Do hyeon LEE, Chang-Joo KIM, Sung wook HUR, Seong han LEE

School of Aerospace Information Engineering, Konkuk University, Seoul 05029, Republic of Korea

KEYWORDS

Abstract This study creates and combines the general maneuver libraries for fixed-wing aircraft to implement tactical maneuvers.First,the generalized maneuver libraries are established by analyzing the characteristics of tactical maneuvers required in battlefields.The 7th order polynomial is applied to both the creation of the maneuver libraries and the generation of the trajectories or flight paths for modal inputs.To track the desired trajectory, we design the Attitude Command Attitude Hold(ACAH)system and the Rate Command Rate Hold(RCRH)system using Model Following Controller (MFC). Moreover, the Line-of-Sight (LOS) guidance law is designed. In particular, the CONDUIT? is employed to optimize the gains so that the control systems meet the aircraft Handling Qualities (HQ) criteria. Finally, flight simulations are performed for the longitudinal loop,immelmann-turn, and climb-slalom-descent maneuvers to verify that tactical aggressive maneuvers are realizable via the combination of maneuver libraries. This study can contribute to the development of flight techniques for aircraft tactical maneuvers and to the revision of air force operational manuals.

1. Introduction

The required maneuvers for an entire mission should be automated so that the mission can be successfully performed, the mission efficiency of manned or unmanned aircraft can be maximized in dynamically changing environments such as battlefields, and the variability of the types of aggressive maneuvers according to situations can be addressed.

Nazim1,2conducted a study on the flight path generation required to implement the mission for the Unmanned Combat Aerial Vehicle(UCAV).He also examined the construction of the control framework for aggressive maneuvers, using a sliding mode controller. Koo et al.3studied the conditions required for flight maneuver transition and the diversity of missions according to flight path combination. Wang4identified aircraft maneuvers from flight test data and then stored the data as libraries.In Ref.5,Sankalp et al.studied the generation of maneuver libraries to ensure the stability of a helicopter in a given environment. Adam et al.6investigated the construction of the control framework for aggressive maneuvers of fixed-wing and quadrotor aircraft.Andrew et al.7researched the autonomous obstacle avoidance algorithm for agile flight. Brian8researched the aerobatic maneuver of fixed wing aircraft, using classical control techniques, and Willem9studied the aerobatic maneuver of fixed wing aircraft, using nonlinear control techniques. Edwards10and Tatsch11described the flight procedure of aggressive maneuver for fixed wing aircraft. Thus, these researches mean that the maneuver and flight controller transition are needed to perform the aggressive maneuvers.

Herman and Visser12optimized the flight path with a minimum time problem after dividing the air race section into several segments. Based on a point mass model, Hiroyuki and Baba13studied the flight path optimization and tracking control for the barrel roll maneuver. These studies optimize the trajectories of state variables and control variables, or flight paths, at one time, based on initial values, final values, and constraints of the maneuver. The methods developed can provide optimal solutions if there exists one,but they do not guarantee the existence of the solution that satisfies given boundary conditions and constraints. Further, the optimization of the trajectories for state and control variables or for flight paths is possible when designers know both the physical characteristics and information of the target maneuver. Therefore, the methods in the existing research cannot be used in those environments which change rapidly, such as battlefields. Thus,Douglas and Roy14studied the trajectory generation method using polynomials and Lee et al.15,16researched the trajectory generation using polynomial and tracking control. Especially,Lee15,16proposed the new concept of the trajectory generation and tracking control by using maneuver libraries.

The all of flight controllers have to satisfy the HQ requirements. Firstly, Department of Defense17defined MIL-F-8785C. After then, David18and Samuel19et al. developed the MIL-STD-1797A for fixed wing aircraft and ADS-33 for rotorcraft,respectively.Especially,MIL-STD-1797A is revised as MIL-HDBK-1797 by Department of Defense.20Eugene21studied the Low Order Equivalent System (LOES) identification for supersonic transport aircraft and John22researched the history of LOES.David et al.23analyzed the physical property of HQ requirements for fixed-wing aircraft. By using HQ requirements of fixed wing aircraft, Tom et al.24,25proposed the new control law for business jet aircraft and Mark et al.26,27studied the integrated design framework of the flight controller. Moreover, Frank28, Lee29, and Larry30et al. designed the flight controller of fixed-wing Unmanned Aerial Vehicle(UAV) and ducted fan UAV by using HQ requirements of piloted aircraft. Here, CONDUIT? was used to calculate the control gain satisfying HQ requirements in most of flight controller design studies. The user manual of CONDUIT?is described in Ref.31. The most of existing researches used the MFC to satisfy the HQ requirements. In Ref.32–38, the design procedure and performance of MFC had been defined and proved. Katsuhiko39and John40described the basic theory for flight control. Finally, Lee et al.41generalized the LOS and Kim et al.42–43proposed the high fidelity flight dynamics modeling method of propeller driven aircraft.

