Flight control law design for fighter aircraftsexploiting nonlinear control techniques

Abstract

Fighter aircrafts are military aircrafts that are designed to conduct mainly air-to-air missions which require high agility and maneuverability. The high agility and maneuverability are provided by a suitable aerodynamic design and a fly-by-wire flight control system that augments the stability and control characteristics and improves the handling characteristics of the airframe such that the pilot workload for flying the aircraft is minimized. The measure of pilot workload and handling qualities are determined based on quantitative flying and handling quality metrics that are provided in various military standards. These metrics sort of guide a flight control law design to achieve predicted Level 1 handling qualities, therefore flight control law design is based upon these criteria in order to achieve minimal pilot workload. However, satisfying solely handling quality metrics is not sufficient by itself in order to meet airworthiness which requires satisfaction of additional requirements that are related to stability robustness of the flight control loop which are essential for the safety of flight. There are various flight control law approaches utilized in the industry for fighter aircrafts. The first production fly-by-wire fighter aircraft F-16 utilizes classical linear control laws which use pitch rate and angle of attack as feedback variables for the pitch axis. And it uses stability axis roll and yaw rate along with lateral acceleration feedback for the lateral-directional axes. In addition to the linear control law, a nonlinear prefilter called the dual lag filter is used in the roll axis for improved handling qualities. The use of nonlinear components falls back to as early as the first production fly-by-wire fighter aircraft in the 1970's. The Swedish fighter aircraft JAS-39 that conducted its first flight in 1988 also utilizes nonlinear filters in its flight control law to complement its linear control laws. The nonlinear filter that is used in this aircraft is called phase compensating rate limiter and it is used to recover the sudden phase loss that is experienced once the nonlinear control surface rate saturation occurs. The sudden phase loss during control surface rate saturation increases the effective delay of the loop which can cause instability and result in a catastrophic event as experienced with JAS-39. The nonlinear phase compensating rate limiter had solved this issue for this fighter aircraft. EF-2000 developed during the late 1990's and early 2000's has utilized a linear differential PI algorithm along with nonlinear control laws to cope with nonlinear dynamics which cannot be attenuated with linear control laws. The nonlinear control law was composed of a partial dynamic inversion that cancels specific adverse nonlinear dynamics that the linear control law cannot satisfactorily mitigate. Moreover, the state-of-art F-35 utilizes a flight control law that is based on nonlinear dynamic inversion. This solution theoretically allows one to replace the aircraft's dynamics with the desired dynamics however requires highly complex aerodynamic and inertial database of the aircraft in its flight control computer and its performance highly depends on the fidelity of the model implemented in its flight control computer. In this thesis, nonlinear control techniques applied in various industrial flight control law applications are gathered under one application and exploited during the flight control law design of a fighter aircraft for improved flying and handling qualities. A linear flight control law design is conducted based on a multi-stage optimization scheme that is inspired from industrial optimization toolboxes. The dual lag filter of the F-16 and the phase compensating rate limiter used in JAS-39 are re-evaluated and included in the linear design and analysis activities using describing function techniques. The partial dynamic inversion approach method used in EF-2000 are added to the flight control law such that the nonlinear dynamics that cannot be captured during the linearization are compensated using these terms while not altering the linear design. In the first chapter, a brief review of flight control laws used in the industry for several fighter aircrafts are explained. The nonlinear components used in these fighter aircrafts are highlighted and explained for their reasonings. In the second chapter, the derivations of the equations of motion of an aircraft used in the nonlinear six-degree of freedom aircraft simulation model are explained. The common axis types used for the depiction of the aircraft motion are given and dynamic equations for the translational and rotational motion of an aircraft are derived using the transport theorem and Newton's second law. Moreover, Euler's kinematic equation that relate body axis angular rates to Euler angle rates are depicted. The aerodynamic model of the subject fighter aircraft retrieved from NASA Langley wind tunnel tests are provided. The mass and inertial properties of the subject aircraft are given. The environmental model used for the calculation of air density, dynamic pressure and equivalent airspeed is explained. The third order actuator models for each control surface of the subject aircraft with their rate and position saturation values retrieved from the literature along with latencies and noise filters for each control variable are provided. In the third and fourth chapters, trim and linearization of the nonlinear simulation model are explained and stability and control analysis of the bare airframe is conducted using the aerodynamic database and linear aircraft models. Static lateral and longitudinal stability derivatives are inspected with respect to angle of attack for various sideslip angles with leading edge flap and aileron to rudder interconnect gain schedule to determine the maximum safe angle of attack that the aircraft can reach without loss of control or departure. For this, commonly used metrics LCDP, 〖C_n〗_(β,dyn) and deep stall angle of attack are investigated and the smallest angle of attack from these metrics determined the maximum safe angle of attack. After that, rigid body mode natural frequencies and damping ratios of the lateral and longitudinal axes are inspected with respect to equivalent airspeed and altitude to determine