p = -.55, the gain value i choen to mooth the repone trajectory of roll tracker. After that, the next inner loop i the roll angle (φφ) tracker by integrating the roll rate tranfer function to extract the roll attitude, and deign the controller uing PI- controller MATLAB tructure a in Fig.. The performance analyi of roll tracker with two controller in linear and nonlinear model i howed in the next ection. The UAV Laboratory Web ite provide detailed information on the airframe, avionic, and oftware architecture []. The flight oftware i available a an open ource oftware package available upon requet, thi open ource package ha a claic PID controller for autopilot, and ISBN:

3 Recent advance on Mathematical Model for Engineering Science the propoed autopilot deign modifie the performance of the claic one. Again the claic controller parameter for roll tracker (k d_p = -.7, k p_ φφ = -.5, and k i_ φφ = -.) and the parameter (k d_p = -.55, k p_ φφ = -.9, and k i_ φφ = -.5). -K- raddeg ki_phi -Kkp_phi Int.33 d/dt. Hz P <. BW L -.33 Aileron Servo p/delta_a bia/cf/noie phi_int -K- phi kd White Noie diturbance -.55 phi_ref the claic parameter kd_p = -.7 kp_phi = -.5 ki_phi = -. the deigned parameter kd_p = -.55 kp_phi = -.9 ki_phi = -.5 Fig. MATLAB tructure of bank angle hold controller. IV. INNER LOOPS OF LATERAL MOTION CONTROLLER TEST RESULTS. The tet executed are the following tet: - Time domain analyi. TABLE I TIME DOMAIN ANALYSIS OF ROLL TRACKER The property Claic con. Deigned con. t r [ec].9.5 t [ec] Max.o.% Underhoot% Peak..7 Peak time [ec] Doublet ignal repone. roll angle[deg/ec] - Doublet repone comparion between the claical and fo roll tracker claical controller When the input (deired output) in the roll attitude i five degree doublet ignal, the output repone with the two controller are hown in Fig. 3 where the graph i better than the claic auring that the time domain characteritic in Table I. - The effect of enor noie in the repone. The effect of the enor noie with igma =.* -3 rad /ec in the repone of the roll attitude a hown in Fig. roll angle[deg/ec] doublet repone for roll tracker in the exitence of noie Fig. The effect of noie in the roll tracker - The effect of diturbance in the doublet repone. claical controller The ability of the diturbance rejection between two controller i hown in Fig. 5 where the repone to diturbance i high in the value, but it attenuated more peed than the claic controller. - - Fig degree doublet ignal in roll repone. ISBN:

4 Recent advance on Mathematical Model for Engineering Science roll angle[deg/ec] +5 deg repone for roll tracker in the exitence of diturbance claical controller By the previou tet, the roll tracker of the deigned controller aure that it ha a good performance and good robutne and diturbance rejection; it cloely matched with the deired requirement. The next controller i the direction heading controller, it conidered a an outer loop of the roll tracker and related with the guidance and control navigation ytem of SUAV. Fig. 5 The effect of diturbance in the roll tracker. - Multi-tep of roll attitude repone. multi tep repone for roll tracker claical controller V. OUTER LOOP LATERAL MOTION CONTROLLER (HEADING HOLD CONTROLLER) DESIGN. From equation () [], the heading rate ψ i related with the pitch rate q and yaw rate r and pitch attitude θ and roll attitude ϕ. From thi equation we can get a new implified linear relation between the heading angle and the roll angle, thi relation i obtained from the coordinated turn aumption []. During a coordinated turn, in the abence of wind or idelip, we have that vvvv = vvvv, and ψψ = χχ. roll angle[deg/ec] - ψψ = qq + rr cccccccc () χχ = gg tttt n φφ = ψψ = gg tttt n φφ (3) VV gg VV aa Equation (3)can be rewritten a: ψψ = gg φφ + gg (tan φφ φφ) VV aa VV aa Fig. Multi-tep repone of roll tracker Multi tep repone i ued for commanding the