This study proposes a method to realize various tactical maneuvers by using the combination of basic maneuvers.This study also attempts to show the possibility of tactical maneuvers with the method proposed by performing flight path tracking control and aerobatic maneuvers with the combination of general maneuver libraries. Several general maneuver libraries are defined, and modal inputs are specified to identify these libraries.Then,a polynomial is used to generate maneuver libraries and the method of this study is established. The Line-of-Sight guidance law, Attitude Command Attitude Hold (ACAH) system, and Rate Command Rate Hold (RCRH) system are then designed to perform tactical maneuvers through the combination of maneuver libraries.In particular, we optimize the gains of the control system to meet the Handling Qualities (HQ) criteria of fixed-wing aircraft by using the CONDUIT?. Finally, flight simulations for the longitudinal loop, immelmann-turn, and climbslalom-descent maneuvers are performed to confirm the usefulness of the proposed method.

The rest of this paper is organized as follows. Section 2 introduces general maneuver libraries, and Section 3 describes the creation of maneuver libraries based on a polynomial. In Section 4 we present the design of the Flight Control System(FCS) and the optimization with the CONDUIT?. Section 5 analyzes the flight simulation of tactical maneuvers, followed by the conclusion in Section 6.

2. General maneuver libraries

Fig.1 illustrates the procedure for performing an air-tosurface mission. Terrain masking maneuvers are performed in ②across the front line. The target may be successfully hit in ③and ④by a series of aggressive maneuvers to avoid both enemy radars and surface-to-air missiles. Terrain masking maneuvers are performed again to escape the area of operations in ⑤. Therefore, tactical maneuvers are required in the areas of ②–⑤.18,20The maneuver properties for each area are shown in Table 1.

MIL-STD-1797A18,20classifies aircraft maneuvers into four types from Categories A to D depending on the required level of maneuver agility,as shown in Table 1.Typically,aggressiveness and precision are collectively called the agility in the HQ society. Therefore, tactical maneuvers can be classified into Categories A to D according to the extreme agility. Various well-known tactical maneuvers1can be divided into different maneuver modes depending on the variations in altitude and roll angles, and on the existence of longitudinal/lateral loops during the maneuver, as shown in Table 2. In Table 2: A1:The maneuver without altitude change, A2: The maneuver with altitude change B1: The maneuver without roll angle change, B2: The maneuver with roll angle change, C1: The maneuver without loop maneuver,C2:The maneuver with longitudinal loop maneuver, C3: The maneuver with lateral loop maneuver.

In terms of flight-control,a maneuver can be performed by tracking required state variables which are commonly called modal inputs for FCS.1,16. To implement the aggressive maneuver, the modal inputs and the required structure of FCS are designated for each maneuver library, as shown in Table 3. The modal inputs are the most basic state variables in maneuver library identification, and should be tracked by the FCS with the required precision and aggressiveness. The changes in altitude and roll angles are reflected inq1andq2,respectively. The loop maneuvers are represented byq3andq4.If required for a specific mission,other kinds of maneuvers can be added to the library table.

Table 1 Required maneuver properties for each mission phase.18,20

Table 2 Maneuver modes in each of tactical maneuver.1

The physical meaning of modal inputs should be grasped to specify the sequence of each maneuver library and to select the control method.The modal inputs ofq0andq1have been specified with the flight velocity, the Angle of Attack (AOA), and the altitude rate of changes. This means that the durationand target values of a maneuver must be definitely specified.In other words, the maneuver can be performed when the trajectories of AOA, altitude, and speed are generated and tracked precisely by using the FCS. In the same vein, the trajectories of the flight velocity and angular rate should be generated forq2,q3, andq4. Thus, the creation of maneuver libraries means the generation of trajectories corresponding to the prescribed modal inputs for the maneuver.

