Narayan Ananthkrishnan

Level Flight Trim and Stability Analysis Using Extended Bifurcation and Continuation Procedure

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Aircraft Spin Recovery, with and without Thrust Vectoring, Using Nonlinear Dynamic Inversion

The present paper addresses the problem of spin recovery of an aircraft as a nonlinear inverse dynamics problem of determining the control inputs that need to be applied to transfer the aircraft from a spin state to a level trim flight condition. A stable, oscillatory, flat, left spin state is first identified from a standard bifurcation analysis of the aircraft model considered, and this is chosen as the starting point for all recovery attempts. Three different symmetric, level-flight trim states, representative of high, moderate, and low-angle-of-attack trims for the chosen aircraft model, are computed by using an extended-bifurcation-analysis procedure. A standard form of the nonlinear dynamic inversion algorithm is implemented to recover the aircraft from the oscillatory spin state to each of the selected level trims. The required control inputs in each case, obtained by solving the inverse problem, are compared against each other and with the standard recovery procedure for a modern, low-aspect-ratio, fuselage heavy configuration. The spin recovery procedure is seen to be restricted because of limitations in control surface deflections and rates and because of loss of control effectiveness at high angles of attack. In particular, these restrictions adversely affect attempts at recovery directly from high-angle-of-attack oscillatory spins to low-angleof-attack trims using only aerodynamic controls. Further, two different control strategies are examined in an effort to overcome difficulties in spin recovery because of these restrictions. The first strategy uses an indirect, two-step recovery procedure in which the airplane is first recovered to a high- or moderate-angle-of-attack level-flight trim condition, followed by a second step where the airplane is then transitioned to the desired low-angle-of-attack trim. The second strategy involves the use of thrust-vectoring controls in addition to the standard aerodynamic control surfaces to directly recover the aircraft from high-angle-of-attack oscillatory spin to a low-angle-of-attack level-flight trim state. Our studies reveal that both strategies are successful, highlighting the importance of effective thrust management in conjunction with suitable use of all of the aerodynamic control surfaces for spin recovery strategies.

Use of Bifurcation and Continuation Methods for Aircraft Trim and Stability Analysis - A State-of-the-Art

The bifurcation and continuation methodology has evolved over the last two decades into a powerful tool for the analysis of trim and stability problems in aircraft flight dynamics. Over the years, bifurcation methods have been employed to deal with a variety of problems in aircraft dynamics, such as predicting high angle of attack behavior, especially spin, and studying instabilities in rolling maneuvers. The bifurcation methodology has served as a tool for the design of flight control systems, and is promising to be a useful tool in the aircraft design, simulation, testing, and evaluation process. In the present paper, we describe the state-of-the-art in the use of bifurcation and continuation methods for the analysis of aircraft trim and stability with a few illustrative examples. Both the standard and extended bifurcation analysis procedures are discussed and typical results for instabilities in high-α flight and in inertia-coupled roll maneuvers are shown. This is followed by several problems in nonlinear flight dynamics where bifurcation and continuation methods have been fruitfully applied to yield effective solutions. Finally, the use of bifurcation theory to arrive at analytical instability criteria is demonstrated for the aircraft roll coupling and wing rock problems. 76 references have been cited in the text.

Analytical Criterion for Aircraft Spin Susceptibility

from the point of view of bifurcation theory. Two versions of an analytical criterion for predicting spin susceptibility are derived and their use is described. The rst version requires plotting the zero crossings of a simple algebraic equation in angle of attack, while the second involves plotting the locus of zeros of a single algebraic equation in two variables (angle of attack and yaw rate) { both equally quick and easy to use. Both versions of the criterion are tested with data for the F-18 HARV aircraft and they show an excellent match with spin prediction from exact numerical computations.

