Doctor of Philosophy (PhD)
Electrical and Computer Engineering
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Aircraft technology has undergone momentous improvements over the decades due to the growing demand and competition among industries. The performance requirement and stability of fighter aircraft is a major factor due to the ever-increasing flight envelope. Advanced fighter aircraft are expected to be highly maneuverable. To achieve extreme maneuverability a very good aircraft design with multiple redundant control actuators having static instabilities in certain modes, near accurate nonlinear aircraft mathematical model, and suitable nonlinear control design technique is required. Conventionally, training aircrafts such as Cessna and Piper aircraft are built for static and dynamic stability, making them easy to trim and fly hands-off. However, this hinders the ability of extreme maneuvers. Modern fighter aircraft like F/A-18s are built to be unstable and require Fly-by-wire system for flying, enabling them to be highly maneuverable and easy to aggressively pitch, roll and yaw.
Thrust vectoring method by directing engine exhaust flow coupled with advanced flight control systems provides a very high angle of attack which provides superior close-in air dogfight capabilities in air combats. The result of enhanced maneuverability in a fighter provides a very significant upper hand over the conventional fighter aircraft. A good example is the Rockwell-MBB X-31 test aircraft designed for super maneuverability. Two experimental X-31 jet fighters designed to test fighter 3D thrust vectoring technology flown by NASA successfully demonstrated the envisioned concept. Lockheed Martin F-22 Raptor makes use of thrust vectored control to achieve extreme maneuvers. Considering sea change in technologies of aircraft design and survivability requirements designing the control schemes pose a huge challenge for flight control designers.
Traditionally, aircraft flight controllers are designed by linearizing non-linear aircraft models at a large number of operating points, and then gain scheduling is used to cover the entire flight envelope. But the gain scheduling is a comparatively difficult task to achieve in a large flight envelope. Various design methods, such as pole placement, H-infinity robust control, optimal control, etc., have been used for flight control of linear aircraft models in the past. But the equations of motion of aircraft include nonlinear aerodynamic forces and moments. Also, at a high angle of attack, the aerodynamic forces and moments depend on the history of the flow. When aircraft perform high roll rate maneuvers, mainly two precarious situations are encountered, first one is an instability of the short-period longitudinal and directional oscillations and the second is auto-rotational rolling, in which the fighter can suddenly jump to a higher roll-rate, where, additionally, controls can become inefficient. All these phenomena can lead to a high angle of attack or sideslip, causing unusual loading on the structure leading to accidents.
Shortcomings of linear controllers can be overcome by performing input-output linearization (also termed as nonlinear dynamic inversion (NDI)). This method decouples the dynamics of selected controlled output variables by canceling known nonlinear functions of the model, and then linear stable tracking error dynamics are obtained by the feedback of additional signals. Obviously, for exact cancellation, the dynamics of aircraft must be known precisely. This transforms the nonlinear system into a constant linear system provided all nonlinearities to be precisely known. However, it's an extremely difficult feat to achieve considering complex nonlinear aerodynamic characteristics of the modern aircraft. Wind tunnel experiments and flight tests with computational fluid dynamics results are used to obtain empirical data, which are not perfectly accurate. These shortcomings are attenuated by feedback control with a robust linear controller. Despite that desired performance cannot be guaranteed hen sudden change in aerodynamics resulting from structural damage, control effector failures or adverse environmental conditions.
Variable structure controllers (VSC) have been designed for nonlinear aircraft models in the presence of uncertainties. However, VSC controllers are discontinuous functions of state variables. Even though some smoothing of control law can be done in the boundary layer, it might cause terminal tracking error.
Nonlinear adaptive flight controllers based on the back-stepping control method have been designed for large parametric uncertainties and unknown functions in the model. The back-stepping design method is completed in several steps because this method is iterative in nature. The number of steps required depends on the relative degree of the controlled output variables. Also, neural networks (NN) based flight control systems have been designed. In the recent past, adaptive flight controller design with state and control constraints has been attempted. These adaptive flight controllers belong to the class of certainty-equivalence adaptive control systems. In these controllers, the parameter estimates obtained by integral update law are directly used. Non-certainty-equivalence adaptive control systems based on immersion and invariance (I\&I) method for control of aircraft. From the viewpoint of implementation, adaptive control laws are not elementary because the parameter estimator needs to estimate a large number of aerodynamic parameters. Also, Considerable effort has been made in the past to analyze the stability property of fighter aircraft. The analysis shows rich dynamical behavior in rotationally-coupled maneuvers of aircraft, including linear and aerodynamic nonlinearities. Based on the bifurcation method and pseudo-steady-state analysis, authors have observed that roll-coupling can lead to undesirable jump phenomenon and rapid divergence of sideslip angle in the transient phase for certain combinations of control surface deflections. Bifurcation theory, invented by Poincare to analyze nonlinear systems, was first applied to the cross-coupling problem and then extended to the fully nonlinear problem of flight at a high angle of attack.