aircraft many equence of heading angle a will be een in the rectangular motion, from Fig. it can be hown that the repone to the i fater than the claic one. = gg VV aa φφ + gg VV aa dddd By expreing the equation in Laplace form ψψ = gg φφ() + dddd() () VV aa Equation () i the lat expreion that we can ue it to control the heading from roll attitude; Fig. 7 illutrate the MATLAB tructure block diagram of the lateral autopilot. ki_pi.5 kp_pi Int -K- -Kki_phi -.9 kp_phi Int d/dt <.. Hz BW Aileron Servo.33 P L p/delta_a bia/cf/noie White Noie roll Int 9./7 pi int raddeg pi kd_p -.55 pi_ref the claic parameter are kd_p = -.7 kp_phi = -.5 ki_phi = -. kp_pi =. ki_pi = the deigned parameter are kd_p = -.55 kp_phi = -.9 ki_phi = -.5 kp_pi =.5 ki_pi = diturbance VI. LATERAL DIRECTION CONTROLLER TESTS RESULTS After deigning the heading controller, the following tet were executed to check it performance a hown in the following figure (, 9, and ); the comparion between the Fig. 7 MATLAB tructure block diagram of the lateral autopilot. claic and i matched o much, but the contribution here i the analytical linearized model and a controller with a new Simulink model and compare it with the Minneota univerity tet platform []. The firt tet i the time domain pec, then linear analyi, and the nonlinear ISBN:

5 Recent advance on Mathematical Model for Engineering Science analyi with a cenario of rectangular motion. The effect of diturbance in the heading hold controller - Time domain analyi. TABLE II TIME DOMAIN ANALYSIS OF ROLL TRACKER The property Claic con. Deigned con. t r [ec].3.5 t [ec] Max. O.S. %.5.39 Underhoot% Peak.5. Peak time [ec].9. From Table II the i better than the claic one in the rie time and ettling time, and maximum overhoot (thi property i obviou in the tep repone tet). - Doublet ignal from tandalone Simulink model Fig. Doublet ignal repone of the heading hold controller. Fig. illutrate the matching between two controller if the input i a doublet repone. - The effect of enor noie. The noie tet i executed under the noie at igma= * -3 rad/ - - Fig.9 The effect of noie in the heading hold controller. - The effect of diturbance (the ability to diturbance rejection). +5 degree Doublet repone of the heading angle pi The effect of noie in the heading angle claical controller Fig. The effect of diturbance in the heading hold controller. The diturbance ignal i a ignal with amplitude 5 degree and pule width of. ec applied after teady tate of the repone at a time from to Second. From Fig., the two controller are good in the rejection of diturbance. In the tet platform linear imulation; the executed cenario i the rectangular motion, the command and repone i hown in Fig Rectangular motion with heading angle pi Fig. Rectangular motion heading command and it repone in linear imulation model. VII. YAW DAMPER DESIGN claical controller Yaw rate i fed back to the rudder to modify the dutch roll mode. The purpoe of the tability augmentation of the yaw rate feedback i to ue the rudder to generate a yawing moment that oppoe any yaw rate that build up from the dutch roll mode. The reulting feedback i a type yaw rate with zero command input [3]. We will ue a wahout filter on the output of the yaw rate enor to remove the teady tate component of the yaw rate during turn Wahout filter time contant i a compromie; too large value i undeirable ince the yaw damper will then interfere with the entry into turn []. Too mall value will reduce the achievable dutch roll dumping. Time contant (ττ) wa choen to be.5. The tranfer function of yaw rate loop can be found by uing a root locu technique [] to get the gain value which damp the rate and make it uitable for maintaining yaw rate from rudder to be zero. Yaw damper i deigned with wahout filter a mentioned above. From the lateral tate pace linearized model [], the linearized tranfer function of yaw rate to rudder wa called to be ued. ISBN:

6 Recent advance on Mathematical Model for Engineering Science rr (SS) δδ rr (SS) =. SS3 35 SS SS 35 SS +9.7 SS SS +5. SS+.9 The lateral model ha two pair complex pole (-. ± 5.i) with a lightly damping ratio (.39) and natural frequency (5.59 rad/ec). The purpoe of the damper i to increae thi damping ratio. The controlled ytem wa deigned by aigning the gain k d_r =.5 and the wahout filter with tranfer function: HH() = ττττ () ττττ+ Time contant ττ =.5 VIII. CHECK THE PERFORMANCE OF THE LATERAL MOTION CONTROLLER FOR SUAV. The following tet; the rectangular motion repone in Software In Loop (SIL) which i applied in the non-linear model of aircraft, Fig. illutrate the repone of heading angle due to rectangular motion command, Fig. 3 how the relation between the latitude and longitude, and Fig. how the roll change (inner loop command) which make the rectangular motion. LON claic controller Rectangular motion with heading angle pi in SIL (5) Fig. Heading command rectangular motion repone LAT Fig.3 The hape of the aircraft trajectory due to rectangular motion command in the heading angle. 5 The trajectory of the plane due to rectangular command in the heading angle Rectangular motion with change in roll in SIL The trajectory of the plane claic controller IX. CONCLUSION In thi paper, the deign of autopilot i overviewed with the detailed deign of lateral motion controller. Mot inner loop wa deigned with feedback gain, and then roll attitude hold controller wa deigned with PI-controller far away from complexity with good performance in the time domain characteritic. The deign procedure began with roll rate feedback, the roll attitude controller, Linearization of the nonlinear equation of motion of heading rate i derived to get a linear relation between heading angle and roll attitude. The outer loop controller i a imple P-controller. Yaw damper wa deigned with wahout filter. At lat a rectangular motion command i applied in the non-linear model to check the behavior of the aircraft. The environment diturbance and enor noie are modeled and the performance of the ytem i checked in the exitence of them. Longitudinal motion controller i in the development tage to deign the whole autonomou SUAV with a robut autopilot. X. REFERENCES [] B. L. Steven and F. L. Lewi, Aircraft Control and Simulation, nd Ed., Hoboken, NJ: John Wiley & Son, Inc., 3. [] Gleaon, D. Gebre-Egziabher, GNSS Application and Method Artech Houe, Boton, 9. [3] Stewart, Calculu: Early Trancendental, th Ed. Cole, Belmont,. [] Ahmed EA, Hafez A, Ouda AN, Ahmed HEH, Abd-Elkader HM "Modeling of a Small Unmanned Aerial Vehicle" international journal of mechanical, aeropace, indutrial and mechatronic engineering Vol: 9, No: [5] Reed Siefert Chritianen, Deign of An Autopilot for Small Unmanned Aerial Vehicle Brigham young univerity, augut. [] Andrei Dorobantu, Peter J. Seiler, Gary J. BALAS, Tet Platform for Model-Baed flight reearch, Univerity of Minneota, 3. [7] G. F. Franklin, J. D. Powell, and M. Workman, Digital Control of Dynamic Sytem, 3 rd Ed. Menlo Park, CA: Addion Weley, 99. [] Thoma R. Yechout, Introduction to Aircraft Flight Mechanic, AIAA, 3. [9] Peter J. Swatton, Principle of Flight for Pilot, John Wiley & Son, June. [] Randal W.Beard, Timothy W.Mclain, Small Unmanned Aircraft: Theory and Practice, Princeton univerity pre,. [] Murch, A., Dorobantu, A., and Bala, G., Univerity of Minneota UAV Flight Control Reearch Group, January, ]. [] W. F. Phillip, Mechanic of Flight, nd Ed. New Jerey: Wiley,. [3] Dongwon Jung, Hierarchical Path Planning and Control a Small Fixed- Wing UAV: TheoryaAnd Experimental Validation Georgia intitute of technology, December 7. [] Farid Colnaraghi, Benjamin C.kuo, Automatic Control Sytem, 9 th Ed., john wiley&on, Fig. The change in the bank angle due to rectangular motion in the aircraft. ISBN: