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MINISTRY OF EDUCATION AND TRAINING MINISTRY OF DEFENCE ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY LE NGOC LAN VU QUOC HUY DESIGN OF A STABILIZER AND ALGORITHMS OF FLIGHT PATH FOLLOWING CONTROL FOR THE FIXED-WING UAV Specialization: Control Engineering and Automation Code: 52 02 16 SUMMARY OF Ph.D THESIS IN ENGINEERING HA NOI - 2020 The thesis has been completed at ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY Scientific supervisors: Assoc.Prof.Dr Nguyen Vu Dr Hoang Minh Dac Ass.Prof D Reviewer 1: Prof.Dr Le Hung Lan Ministry of Science and Technology Reviewer 2: Assoc.Prof.Dr Pham Trung Dung Military Technical Academy Reviewer 3: Assoc.Prof.Dr Nguyen Quang Hung Academy of Military Science and Technology The thesis will be defended in front of the Doctoral Evaluating Committee at Academy level held at Academy of Military Science and Technology at …., date… month…., 2020 The thesis can be found at: - Library of Academy of Military Science and Technology - Vietnam National Library INTRODUCTION Research necessities With the goal of using the UAVs for military combat missions, it is necessary to study the synthesis of an automatic flight control system for the fixed-wing UAV Hence, applying research results to the mission of converting retired aircrafts into the UCAVs for performing special combat missions: attacking (suicide UAV) mobile target on the sea or on the ground… In our country, there is currently no research on this issue, so the thesis is being conducted to solve the above problem To solve the above problem, this thesis takes following approaches: - Studying the fixed-wing UAV model, aircraft documents and basic Autopilot of MiG-21, to design a full nonlinear model for the fixed-wing UAV associated with the characteristics of the MiG-21 - From the built full nonlinear UAV model, proceeding to synthesize a “Stabilizer” The Stabilizer has the role of controlling tracking the guide parameters (reference parameters) in vertical and horizontal channels based on the Back-stepping control algorithm This Stabilizer will be an innerloop controller that calculates the values of the control inputs for fixed-wing UAV - Researching to design a “Guidance controller” for guiding the UAV to follow the trajectory to perform tasks: tracking the cruise trajectory by using the virtual target point (VTP) method; attacking maritime mobile targets for UAVs; returning to the airport to land and landing The Guidance controller has the output parameters that are input (reference) parameters for the Stabilizer - Developing a program to simulate the full nonlinear model of the fixed-wing UAV, in which the characteristics of the UAV model use the characteristics of the MiG-21 model This simulation program combined with the simulation programs of the aircraft simulator constitutes the “Flight Simulation System for UAV” to survey and evaluate the integrated control algorithms visually and fully In this approach, the thesis focuses on developing the guidance laws for mixed orbits to perform the task of attacking the maritime moving target for the fixed-wing UAV (using aerodynamics of MiG-21) and synthesize a Stabilizer for vertical and horizontal channels Research objectives The research objective of the thesis is to design an automatic flight control system for a fixed-wing UAV to perform combat missions An Automatic flight control system consist of a “Stabilizer” and a “Guidance controller” They control the UAV to perform flight stages: cruise flight, attacking the targets and landing; towards the conversion of retired aircrafts into suicide fixed-wing UAVs that can attack the moving targets Object of the research Research methods of flight control for fixed-wing UAVs, ensuring that UAVs can automatically perform combat missions Applying research results to convert the retired aircraft into a suicide UCAV, to perform some special combat flight missions Scope of the research Scope of the thesis research: flight model for UAV and fixed-wing flying vehicles; algorithms follow the trajectory paths when performing tasks in 3D; research and develop methods to land and attack maritime moving targets Research modern control methods for synthesize a Stabilizer for a fixed-wing UAV Research contents The thesis focuses on the use of UAVs to perform the military combat missions Applying the research results of the thesis to convert retired aircraft into UAV, to perform suicide mission Research content includes: - Designing a dynamic model for the fixed-wing UAV and a simulation program in Matlab/Simulink, which using dynamic coefficients of the MiG-21 - Synthesizing a Stabilizer that acts as flight-path angle and bank angle controllers These controllers are synthesized by using the Back-stepping technique - Designing cruise paths and guidance methods for UAV to perform the task of following the cruise path - Researching methods of intercept attacking and guidance for attacking the moving targets on the sea - Researching the methods of landing and automatic landing Research methodology a Theoretical research Researching flight models, methods of flight control, and documentation of fighter aircraft, study the methods of path-following control Study the guidance laws, the interception laws and the landing methods for UAVs Research methods of synthesizing controllers by using Back-stepping technique From the above research, flight models for fixed-wing UAVs are developed by using dynamic coefficients of the MiG-21 Plan paths to perform tasks for UAV and design an automatic flight control system for the UAV b Simulation, verification Based on the flight model in theory and applying the Matlab/Simulink tool, to design a full nonlinear model simulation program for fixed-wing UAVs, which used dynamic coefficients of the MiG-21 aircraft Combine this model with the simulation programs in the aircraft flight simulator, to create a complete UAV flight simulation system Thus, the simulation and survey of the guidance laws and controllers need to be developed Scientific and practical significance of the thesis a Scientific significance of the thesis The thesis built a full nonlinear flight model, models for each channel of UAV, which uses aerodynamics of the MiG-21 and the full nonlinear model simulation program in Matlab/Simulink (flight simulation system for fixedwing UAVs) as a basis for developing and verifying other research results of the thesis such as: - Designing a Stabilizer to implement the control of flight-path angle and the bank angle by using Back-stepping methods This stabilizer is an inner-loop controller for guidance controllers for UAV, with the input parameters of the stabilizer taken from the output parameters of the guidance controllers - Designing a guidance controller to control the path following for the UAV to perform tasks: cruise flight, attack moving target, and landings The results of this research apply to fixed-wing UAVs, and apply the results to convert retired aircrafts to UAVs for performing special combat missions b Practical significance of the thesis Introduce the idea and goal of designing a flight control system to perform combat missions for the fixed-wing UAV Applying the research results to the mission to convert retired manned aircrafts into UCAVs, which can handle special combat missions The research of the thesis contributes to the realization of converting retired manned aircrafts into UCAVs to perform combat missions, creating strange elements in combat and improving combat capabilities When the mission to convert retired aircrafts into UCAV is successful, it will open up a new way for our army's combat tactics In addition, the Flight simulation system for UAV is the basis for application of surveys and verification of other control algorithms for UAV Chapter A FIXED-WING UAV MODEL AND THE BASIC STABILIZER 1.1 The coordinate system and trigonometric equation In the thesis, the coordinate frames are used: Earth-Centered Earth- Fixed frame, Inertia reference frame (NED), Body-fixed frame, Vehiclecarried vertical frame, Stability frame, Wind frame, and Flight-path frame 1.2 Fixed-wing UAV Model 1.2.1 Full nonlinear model of the fixed-wing UAV The full nonlinear equations of motion for the fixed-wing UAV are shown by following equations: u r.v q.w g sin P M aircraft S Va2 CD S Va2 CY S Va2 CL cos cos cos sin sin M aircraft 2 v p.w r.u g sin cos S Va2 CD S Va2 CY S Va2 CL sin cos sin M aircraft 2 w q.u p.v g cos cos 1 M aircraft S Va2 C D S Va2 CY S Va2 C L sin cos sin sin cos 2 ( J y J z ) J z J xz2 ( J x J y J z ) J xz p r p q J x J z J xz J x J z J xz2 Jz J xz Va SbCl Va2 SbCn J x J z J xz2 J x J z J xz2 q Jz Jx J 1 pr xz ( p r ) Va2 ScCm Jy Jy Jy ( J x J y ) J x J xz2 ( J x J y J z ) J xz r p r q J J J J x J z J xz2 x z xz J xz J x Va2 SbCl Va2 SbCn J x J z J xz2 J x J z J xz2 p q.sin tan r.cos tan q.cos r.sin q.sin / cos r.cos / cos p n VN u.cos cos v.