Table 3 Modal inputs and FCS modes for each maneuver.1,15,16

3. Maneuver library generation

This study attempts to create maneuver libraries by using the 7th order polynomial.A polynomial is employed for maneuver library generation because it can overcome the two disadvantages of the optimization method.15First, this method does not guarantee real-time trajectory generation, which is a fatal disadvantage in battlefields. Second, this method does not guarantee mathematically that there is always a solution satisfying the given boundary conditions and constraints at the connecting point of two different libraries. This means that alternatives to cope with failures of the optimization method must always be prepared.Several solutions to these two problems have been suggested,but to our best knowledge,complete solutions have never been developed.This paper thus presents a solution to trajectory generation using a polynomial which enjoys the advantages of real-time applicability and easy satisfaction of the required boundary conditions or constraints.

Due to these advantages,Ref.14utilizes the polynomial trajectory generation method to create the helicopter flight path.The maneuver libraries in this study are created with the 7th order polynomial and acceleration model proposed by Ref.14.

As shown in Fig.2,a trajectory for each phase can be generated after the maneuver is divided into the entry, maximum acceleration,transition,minimum acceleration,and exit phases to reflect the required maneuver aggressiveness.The maneuver aggressiveness is characterized by the durations at the entry and exit phases and by the amplitude of the acceleration.

3.1. Entry phase

where Δt1=t1-t0In Eq.(1),θ0and θfrepresent the initial and final conditions oft0andt5, respectively. The timetis transformed into the non-dimension variable τ, as shown in Eq. (2), which easily implements the boundary conditions and trajectory θ（t） for the entry phase.

Fig.2 Modeling the acceleration for trajectory.12

The coefficientsa,b,c,anddare simply determined by the initial conditions ande,f,g, andhby the final conditions, as shown in Eq. (5). Therefore, Eq. (6) can be used to efficiently compute the remaining coefficientse,f,g, andh.

3.2. Calculation of the maximum acceleration

Table 4 Boundary conditions for attitude trajectory.

4. Design of the guidance and control laws

This section deals with the design of the guidance and control laws for tactical maneuvers.The guidance law is designed with the LOS technique,and the ACAH system and RCRH system are designed with the MFC technique. The Proportional-Inte gral-Derivative (PID) control technique is used for the Speed Hold (SH) system. This section focuses on the design of the ACAH and RCRH systems that meet the HQ criteria for fixed-wing aircraft. Details of the LOS guidance law and the SH system are given in Ref.39–41. Fig.5 illustrates the KLA-100 sports light aircraft and its configuration data are defined in Table 5.

Fig.3 Exact maximum acceleration calculation with Newton-Rapson method.

Fig.4 Trajectories of the angular acceleration, angular rate, and attitude angle for the five phases.

Fig.5 Three-view drawing of KLA-100 aircraft.

Table 5 Configuration data of KLA-100 aircraft.

MIL-STD-1797 defines the level of flying quality according to the aircraft classification and flight phase. Furthermore, it describes in detail the requirements for the short-period mode,phugoid mode, Dutch roll mode, roll mode, spiral model, and Low Order Equivalent System(LOES).17,18,20LOES is used to specify the dynamic response characteristics in the longitudinal, lateral, and directional axes. The HQ specifications for the short-period mode, phugoid mode, Dutch roll mode, roll mode, and spiral model are the stability requirements in static conditions.This means that the stability and responsiveness of the aircraft are guaranteed when the requirements for each mode and LOES are met. Therefore, the requirements related to the LOES, damping ratio, and natural frequency of each mode must be satisfied.

Eq. (8) represents the LOES model24–26of the short-period mode as specified in MIL-STD-1797

whereTθis time constants for the short period mode;τθand τnzrepresent the equivalent time delays for the control system implementation; andMδlongandZδlongare the control derivatives of longitudinal moment and force, respectively.nz, ζsp,and ωspare the normal load factor,damping ratio,and natural frequency of LOES model for short period mode,respectively.To specify the response characteristics of the airframe equipped with the FCS(Eq.(8)),the requirements must be satisfied for the Control Anticipation Parameter (CAP), i.e.,‘‘steady-state normal acceleration change per unit angle of attack”. Moreover, the requirements for the damping ratio and natural frequency related to the short-period mode should be met.

