William L. Garrard

Nonlinear inversion flight control for a supermaneuverable aircraft

Nonlinear dynamic inversion affords the control system designer a straightforward means of deriving control laws for nonlinear systems. The control inputs are used to cancel unwanted terms in the equations of motion using negative feedback of these terms. In this paper, we discuss the use of nonlinear dynamic inversion in the design of a flight control system for a Supermaneuvera ble aircraft. First, the dynamics to be controlled are separated into fast and slow variables. The fast variables are the three angular rates and the slow variables are the angle of attack, sideslip angle, and bank angle. A dynamic inversion control law is designed for the fast variables using the aerodynamic control surfaces and thrust vectoring control as inputs. Next, dynamic inversion is applied to the control of the slow states using commands for the fast states as inputs. The dynamic inversion system was compared with a more conventional, gain-scheduled system and was shown to yield better performance in terms of lateral acceleration, sideslip, and control deflections.

Paper: Design of nonlinear automatic flight control systems

A method for the synthesis of nonlinear automatic flight control systems is developed, and the performance of a control system synthesized by use of this method is compared to the performance of control system designed by use of linear quadratic optimal control theory. Comparisons are made on the basis of aircraft dynamic response at high angles of attack. It is found that the nonlinear controller reduces the altitude loss during stall and increases the magnitude of the angle of attack for which the aircraft can recover from stall.

Flight control design using robust dynamic inversion and time-scale separation

This paper presents a new method for design of flight controllers for aircraft: feedback linearization coupled with structured singular value (μ) synthesis. Feedback linearization uses natural time-scale separation between fast and slow variables. The linear μ controller enhances robustness to parameter variations and requires no scheduling with flight condition. This methodology is applied to an angle-of-attack command system for longitudinal control of a high performance aircraft. Nonlinear simulations demonstrate that the controller satisfies handling quality requirements, provides good tracking of pilot inputs, and exhibits excellent robustness over a wide range of angles-of-attack and Mach numbers.

Robust Dynamic Inversion for Control of Highly Maneuverable Aircraft

This paper presents a methodology for the design of flight controllers for aircraft operating over large ranges of angle of attack. The methodology is a combination of dynamic inversion and structured singular value (p) synthesis. An inner-loop controller, designed by dynamic inversion, is used to linearize the aircraft dynamics. This inner-loop controller lacks guaranteed robustness to uncertainties in the system model and the measurements; therefore, a robust, linear outer-loop controller is designed using /i synthesis. This controller minimizes the weighted HQO norm of the error between the aircraft response and the specified handling quality model while maximizing robustness to model uncertainties and sensor noise. The methodology is applied to the design of a pitch rate command system for longitudinal control of a high-performance aircraft. Nonlinear simulations demonstrate that the controller satisfies handling quality requirements, provides good tracking of pilot inputs, and exhibits excellent robustness over a wide range of angles of attack and Mach number. The linear controller requires no scheduling with flight conditions. HE objective of this paper is to present a method for design of flight controllers that provides desired handling qualities over a wide range of flight conditions with minimal scheduling. Acceptable stability and performance robustness must be maintained in the presence of unmodeled dynamics, uncertainties in the aircraft design model, and noisy sensor measurements. The aircraft considered in this paper is the NASA high angle-ofattack research vehicle (HARV), which is typical of future fighter aircraft. It is capable of flight at very high angles of attack and has thrust vectoring as well as conventional aerodynamic control surfaces.1 The unaugmented aircraft does not meet handling quality requirements and some type of augmentation is necessary. This paper considers only the longitudinal control. The controller relates pilot longitudinal stick input to the symmetric deflection of the stabilizer and the longitudinal deflection of the thrust vectoring vanes. The control design philosophy is to use an inner-loop, dynamic inversion controller and an outer-loop, linear \JL controller. The dynamic inversion controller linearizes the pitch rate dynamics of the aircraft; however, since model uncertainties prevent exact linearization, there will always be errors associated with this controller. A simple linear fractional transformation model of these errors is developed for use in design of the outer-loop /^ controller. This controller provides pitch rate following by minimizing the weighted //oo-norm of the difference between the actual aircraft pitch rate response to pilot stick inputs and the desired response to these inputs as given by a transfer function model based on standard handling quality specifications. Thus the outer-loop \Ji controller is an implicit model following design, which provides robustness to errors due to the lack of exact cancellation of the pitch rate dynamics by the dynamic inversion controller. Recently a number of papers have appeared that describe controllers for a highly maneuverable aircraft. In Refs. 2-5, application of linear multi-input/multi-output (MIMO) control design techniques to this problem were presented. In every case, excellent

Model predictive control of transitional maneuvers for adaptive cruise control vehicles

In this paper, model predictive control (MPC) is used to compute the spacing-control laws for transitional maneuvers (TMs) of vehicles equipped with adaptive cruise control (ACC) systems. A TM is required, for example, to establish a steady-state following distance behind a newly encountered vehicle traveling with a slower velocity. These spacing-control laws are computed by formulating the objective of a TM as an optimal control problem (OCP). The steady-state following distance, collision avoidance, and acceleration limits of the ACC vehicle are incorporated into the OCP as constraints. The spacing-control laws are then obtained by solving this constrained OCP by using a receding-horizon approach, where the acceleration command computed at each sampling instant is a function of the current measurements of range and range rate. A baseline scenario requiring a TM is used to evaluate and compare the performance of the MPC algorithm and the standard constant time gap (CTG) algorithm. The simulation results show that the ACC vehicle is able to perform the TM of the baseline scenario using the MPC spacing-control laws, whereas the ACC vehicle is unable to perform this TM using the CTG spacing-control laws. The success of the MPC spacing-control laws is shown to depend on whether collision avoidance and the acceleration limits of the ACC vehicle are explicitly incorporated into the formulation of the control algorithm.