(sin sin cos cos sin ) w.(cos sin cos sin sin ) p e VE u.cos cos v.(sin sin sin cos cos ) w.(cos sin sin sin cos ) h VD u.sin v.sin cos w.cos cos (1.28) (1.29) (1.30) (1.31) (1.32) (1.33) (1.34) (1.35) (1.36) (1.37) (1.38) (1.39) There are also relationships between other parameters such as the flightpath angle, the course angle, the angle of attack, the angle of sideslip and the air speed of the UAV These equations constitute a full nonlinear model describing the motion of a fixed-wing UAV in space 1.2.2 The equations of motion for each channel The equations of motion for each channel was built by separating and reducing from the full nonlinear equations of motion above, which are used to synthesize a stabilizer for UAV (details are presented in the thesis) 1.2.3 Aerodynamic coefficients and inertial coefficients of the UAV - Aerodynamic force coefficients The aerodynamic force coefficients are indicated in following equations: D Va2 SCD , Y Va2 SCY , L Va2 SCL (1.56) With the fixed-wing UAVs, the aerodynamic force coefficients (the drag, side force, lift coefficients CD, CY, CL) are determined: CD CD0 (CL CL0 ) CD f CDleg leg e A.R CD missile CD f (1.57) break CDAddfuel Addfuel break missile (1.58) CY CY CY a CY r a r (1.59) CL CL0 CL CL f CL e f e The f , leg , missile , break , Addfuel are respectively signs when extract flaps, extract landing gear, carrying rockets, extract air-break, carrying drop tanks and CD , CD , CD , CD , CD are respectively the drag f missile leg break Addfuel coefficients of the flaps, landing gear, rockets, air-break and drop tanks - Aerodynamic moment coefficients Aerodynamic moment coefficients (the current roll, pitch, yaw moment coefficients Cl, Cm, Cn) are determined as follows: Cl Cl Cl a Cl r a r b (Cl p Clr r ) 2.Va p Cm Cm Cm f Cm e f Cn Cn Cn r r e b Cn r 2.Va r c Cm q 2.Va q (1.60) (1.61) (1.62) The component parameters of aerodynamic moment coefficients are described the aircraft document or appendix A of the thesis - Inertia coefficients of UAV The inertial coefficients are provided by UAV documentation, when using the coefficients of MiG-21, they are determined: Jxy = Jxz = Jyz = [kg.m2]; Jx = 5400 [kg.m2]; Jy = 31000 [kg.m2]; J z 62000.(0,8 0, 2.gt )[kg m ] M fuel , gt is the current oil weight (1.63) 1.2.4 Actuators of the fixed-wing UAV - UAV’s deflections: The Fixed-wing UAV uses ailerons, elevator and rudder deflections to control flight For example, the permissible operating range of the respective deflections: a 200 200 , e 15.70 7.50 , r 250 250 - Other actuators: The throttle is used to control the engine rotation speed (thrust) In addition, there are other actuators: Gears handle, flap, air break… 1.3 Flight stages of the combat mission and structure of the combat UAV (UCAV) control system 1.3.1 Flight stages of the combat mission A UAV performing a combat mission (attacking the target) needs to perform the following flight stages (shown in figure 1.6): Approach for landing D E F Cruise flight M C Landing G L H I Take-off Attacking target K T A B’ B Figure 1.6 Flight stages of UAV combat missions - Takeoff stages: Take-off run, Rotate, takeoff and takeoff climb - Cruise flight: is the stage when the UAV flies to the desired areas (points) and attacking target area (C-D-E-F-G) - Attacking target: is the process when the flying vehicle follows the target and attacks the target (shoot, bombing or suicide directly at the target), corresponding to H-I-K-T - Landing stages: cloud penetration, glide slope, approach for landing, flare, landing run, and parking These stages are from H-L-M-A-B’ The takeoff stages, landing run and parking of landing stages for the UAV are not investigated in the scope of this thesis 1.3.2 Structure of the UCAV control system The structure of the fixed-wing UAV control system as shown in figure 1.7 From the battle plan, a flight plan for the UAV is developed The flight plan sends the control command to the guidance controller to perform the mission Corresponding to each different flight stage when performing the task, the guidance controller calculates desired guidance parameters d and d of UAV The desired guidance parameters are applied to the