The CAP represents the Numerator effect of Eq. (8),expressed by the ratio of the initial pitch acceleration to the final normal acceleration, as shown in Eq. (9). The value of the CAP provides the necessary criteria for pilots to recognize the suitability of the pitch acceleration and vertical acceleration.23

whereV0andggravare the trim velocity and gravity acceleration, respectively. The ‘‘steady-state normal acceleration change per unit angle of attack” specification is used to determine an acceptable maneuvering stick-force gradient. This indicates the absence of nonlinearity in the force variation of pitch controller within a specific load factor range.10. Eq.(10) represents the damping ratio and natural frequency24,25of the airframe with the pitch controller to achieve Level 1 HQ.

The natural frequency requirement for the LOES model of Eq. (8) in the short-period mode is 0.5 ≤ωsp≤12 rad/s24.Therefore, the conditions ?sp≥0.4 and 0.5 ≤ωsp＜20 rad/s in Eq.(10)become Level 1.The damping ratio and natural frequency for the phugoid mode are guaranteed to ?ph≥0.04 and ωph≤0.5 rad/s, respectively. In particular, Level 1 conditions of Eq.(10)must be satisfied since they directly affect the stability and responsiveness of the FCS.

In this study,the CONDUIT?is used to optimize the control gains satisfying the HQ criteria. Tables 6 and 7 show the HQ specifications for the longitudinal and lateral/directional axes selected by the CONDUIT?.

‘‘EigLcG1” and ‘‘StbMgG1” are the HQ specifications for the stability of the FCS. ‘‘CosLoG1” and ‘‘CapPiL2” are the HQ specifications corresponding to Eqs. (8) and (9), respectively. ‘‘FrqSpL5” corresponds to the ‘‘steady-state normal acceleration change per unit angle of attack”. ‘‘EigDpG1”and ‘‘FrqSpL5” are the HQ specifications corresponding to Eq. (10). Finally, ‘‘EnvTmG1” is the specification for the step response. The reason for adding this specification is to satisfy the HQ specifications and track the reference signal simultaneously. A detailed description of each HQ specification in Table 6 and Table 7 can be found in Ref.17,18,20,24–26,31.

This study uses the HQ specifications in Tables 6 and 7 and the CONDUIT? to optimize the control gains of the ACAH and RCRH systems. These two different control structures are required to simultaneously track both the required attitude and angular rate as classified in Table 3 for the maneuver library.8

4.1. ACAH system with MFC controller

Table 6 HQ longitudinal motion for ACAH and RCRH system.24,26,31

Table 7 HQ of lateral motion for ACAH and RCRH systems.25,26,31

The states and matrices used in Eq. (12) are defined as

Fig.6 Block diagram of MFC for ACAH system.35–37

The estimated HQ ratings for all the cases are presented in the Pcomb as shown in Fig.7. The numerical values in the Pcomb indicate the goodness estimation for each of the HQ ratings.Fig.8 depicts the computed levels of the HQ as a point in the CONDUIT HQ window with the boundaries for Level 1, Level 2, and Level 3 HQ specifications defined with MILSTD-1797 and MIL-DTL-9490E. The blue, pink, and red stand for Level 1, Level 2, and Level 3, respectively.

Table 8 Optimized gain for ACAH system.

Fig.7 Gain optimization results for ACAH system.