Effect of Thrust Vectoring on Aircraft Post - Stall Trims, Stability, and Maneuvers

High performance airplanes require maneuvering at high rates and under conditions of high incidence where the dynamics can be extremely nonlinear and is often accompanied by control input saturation, thereby limiting the igh t envelope. In recent times, the urge to expand the igh t envelope, beyond that achievable using aerodynamic control surfaces, has been addressed using thrust vectoring due to its superior characteristics at high angles of attack. In this paper, eectiv eness of thrust vectoring as a control input has been discussed in detail. Improvement in the post-stall angle of attack capture using thrust vectoring on saturation of aerodynamic controls has been demonstrated by extended bifurcation analysis. Furthermore, the eect of control input saturation on stability of closed-loop airplane dynamics has been illustrated. Key maneuvers, such as turns, have been analyzed in detail to demonstrate eectiv eness of closed-loop in stabilizing otherwise unstable openloop turn trims. Instantaneous turn maneuver has been remodeled to incorporate realistic eects of throttle saturation and negative specic excess power on maximum achievable turn rate. Improvement in the instantaneous turn rate with thrust vectoring is qualied and quantied. Finally, using thrust vectoring, controlled departure and subsequent recovery to level igh t is simulated for igh t instabilities as pitch bucking and oscillatory spin.

A Simple, Correct Pedagogical Presentation of Airplane Longitudinal Dynamics

Various shortcomings and inaccuracies in the existing approach and presentation of airplane flight dynamics in pedagogy have been identified. An improved pedagogical presentation is offered which is clean – uses the two timescales in longitudinal dynamics to derive short period and phugoid mode parameters, simple – starts with the longitudinal dynamics equations rather than the complete six degree of freedom formulation, and correct – uses a physically correct model of the dynamic (rate) derivatives and employs the concept of a static residual in deriving the slower (phugoid) mode approximations. The redundant and confusing concepts of dimensional derivatives and static stability are junked. A companion paper presents a similar approach to the lateral-directional dynamics.

A Simple, Correct Pedagogical Presentation of Airplane Lateral-Directional Dynamics

Various shortcomings and inaccuracies in the existing approach and presentation of airplane flight dynamics in pedagogy have been identified. An improved pedagogical presentation is offered which is simple – uses the different timescales in lateral-directional dynamics to cleanly derive roll, dutch roll, and spiral mode parameters, more acceptable – starts with the lateral-directional dynamics equations rather than the complete six degree of freedom formulation, and correct – uses a physically correct model of the dynamic (rate) derivatives and employs the concept of a static residual. The redundant and confusing concepts of dimensional derivatives and static stability are junked following a companion paper using a similar approach to the longitudinal dynamics.

The Bifurcation and Continuation Method from an Aerospace Systems Design Point of View

The purpose of this paper is to evaluate the strengths and weaknesses of the bifurcation and continuation method from the standpoint of aircraft design, and suggest ways to integrate it with the design cycle. The unique analytical and computational capabilities of this method are reviewed as the rst step in this evaluation. Next, we review its evolution and, in particular, some speci c problems where this method has been fruitfully employed. Applications to control design are particularly emphasised in this paper. We brie y review the preliminary design stage of an aircraft, and suggest approaches which will aid the integration of bifurcation methods into this stage.

Adaptive Control of a Combustion Acoustics Model with Input Saturation Using Control Hedging

The presence of acoustics in combustion chambers is a major but unavoidable irritant. A positive coupling between the acoustics field and the heat release source leads to thermoacoustic instability, manifested with severe pressure oscillations. An effort has been made to suppress the limit cycle oscillations using an adaptive feedback linearisation scheme. However, the problem is made difficult by the fact that the control effort required is normally not available due to actuator saturation limits. In this paper, a technique known as control hedging is used to combat the effect of input saturation on the system dynamics. Also, an observer has been used to estimate the unmeasured states and a band-limited differentiator is used to estimate the acoustic velocity. Simulation results have been obtained to observe the effect of variation in the parameters of higher modes of the instability model, and unmodeled dynamics.

Automated gain scheduling using continuation techniques

Abstract Use of a continuation technique to automate the computation of gain schedules for a flight control application is demonstrated. An interesting feature of this approach is that the computation of gain schedules and that of the equilibrium points over which the gains are to be scheduled are carried out simultaneously. The technique is illustrated with a stability augmentation system for an aircraft using data for the F-18/HARV open-loop dynamics available in the literature.