stabilizer The stabilizer calculates and gives the desired deflections angle to control the UAV according to the desired guidance parameters, thereby sterling the UAV follow the desired path Automatic Flight Control System Flight plan + _ Situational analysis Guidance Controller , + d d Stabilizer _ a ,e ,r UAV Model Inner control loop Outer control loop Figure 1.7 Diagram of overall structure of UAV control system 1.4 The research works are related to the thesis The content of the thesis focuses on synthesizing an automatic flight control system for UAV, including designing a stabilizer (using Backstepping technique) and a guidance controller for UAV In which, the stabilizers of CAУ-23 are mentioned as the basis to compare the results achieved when synthesizing the stabilizer The CAУ-23 has the stabilizers with the following control laws: (1.64) a K ap p K a ( d ) - Bank control (hold): q (1.65) e K e q K e ( d ) - Pitch control (hold): p (1.66) - Heading control (hold): a K a p K a K a K a ( d ) n q H (1.67) - Altitude hold: e K e q K e K e K e nz K e ( H H d ) 1.5 Conclusion of chapter The full nonlinear flight model and models of each channels for fixedwing UAV are built in this chapter The models of the UAV for each channel is the basis for synthesizing a “Stabilizer”; the stabilizer has the role of controlling the UAV to follow the guidance parameters for each channel The full nonlinear fixed-wing UAV model is the basis for designing a simulation program for the survey and evaluation of control algorithms When using the UAV to perform combat tasks, flight control issues include two main issues: the guidance (navigation) control and stability (control) of attitude parameters The stability issue: implementation of UAV's deflections control so that UAV's attitude achieves desired guidance parameters (desired flight-path angle d and desired bank angle d) The stability issue is solved in chapter of the thesis Guidance issue: control UAV z to the mission area, attack the target or return to the airport and land The output parameters of the controllers in the guidance issue are the guidance parameters (d,d) These parameters are the input parameters for the stability issue The stability issue will be mentioned in chapter 2, and the guidance issue is mentioned in chapter of the thesis The proposed algorithms are simulated and verified in UAV's full nonlinear flight simulation program by using the characteristics of the MiG-21 model that will be mentioned in chapter Chapter SYNTHESIS OF A STABILIZER FOR FIXED-WING UAV USING THE BACK-STEPPING TECHNIQUE In chapter of the thesis, the Back-stepping algorithm is applied to synthesize controllers: flight-path angle controller (vertical plane) and bank angle controller (horizontal plane) for UAV; simulation, verification, evaluation of achieved results 2.1 Synthesis of the longitudinal Back-stepping controller 2.1.1 The longitudinal model of UAV (used to perform the flight-path angle control), with the assumption β0, v0 From the model of UAV presented in chapter 1, the longitudinal model of UAV used in the flight-path angle control, includes: D.tan L mg cos mV a q q M M q q M e e (2.12) 2.1.2 Synthesis of flight-path angle control Applying the Back-stepping control technique and using longitudinal model equations (2.12), to synthesize a flight-path angle controller for UAV The law of the flight-path angle control is determined: e k4 q [ M (k4 M q ).k2 k1 ]. k2 (k4 M q ).(1 k1 ). M e (2.92) k2 (k4 M q ).(1 k1 ). ref k2 (k4 M q ). Constraints: k1 1, k2 0, k4 M q k3 ( 1 k1 0) k3 k , k k ( k 1), ( k 0) 1 (2.93) To determine the parameter (which is the value of α when ), comes from the equation: (2.94) D.tan L( ) mg cos ref Considering to be small enough to have tan , the result is 11 of ref=400, after 5s for the reference bank angle reaching ref=00 - Perform simulation of a Back-stepping controller and perform simulation with the CAY-23 of MiG-21: Perform simulation of a Backstepping controller with an airspeed Va= 800km/h, responses of UAV are shown in figure 2.8 Perform simulation with the CAY-23 of MiG-21, with an airspeed Va=800km/h, responses of UAV are shown in figure 2.11 In which, the parameters are: ref, δa, and p respectively Figure 2.8 Responses of UAV using a Back-stepping bank angle Figure 2.11 Responses of UAV using a bank angle controller of CAУ-23 - Note: The Back-stepping