In the Fig.8, (b), (d), (f), and (n) are the HQ specification for SH system. The other specifications in Fig.8 are the HQ specifications for ACAH system. ‘‘Zeta” means the damping ratio of LOES for each mode and the damping ratio of closed loop system for SH system.Generally,‘‘Zeta”is expressed as a symbol‘‘ζ”.So,ζspis the damping ratio of LOES for short period mode indicated in Eq.(8)and ζDRmeans the damping ratio of LOES for dutch roll mode. ‘‘EigLcG1” and ‘‘StbMgG1”correspond to the eigenvalue and gain margin achievable with the FCS, respectively. The optimized FCS satisfies the Level 1 requirements for‘‘EigLcG1”and‘‘StbMgG1”;thus,the stability of the FCS is guaranteed.‘‘EigDpG1”is the damping ratio requirement for the short-period,roll,Dutch-roll mode.Fig.8 shows that the FCS meets the Level 1 requirement for‘‘EigDpG1”. The damping ratio and natural frequency in‘‘EigDpG1” also affect the Level of HQ for ‘‘CosLoG1”(LOES). From the Level 1 HQ result for ‘‘CosLoG1”, it can be judged that the values are appropriate for the system stability and the response characteristics. The tracking performance to the step input is measured by ‘‘EnvTmG1” and‘‘RisTmG1”. The estimated Level of HQs for these specifications are located near the Level 2 HQ area. To enhance the performance associated with ‘‘EnvTmG1” and ‘‘RisTmG1”,the values of damping ratio and the natural frequency for FCS must be raised. However, the scopes of damping ratio and the natural frequency are limited by ‘‘EigDpG1”.Thus, it is judged that the tracking performance of the FCS associated with ‘‘EnvTmG1” and ‘‘RisTmG1” has been maximized.

Fig.8 HQ window of MIL-STD-1797 A and B for ACAH system.

4.2. RCRH system with MFC controller

Fig.9 Block diagram of MFC for RCRH system.36,37

Details of the RCRH system are given in Ref.36,37. The control gains of the RCRH system have been optimized with the HQ specifications of the ACAH system. The results are shown in Table 9. Figs. 10 and 11 are the optimization results of the RCRH system for the standards of MIL-STD-1797 A and B. The RCRH system also meets the Level 1 criteria.

5. Application

A series of simulation studies are carried out for the longitudinal loop, Immelmann-turn, and climb-slalom-descent maneuvers to demonstrate the applicability of the proposed techniques for implementing tactical maneuvers with maneuver libraries. The first two applications intend to show that each of the extremely aggressive maneuvers can be implemented using the method proposed in this paper. The last application is specifically designed to show that tactical maneuvers required for a desired mission can be combined to define the complete trajectory over the whole-mission flight phases and that the mission can be successfully performed by using precise tracking controllers.

Table 9 Optimized gain for RCRH system.

Fig.10 Gain optimization results for RCRH system.

5.1. Longitudinal loop maneuver

Fig.11 HQ window of MIL-STD-1797 A and B for RCRH system.

Table 10 Longitudinal loop maneuver.

Fig.12 Simulation results for the longitudinal loop maneuver.

Fig.13 Loop radius versus

Fig.12 shows the simulated trajectory for the longitudinal loop. Fig.12(a) indicates the flight path for the longitudinal loop, and Fig.12(b) the corresponding flight velocity. Here,the vertical velocity is dramatically increased during the maneuver, which indicates the extremely high AOA operation of the aircraft. Fig.12(c) shows the variations of the angular rates during the maneuver. The pitch rateqis maintained around 40 (°)/s while the other rates show minor changes about 0 (°)/s. These values correspond to the commanded angular rates for each axis and are tracked effectively by the FCS proposed in this paper. This means that the RCRH system has been designed properly and the loop maneuver has been performed as expected.11Fig.12(d) shows the attitude variations.The sudden change in the roll angle φ up to around-180°with the duration of about 5 s indicates that the aircraft enters the upside-down flight phase.Then,the roll is recovered to the normal attitude required to maintain the level flight after the maneuver is finished.The variations in the pitch and heading angles also well represent their expected changes required to complete the loop maneuver.This means that the longitudinal loop maneuver can be successfully carried out with the proposed maneuver libraries and control systems.

5.2. Immelmann-turn maneuver

Fig.14 shows the simulated trajectory for the immelmann turn. Fig.14(a) and (b) present the flight path and velocity computed for the immelmann turn, respectively. The vertical velocity is increased significantly during the loop maneuver phase. The property of the loop maneuver has already been explained in Fig.12. The lateral velocity is dramatically increased in the roll maneuver. Generally, when the roll maneuver starts, the large side force is generated, which increase the lateral velocity. The lateral velocity is thus increased to -10 m/s. Furthermore, the lateral velocity is changed to -20 m/s in the final level flight phase since the directional angular rate is increased to reduce the roll ratep.The pitch rateqin Fig.14(c) remains around 40 (°)/s in the loop phase while the other rates show slight changes around 0 (°)/s. Afterwards, the roll ratepreaches around 60 (°)/s as required for the roll maneuver phase while the corresponding pitch rate recovers to about 0 (°)/s. The large variation in the yaw rateris remarkable during the final recovery phase of the level flight.The attitude angles in Fig.14(d)are changed as expected for the completion of the immelmann turn. As a result,it can be concluded that the immelmann turn maneuver can be successfully performed with the proposed maneuver libraries presented in Table 11 and the corresponding control modes.

5.3. Trajectory tracking maneuver

Fig.15 presents the required and tracked trajectories for the climb-slalom-descent maneuver with the application of the LOS guidance law and MFC controller. Fig.15(b)–(d) shows the trajectories in two-dimensional space for each maneuver phase. The height deviation, as shown in Fig.15(b), varies in the range of around 0.5–2.5 m with the present FCS design.This range is extremely small, considering the transient nature of the climb maneuver.The trajectories for the slalom and descent maneuver phases are more accurately tracked than those for the climb maneuver phase. These results demonstrate that the tactical mission can be planned successfully with the approach proposed.

6. Conclusions

Various techniques to implement complex tactical maneuvers have been proposed and validated in this paper. Based on the specific mission phases required for a typical air-toground mission, the required maneuvers can be classified as different maneuver modes depending on the variations in the altitude and roll angles, and on the existence of the longitudinal/lateral loops during the maneuver. This paper shows that the maneuver libraries required to perform a mission can be built by designating modal inputs for each of the maneuver modes and the corresponding structure of the Flight Control System (FCS). The trajectory is generated with the modal inputs and the relevant trajectory tracking controller designed to satisfy the precision and aggressiveness specifications, realizing the implementation of tactical maneuvers.

Each maneuver trajectory based on modal inputs in the libraries is built with the 7th order polynomial. The trajectory tracking controllers adopt the Model Following Controller(MFC) to provide the required maneuver agility, consisting of the Attitude Command Attitude Hold (ACAH) system,the Rate Command Rate Hold (RCRH) system, and the Line-of-Sight (LOS) guidance law applied to track the desiredtrajectory corresponding to the modal inputs.In particular,the CONDUIT? is used to optimize the gains so that the control systems meet the aircraft Hhandling Qualities (HQ) criteria.Finally, a series of simulation studies have been performed for the longitudinal loop, immelmann -turn, and climbslalom-descent maneuvers to evaluate the effect of the proposed techniques.

Table 12 Flight scenario for trajectory tracking.15

Fig.14 Simulation results for Immelmann-turn maneuver.

The maneuver libraries for the longitudinal loop are composed of the level flight, loop, and level flight. The designed controllers track well the expected variations in the pitch and heading angles. The results show that the longitudinal loop can be successfully performed with the proposed maneuver libraries and control system structures.The second application concerns the immelmann-turn maneuver, including an additional 180° roll-turn maneuver after half of the longitudinal loop. The RCRH modes for the pitch, roll, and yaw channels have been applied to track the commanded pitch,roll,and yaw rates during the loop and roll-turn maneuvers, respectively.These rate controllers also track well the required angular rates, which leads to the successful completion of the immelmann-turn maneuver. Finally, the climb-slalom-descent maneuver is simulated with the proposed techniques. In this application,the complete tactical mission starts from the initial level flight, followed by the climb, slalom, and decent maneuvers,and ending with the prescribed final level flight.To implement this mission flight, the trajectory and the corresponding controller structure for the slalom maneuver are added to the maneuver libraries.The modal inputs for the slalom maneuver could be designated using the desired flight speed and maximum variation in the lateral position of the aircraft. The mission can be successfully simulated with the minor tack error in the altitude during the climb maneuver and with indiscernibly small trajectory deviations at the other maneuver phases. The method in the present paper has no limits in the real-time implementation of trajectory generation and of controller functions; therefore, the results of this study can significantly contribute to the enhancement of mission success and survivability of the manned and unmanned aircraft in complicated battlefields.

Fig.15 Trajectory tracking results for flight scenario in Table 12.

Acknowledgements

This work was conducted at High-Speed Compound Unmanned Rotorcraft (HCUR) research laboratory with the support of Agency for Defense Development (ADD).