linear control law design points. In the fifth chapter, design requirements used in the flight control law design and analysis activities to measure the FHQ level and stability robustness of the closed loop aircraft are explained. The design requirements consist of single loop requirements such as gain and phase margin that are expected to be met according to military standards along with μ analysis of simultaneous broken loop transfer matrices for a more comprehensive stability robustness assessment. The FHQ criteria mostly consist of the military standards, Gibson criteria with an additional criterion to address PIO II issue. In the sixth chapter, the multi-objective optimization scheme used in the design of linear control laws is explained. The multi-objective optimization used in this thesis is mostly inspired from CONDUIT and has multiple stages wherein a certain set of requirements are met. The requirement sets are met in the order of importance regarding the safety of flight. So, in the first stage linear controller parameters are optimized until all of the stability related requirements are met. As soon as stability requirements are satisfied the second stage of the optimization starts wherein FHQ and PIO requirements are met by optimizing the controller parameters. In the following stages, a sum objective is minimized while preserving the feasibility of the earlier results by defining the prior objectives as the constraint function. This way an optimal solution according to the defined objective function can be obtained. A min-max strategy is utilized such that the maximum of the objective functions belonging to the requirement set is used in the optimization process. This way satisfaction of all of the objectives in the requirement set is guaranteed and computational cost is reduced. Each objective function for the requirements is normalized such that an objective score of one corresponds to the Level 1 of its related requirement. This way an objective score of one correspond to the Level 1 value of any requirement normalizing all of the requirements. In the seventh chapter, nonlinear control elements that are composed of nonlinear control laws and nonlinear filters are explained. Inertial coupling phenomenon is experienced under conditions with high angular rates such as loaded roll or high angle of attack maneuvering which can cause loss of control and departure of the aircraft. Linear controller can lack the performance to suppress this and thereby nonlinear control techniques are utilized. The derivation of the nonlinear control law that cancels the inertial coupling terms of the nonlinear aircraft dynamics is conducted performing a partial dynamic inversion. This way only the terms that cause the inertial coupling phenomenon are cancelled leaving the remaining terms to be handled with the linear control laws. In addition, a nonlinear control law that generate the required yaw acceleration to cancel out the gravitational acceleration terms that cause sideslip angle build up is derived. This way additional sideslip angle suppression is attained. Moreover, a nonlinear filter called the dual lag that is used as a prefilter for the roll axis and provides a smooth roll in and abrupt roll out motion for improved roll handling is analyzed using describing function methods. The parameters of this filter are chosen based on an agility metrics study. Also, phase compensating rate limiters for each primary control surfaces are determined and the behavior of a phase compensating rate limiter is explained in the frequency domain using again the describing function method. In the eighth chapter, the linear control law designs for the longitudinal axis are explained. Two distinct control laws are designed with one of them commanding normal acceleration and the other one commanding pitch rate. A stability and control augmentation system (SCAS) that is composed into feedforward and feedback paths is employed. The feedforward path consists of a prefilter that is used to replace or sort of mask the T_(θ_2 ) of the airframe and replace it with a desired T_(θ_(2,des) ) such that the desired FHQ is achieved. The feedforward component places a zero on the forward path such that the integral pole is cancelled and closed loop response resembles that of a classical second order pitch rate response that is important for satisfactory FHQ. Control variable modifications on both normal acceleration and pitch rate are done such that the kinematic coupling between the longitudinal and lateral axes are minimized aiming to achieve a smoother and low order response for each axis that does not alter one another. Objective functions for each optimization stage are tabulated and optimization results are given along with stability and FHQ analysis results. In the ninth chapter, the linear control law design for the lateral axis is explained. A stability and control augmentation system (SCAS) with stability axis roll rate as the command variable is employed as the flight control law. An approximated sideslip angle rate without the use of sideslip angle information is used in the directional axis instead of a stability axis yaw rate for improved sideslip suppression along with Dutch-roll damping augmentation. In addition, a lateral acceleration feedback, that is an alternative to sideslip angle feedback is used in the directional axis for Dutch-roll frequency augmentation and sideslip suppression. An aileron to rudder interconnect is used to minimize sideslip angle build up due to the kinematic relation between angle of attack and sideslip angle. The design of the aileron to rudder interconnect for sideslip minimization and the choice of the location of the sensed lateral acceleration are deeply explained. Again, objective functions for each optimization stage are tabulated and optimization results along with stability and FHQ analysis results are provided. In the tenth chapter, various flight maneuvers are conducted via nonlinear simulations to assess the behavior of the aircraft with both linear and nonlinear control laws. Aileron roll, barrel roll, Herbst J and pull-up push-over maneuvers are conducted to compare the performance of the nonlinear control laws and showcase the improvements with control variable modifications and nonlinear filters. In the last chapter, the study is summarized, analysis results are evaluated and future studies are discussed.