bank angle controller and the bank angle controller of CAУ-23 both control the UAV to track the reference bank angle at difference airspeeds with good control quality (shown in figure 2.8 and figure 2.11) The bank angle controller synthesized by the Backstepping method uses model parameters to result in smaller over-shoot, fewer numbers of sign changes of the p (pitch rate), not increasing the pitch rate (p) and less time for stability This synthesis method ensures good control, adapting to changes of model parameters 2.4 Conclusion of chapter The model of the fixed-wing UAV is suitable to apply the Back-stepping algorithm to synthesize the controller with the calculated parameters depending on the UAV model parameters These controllers ensure the UAV control stable with good control quality and adapt to changing model parameters The results show that the synthesis of Back-stepping controllers for the fixed-wing UAV is simple and not hard to apply Simulation results in some cases show that the stability and control quality of the Back-stepping controllers are better than the ones synthesized by the traditional linear method (PID) This is the basis for designing a guidance controller to control UAV following different trajectories (performing specific tasks), in which the output parameters of this controller becomes the input parameters of the Back-stepping controllers These 12 issues will be presented in the chapter of the thesis Chapter SYNTHESIS OF THE GUIDANCE CONTROLLER FOLLOWING DIFFERENT TRAJECTORIES TO PERFORM THE MISSION FOR THE FIXED-WING UAV 3.1 Designing a controller to follow the cruise path for the fixed-wing UAV 3.1.1 The path following and the path planner The list of waypoints a Lateral VTP path following Path planner d Longitudinal VTP path following d Stabilizer: using Backstepping controller r e UAV (lateral and longitudinal) t Airspeed controller , Va Figure 3.1 Block diagram of the flight guidance and control for UAV The flight guidance and control for UAV consist of: A lateral Virtual target point (VTP) guidance and a longitudinal VTP guidance, an Airspeed controller, a stabilizer (inner-loop) that controls the actuators of the UAV Block diagram of the system is shown in figure 3.1 3.1.2 Designing the method to follow the straight line in the 3D space From the structure diagram of flight guidance and control for UAV, using the virtual target point method in 2D space, the guide system for UAV in 3D space can be built by using geometric methods Wi+1 -z, -z1 x Px1z1 zPlane T e Δ1 R1 zref xi+1 zplane xi f Wi Sxy W'i xPlane f R2 S1 Lxy P Txy ec Δ2 Pxy y1plane W'i+1 x1 x1plane O yi yplane yi+1 y y1 Figure 3.3 Develop a method to follow VTP in 3D space Separate the problem of path following in 3D space into two problems in 2D space: in vertical plane and horizontal plane - The first problem (in the vertical plane): This issue is solved in the axes Ox1y1z1, in which the plane Ox1z1 parallels to a plane containing the path The position of T in the axes Ox1y1z1: 13 x1t xi cos f yi sin f ( R 1 ).cos f y1t xi sin f yi cos f ( R 1 ).cos f z1t zi ( R 1 ).sin f -z1 z1plane z1t zi, z1i Wi O x1i x Px1z1 α1 d e α2 R1 z1ref R2 (3.12) Pv Δ1 * gs xi+1 Wi+1 St T Lxy x1plane x1t e Pxy S1 W’i O x1i+1 Figure 3.4 The method of VTP path following control in the vertical plane d f xi x1 Δ2 Sxy xplane f Pref Sxy W'i+1 Txy yi y yplane yi+1 Figure 3.5 The method of VTP following control in the horizontal plane From the position of the Virtual Target Point and the position of the UAV, the desired flight-path angle is determined: d arctan(( z1t z1 plane ) / ( x1t x1 plane )) (3.13) The elevator control law is: e k4 q [ M (k4 M q ).k2 k1 ]. k2 (k4 M q ).(1 k1 ). M e (3.14) k2 (k4 M q ).