The adaptive flight controllers cited in the section can achieve only asymptotic stability. Researchers have also developed finite-time stabilizing controllers for a class of nonlinear systems. This class of controllers has stronger robustness properties, compared to asymptotically stabilizing control systems. Some research related to finite-time flight control systems has also appeared. It is imperative to explore the applicability of finite-time control methodologies for simultaneous longitudinal and lateral maneuvers and for avoiding roll-coupled instabilities of fighter aircraft in the presence of uncertainties.
The main goal of this thesis is to investigate the potential of the Robust Finite-time control technique in combination with sliding mode control and super-twisting flight control for a modern fighter aircraft. The following contributions are presented:
• a finite time stabilizing (FTS) nonlinear flight control law for a nominal aircraft model with assumed parameters, based on the notion of geometric homogeneity, is designed.
• a discontinuous sliding mode (DSM) flight controller is developed to counter the effect of uncertainties in the model. In the closed-loop system, including the nominal finite time stabilizing (FTS) control law and the discontinuous sliding mode (DSM) control signal, finite-time control of the roll angle, pitch angle, and sideslip angle is accomplished. A DSM control law might cause a control chattering phenomenon.
• for robust control, a super-twisting (STW) sliding mode control law is designed. The STW control law is a continuous function of the state variables. In the closed-loop system, using the FTS and STW control laws, finite-time control of the aircraft is accomplished. Furthermore, this composite control system has the ability to attenuate undesirable control chattering. It is shown that in a closed-loop system, including the composite control law ((i) FTS with DSM, or (ii) FTS with STW control signals), the trajectory tracking error and its first derivative converge to zero in finite time.
• using similar steps, composite control systems (FTS with DSM and FTS with STW laws) for finite-time control of the roll angle, angle of attack, and sideslip angle are designed.
• simulation results for a nonlinear swept-wing fighter aircraft are obtained, which show that the designed composite controllers accomplish satisfactory simultaneous longitudinal and lateral maneuvers of (Roll, pitch, sideslip) or (Roll, Angle of attack, sideslip), despite parametric uncertainties. It is pointed out that the structure of the derived flight controllers is simple compared to adaptive control laws, in which a large number of aerodynamic parameters must be estimated.
Finite-time stabilization (FTS) as a concept was first introduced in the 1950's for the systems with limited operation for a fixed finite interval of time. It requires prescribed bounds on system variable, which is not required for defining classical stability. The nonlinear differential equation of dynamical systems such as fighter aircraft requires fast, accurate, and continuous finite-time controllers. These control schemes are superior to classical control design. First, the structure of a phase portrait for scalar second-order finite-time systems is determined. Then, this characterization is used to develop a class of second-order finite-time systems which are used as controllers. Sliding mode control (SMC) is a nonlinear control method that alters the dynamics of a nonlinear system by application of a discontinuous control signal that forces the system to "slide" along a cross-section of the system's normal behavior. The state-feedback control law is not a continuous function of time. Instead, it can switch from one continuous structure to another based on the current position in the state space.
Super-twisting Control (STW) is a robust continuous flight control scheme which is exactly a PI-controller (with the P-part modulation) with respect to the sign(x)-term. Super twisting control (STW) scheme is applied to dynamic system control to attenuate chattering produced in the control input due to the discontinuous sliding mode control.
Continuous Finite Fixed Time Control (FFTC) is a direct extension of conventional super-twisting control. It estimates a fixed time upper bound and convergence time. Designing a fixed-time continuous control law such that a system state converges to the origin for a pre-defined or fixed time is a challenging problem.
The formation control concept is based on observation of the natural flight behavior of birds that maintain a defined geometrical shape. Migratory birds use upwash provided by lead and rotate lead positions to increase the range of travel with the least individual efforts. This pattern can be used for large by range communication flights or surveillance drones or in a situation of optimum fuel consumption. Various researchers have worked on the formation control of two or more aircraft flight control.
Finite Time Control; Formation Control; Nonlinear Control System; Sliding Mode Control; Supertwisting Control; Unmanned Aerial Vehicle
Electrical and Computer Engineering
University of Nevada, Las Vegas
Raj, Kaushik, "Fighter Aircraft Guidance and Control" (2020). UNLV Theses, Dissertations, Professional Papers, and Capstones. 4073.
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