An Approach to Sub-optimal Feedback Control of Non-linear Systems

ABSTRACT A method is developed for the determination of sub-optimal control laws for non-linear dynamical systems. The control laws determined by the use of this method are in time invariant, feedback form and approximately minimize a performance index which is the integral of a positive definite function of the state plus a quadratic function of the control. The basis of the proposed technique is a method for the determination of approximate solutions for the associated Hamilton-Jacobi-Bellman equation. The method is applied to two examples and the results are shown to compare favourably with those obtained by use of other sub-optimal control procedures. The method developed in this paper is applicable, in a practical sense, to systems of higher than second order and seems to hold promise as a means for solving a large class of optimization problems.

Parameter Varying Control of a High-Performance Aircraft

Thedynamicresponsecharacteristicsofmodern aircraftvary substantially withe ightconditions.Thesechanges require scheduling of the e ight control system with variables such as dynamic pressure and Mach number. This scheduling can be accomplished easily for simple controllers but is much more dife cult for complex controllers, which result from the use of most modern control design techniques. On the other hand, these complex controllers can yield signie cant performance improvements when compared with simple controllers. Recently, linear parameter varying (LPV) techniques have been developed that provide a natural method for scheduling H1 based controllers. LPV techniques are combined with π synthesis methods to develop a self-scheduled longitudinal controller for a high-performance aircraft. The ability of this controller to achieve specie ed handling qualities over a wide range of e ight conditions is demonstrated by nonlinear simulations. I. Introduction M ODERNhigh-performanceaircraftoperateoverawiderange of e ight conditions. This results in dynamic response characteristics that vary substantially during a typical mission. Traditionally, e ight control systems were designed by using mathematical models of the aircraft linearized at various e ight conditions. Relatively simple e xed-structure control laws were formulated and gainswereselectedforeache ightconditionbyusingclassic,singleinput, single-output methods. Because the structure of these control laws was simple, only a few gains needed to be scheduled and, therefore, scheduling was fairly easy. As aircraft have become more complex with a variety of control effectors and sensors and as performance capabilities and requirements have increased, traditional methods for controller design often have not yielded acceptable performance. Thus, the use of various modern multiinput, multioutput techniques for e ight controller design has been extensively studied. These techniques use linearized models of the aircraft dynamics but result in controllers that are much more complex and that use many more gains than those designed by classic methods. Consequently,itismuchmoredife culttoschedulecontrollersdesigned by modern techniques,andthishasbeen amajorimpediment in the use of these theories in the design of e ight control systems. Recently, a number of investigators have proposed the use of dynamic inversion together with π synthesis methods for the design of aircraft e ight control systems. 1i4 Dynamic inversion avoids the scheduling problem by using feedback to cancel the dynamics of the aircraft. Desired dynamics are then substituted for the canceled dynamics. Some promising preliminary results have been obtained by using dynamic inversion but there are some important implementation issues that may inhibit the use of this method in practice. In this paper, we describe the application of an extended H1 technique to the design of a self-scheduled controller for the longitudinal control of a high-performance aircraft. This technique is based on linear parameter varying (LPV) techniques, which result in a controller that is scheduled with dynamic pressure. The closedloop, LPV control structure can be represented as shown in Fig. 1.

Design of Attitude and Rate Command Systems for Helicopters Using Eigenstructure Assignment

This paper describes the use of eigenstructur e assignment in the direct design of attitude and attitude rate command systems for helicopter flight control. Eigenvalue assignment is used to achieve desired bandwidth based on the handling qualities specifications, and eigenvector assignment is used to achieve decoupling of lateral, longitudinal, heave, and yaw modes and the desired command-response characteristics. Eigenstructure techniques are also used to design a state estimator that gives desired closed-loop frequency response. The stability robustness of the control system is evaluated with respect to an error model that includes rotor, actuator, flexure, and sensor dynamics and computational and sampling delays in the flight control system. The controlled helicopter is shown to exhibit both good frequency and time-response characteristics. Nomenclature Scalars g = acceleration of gravity m = number of controls n = number of states p — roll rate, rad/s q — pitch rate, rad/s

Nonlinear feedback control of highly manoeuvrable aircraft

Abstract This paper describes the application of nonlinear quadratic regulator (NLQR) theory to the design of control laws for a typical high-performance aircraft. The NLQR controller design is performed using truncated solutions of the Hamil-ton-Jacobi-Bellman equation of optimal control theory. The performance of the NLQR controller is compared with the performance of a conventional P+I gain scheduled controller designed by applying standard frequency response techniques to the equations of motion of the aircraft linearized at various angles of attack. Both techniques result in control laws which are very similar in structure to one another and which yield similar performance. The results of applying both control laws to a high-g vertical turn are illustrated by nonlinear simulation.

Control Law Synthesis for Flutter Suppression Using Linear Quadratic Gaussian Theory

This paper describes the application of linear quadratic Gaussian (LQG) methodology to the design of active control systems for suppression of aerodynamic flutter. A wind tunnel model of a research wing with associated sensors and actuators comprises the system to be controlled. Results of a synthesis methodology that provide small values of rms response and robust stability are presented. Results of control surface and sensor position optimization are also presented. Both frequency response matching and modal residualization are used to obtain practical flutter controllers. Scalars b c E( ) h (x,y,t) J km /_ q s t u V w x,y