(1 k1 ). d k2 (k4 M q ). - The second problem (in the horizontal plane): Calculate the position of T (which is Txy) in Oxy: xt xi ( S xy ).cos f , yt yi ( S xy ).sin f (3.18) The desired course angle is determined: d arctan 2( yt y plane , xt x plane ) (3.19) (3.20) The desired bank angle is determined: d k k In which: plane d ( plane is course angle of UAV) f i 1 , with i 1 arctan 2(( yi 1 y p ),( xi 1 x p )) The ailerons control law is determined: a K ap p K a ( d ) (3.21) 3.1.3 Designing the method to follow the curve path in 3D space The position of the VTP in the axes Oxyz is determined: xt R.sin t xOi , yt R.cos t yOi ht R1.tan f hOi R.cos t tan f hOi (3.28) The desired course angle and desired flight-path angle are determined: 14 (3.29) We have the control laws of vertical and horizontal channels (3.14) and (3.21) respectively, where χd, γd are determined according to (3.29) 3.1.4 Designing a virtual target distance parameter tuner - The straight line: Proposing a method of changing the distance Δ1 from the UAV to the path according to the exponential law, which depend on the cross track error (Ce), to ensure the ability to follow the trajectory quickly (fast convergence) without increasing the overshoot: d arctan 2(( yt yP ),( xt xP )), d arctan 2((ht hP ),( xt xP )) Ce 1 k1 k2 (1 2.(1 e k3 ) 1 ) , with Ce=d; (3.34) - The curve path: Proposing a method of choice varies according to the exponential law, which depends on the cross-track error of the UAV compared to the orbit Therefore, when the UAV is far away from the path, has a big value suitable for smooth and enough fast convergence, when the UAV flies closer to the path, gradually decreases to ensure the cross-track error is small Turn _ direction.kv (3.35) Ce kv k1 k2 (1 2.(1 e k3 ) 1 ) , with Ce=d; (3.36) 3.2 Develop the UAV guidance laws to attack moving target on the sea 3.2.1 Develop the guidance laws to attack moving target These objects are solved in the inertial reference frame (fixed ground), in this case denoted as the axes Oxyz Pi+1 xi+1 d d i 1 Pi yi+1 d zi+1 T Ti+1 x O hi+1 Fi+1 y z Figure 3.14 Geometry of guidance laws to attack the moving target for UAV - The desired course angle and desired flight-path angle are determined: hi 1 sin i 1 yT t F d arctan tan i 1 hi 1 cos i 1 xT t F tan i 1 (3.67) hi 1 i 1 d arcsin (3.68) - Perform UAV control in vertical plane using the flight-path angle 15 controller: Control command for the elevator as in control law (2.92) with d from equation (3.68) - Perform UAV control in horizontal plane using bank angle controller: Desired bank angle is determined: d k (3.71) The ailerons control law is (2.139): a K ap p K a ( d ) (3.72) Plan flight paths and designing laws to track and attack maritime moving target for UAV, which use low-altitude flight Figure 3.15 shows an image depicting the trajectory of the UAV following (crashing into) a maritime moving target using the planning of the low-altitude flight The process consists of phases: x A B’ B y z C F Figure 3.15 Guidance plan for suicide UAV to track and crash moving target at sea using low altitude flight - Phase 1: The UAV phase performs an altitude reduction (A to B) + The horizontal channel: following the guidance laws described above; the desired course angle of the UAV is determined (3.67) and the control law according to (3.72) + The vertical channel: The law of descending is determined: ( d f (1 e h hd ) hd ) (3.73) Control law is determined according to (2.92) - Phase 2: UAV flying at low altitude follows the target (B to C) +The horizontal channel: Similar to the phase 1, the desired course angle is determined (3.67) and the control law is determined (3.72) + The vertical channel: Performing an altitude hold flight (desired lowaltitude hd ), which is implemented by control law (3.73) - Phase 3: Crashing the moving target (from C to F) + The horizontal channel: UAV's guidance law is determined in the same way as stages and The desired course angle is determined following (3.67) and the control law is (3.72) + The vertical channel: At the end of the altitude stabilization process, the UAV proceeded crashing the target The law of controlling the flight- 16 path angle is determined as presented in above this section, according to (3.68) Control commands are determined according to (2.92) 3.2.2 Simulate and survey the guidance law for UAV to attack maritime moving target The simulation results are shown in figure 3.20 when the UAV flying at a low-altitude for attacking a maritime moving target Figure 3.20 UAV’s orbit when following and attacking a maritime moving target using the low-altitude flight 3.3 Designing automatic landing controller for UAV 3.3.1 Landing stages and planning the trajectory of landing - The stages of landing: + Stage 1: Guiding the UAV to an area of 200250km from the airport; + Stage 2: The cloud penetration (descending) stage; + Stage 3: The glide slope: following the localizer/glide path; Va = 500 ÷ 550km/h, Thả (Va
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