Nandan Kumar Sinha

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

3Hollkamp, J. J., “Multimodal Passive Vibration Suppressionwith Piezoelectrics,” AIAA Paper 93-1683, 1993. 4Hollkamp, J. J., and Starchville, T. F., “A Self-Tuning Piezoelectric Vibration Absorber,” Journal of Intelligent Materials Systems and Structures, Vol. 5, No. 4, 1994, pp. 559–566. 5Rew, K.-H., Han, J. H., and Lee, I., “Adaptive Multimodal Vibration Control of Winglike Composite Structure Using Adaptive Positive Position Feedback,” AIAA Paper 2000-1422, 2000.

Aircraft Maneuver Design Using Bifurcation Analysis and Sliding Mode Control Techniques

In this paper, bifurcation analysis-based methodology is used in conjunction with a sliding-mode-based control algorithm to construct and simulate maneuvers for a nonlinear, 6 degree-of-freedom, F-18 high-alpha research vehicle aircraft model. Three different types of maneuvers, namely, a minimum-radius level turn, velocity vector roll, and spin recovery to a level flight condition, are attempted to demonstrate the usefulness of the proposed approach. The procedure involves constructing the desired maneuvers using constrained bifurcation analysis-based methodology. The results obtained from bifurcation analysis provide the reference inputs for the sliding mode controller to switch the aircraft between desired flight conditions. Robustness of the sliding mode controller is also examined by introducing uncertainties in aerodynamic parameters. Closed-loop simulation results are later presented to show the effectiveness of the proposed technique.

Aircraft Spin Recovery Using a Sliding-Mode Controller

S PIN is an autorotational state of aircraft at high angles of attack characterized by large rotation rate in yaw when compared with rates in roll and pitch. In a typical spin, an aircraft rotates about its center of gravity and an axis perpendicular to Earth descending vertically at high speed following a downward corkscrew path [1]. It is one of themost dangerous phenomena encountered bymany of the modern fighter aircraft required to fly in high-angle-of-attack flight regimes. Improper functioning of aerodynamic control surfaces during spin makes it difficult for the pilot to control the aircraft, leading to many a problem, such as spatial disorientation and uncontrolled motion, resulting in fatal accidents and subsequent loss of aircraft. Spin states for many high-angle-of-attack aircraft models have been computed by using bifurcation analysis and continuation technique methodology. Bifurcation analysis results provide the onset points of bifurcations or the critical values of control surface deflections that may inadvertently or voluntarily land an aircraft into spin. Standard control inputs using proper deflection of rudder to control yaw rate with simultaneous application of elevator to reduce the angle of attack have been recommended for spin recovery [1]. Design of new-generation fighter aircraft with new configurations, however, cannot rely on standard piloting strategies. Instead, a uniform approach to design aircraft-model-based recovery strategies is called for. An introduction to spin problem and needs to design nonlinear controllers to recover aircraft from spin has been reported recently in [2]. Identifying spin and level-trim states from a bifurcation analysis of a nonlinear aircraft model, Raghavendra et al. [2] developed a nonlinear dynamic inversion (NDI)-techniquebased spin-recovery controller. NDI-technique-based methods have emerged as popular control design techniques in aircraft flight dynamics. Controllers based on the NDI techniques, however, come with certain associated disadvantages, such as separation of dynamics based on timescales, resulting in complicated control architecture, lack of robustness due to external uncertainties and unmodeled plant dynamics, and inability to achieve control saturation limits [3]. In this Note, we present a sliding-mode (SM) controller based on variable-structure control technique for spin recovery of aircraft. Variable-structure-technique-based controllers have been found to be robust in the presence of system uncertainties and external disturbances, and, usually result in simpler control algorithms [4]. Controller presented in this Note uses results from a bifurcation analysis of the high-angle-of-attack research vehicle (HARV) model of F-18 available in literature [2]. This Note is organized as follows. In Sec. II, a brief description of the aircraft model with reference states for SM controller design is presented. In Sec. III, SM control design technique is explained. Results and discussions are presented in Sec. IV and conclusions follow thereafter in Sec. V.

Accessible Regions for Controlled Aircraft Maneuvering

DESIGN of maneuvers for carefree access of an aircraft to its complete flight envelope including poststall regimes is useful not only from a combat strategy point of view, but also for devising recovery strategies from an accident scenario. Maneuvers for an aircraft can be efficiently designed if a priori knowledge of its maneuverability characteristics is available to the control designers. Different types of agility metrics that characterize aircraft maneuvering capabilities have been proposed in literature based on different criteria [1,2]. A recent approach to define maneuverability characteristics is based on computing “attainable equilibrium sets,” as suggested in [3] and [4]. This approach involves computing a two dimensional (2-D) section of attainable equilibrium sets of a particular maneuver using an inverse trimming formulation. Construction of maneuvers based on attainable equilibrium sets involves accessing desired aircraft states in the attainable equilibrium set from a normal flying condition, such as a level flight trim condition. Computing an attainable equilibrium set for a given aircraft model and developing control algorithms to switch aircraft states between different operating points lying within the accessible region defined by attainable equilibrium sets are thus essential ingredients of aircraft maneuver design. For aircraft models, which are inherently nonlinear due to nonlinear aerodynamics in the poststall regimes, and because of various couplings, use of nonlinear control design techniques based on dynamic inversion (DI) or sliding-mode control (SMC) have been proposed for control prototyping to design maneuvers [3,5–7]. Using bifurcation theory and continuation methods, Raghavendra et al. [5] computed spin solutions for the F18/high-alpha research vehicle (HARV) model, and demonstrated use of the DI controller to recover the aircraft from a flat oscillatory spin motion. Recently, the authors have proposed a systematic approach using bifurcation analysis and continuation methods in conjunction with a SMC technique to design maneuvers for a nonlinear aircraft model

A New Guidance Law for the Defense Missile of Nonmaneuverable Aircraft

In this brief, a new guidance law for the defense missile of nonmaneuverable aircraft is formulated based on dynamic game considerations. First, a simple differential game of protecting a static target in 2-D, involving simple motions for the attacker and defender, is introduced. The analysis is then extended to a moving noncooperative target in 2-D, in view of the fact that a nonmaneuverable aircraft would not be able to cooperate with the defender. A heuristic solution for the game is proposed and tested, and the results of the 2-D analysis are then extended to 3-D to formulate a new guidance law for the defense missile called the command to optimal interception point (COIP) guidance law. The validity of the new guidance law is checked using trajectory and envelope simulations, built with high-fidelity 6-DOF models using the computer-aided design of aerospace concepts in C++ framework. Performance comparisons are shown between the COIP guidance law and the recently proposed airborne command to line-of-sight (A-CLOS) guidance law. The results show that the performances of COIP and A-CLOS guidance laws are almost identical in a coplanar engagement scenario, but the COIP law has the additional advantage of working with only position information, without the knowledge of motion of the players. In addition, in a noncoplanar engagement case studied, the defense missile is shown to achieve intercept using the COIP guidance law, but fails when using the A-CLOS guidance law.

An assessment of thrust vector concepts for twin-engine airplane

Thrust vector nozzles are finding place on modern fighter airplanes because of the benefits they provide and also due to diminishing weight penalty of such nozzles. They offer additional benefits in the case of a twin-engine airplane. Different vectoring configurations such as multi-axis vectoring, single-axis pitch vectoring and single-axis vectoring with canted nozzles have been studied with respect to twin-engine airplane configuration. Modeling and integration of thrust vector nozzles with rigid airplane six-degrees-of-freedom equations of motion have been carried out in this article. Using the integrated model, a comparative study is carried out to summarize the capabilities and limitations of various nozzle configurations with respect to performance of an airplane in velocity vector roll and in Herbst maneuvers. The airplane model used in this work is the F-18/HARV and all simulation results have been produced using a nonlinear dynamic inversion controller developed in Matlab/Simulink environment. Results show that a multi-axis thrust vectoring provides additional benefits as compared to single-axis vectoring with canted nozzles in high angle of attack velocity vector roll and in Herbst maneuvers. The single-axis pitch only vectoring has roll control power and lacks in yaw control power, to execute the velocity vector roll maneuver.

The Target Guarding Problem Revisited: Some Interesting Revelations

Abstract In this paper, the target guarding problem, posed by Rufus Isaacs in his seminal textbook is revisited. Unlike the simplified version of the problem solved by Isaacs, optimal strategies are discussed for the pursuer and the evader having simple motions with different speeds. Analysis is also done for the case when the intercept occurs if the pursuer reaches within a certain distance of the evader, instead of a strict coincidence of their positions. The importance of the study is that, it is fundamental to building autonomous systems that would be used for protecting a target, for example, unmanned vehicles used in anti-poaching operations.

Computational Bifurcation Analysis of Multiparameter Dynamical Systems

where x is an n-dimensional vector of states, are m independent parameters, and f is an n-dimensional vector of nonlinear functions. These systems show a host of interesting nonlinear dynamic behavior, such as multiple attractors, limit cycles, jump phenomena, hysteresis, frequency locking, and chaos [1]. Nonlinear behaviors such as these are best understood in terms of bifurcations of the dynamical system, which is a record of all critical points in the (n m)-dimensional state-parameter space in which equilibrium and periodic solutions of Eq. (1) are either created, destroyed, or undergo a change in their stability. Results from bifurcation theory can then be used to describe the possible dynamic behavior of the system as it encounters any of these bifurcation points. Bifurcation methods have been widely used, for instance, to study nonlinear phenomena in aircraft flight dynamics [2]. A bifurcation analysis must begin by computing all equilibrium andperiodic solutionsof that systemalongwith information about the stability of these solutions. The equilibrium solutions form (hyper) surfaces in the state-parameter space, for example, a systemwith one state variable and two parameters would have a two-dimensional surface of equilibrium solutions in a (1 2)-dimensional stateparameter space.Unfortunately, for higher-dimensional systemswith multiple parameters, both computing and visualizing the equilibrium surfaces is exceedingly difficult [3]. Instead, the standard procedure until recently [4] has been to compute what is called a bifurcation diagram, that is, curves of equilibrium solutions as one of the parameters is varied while all the other parameters are held fixed. This procedure may be repeated by sequentially selecting another parameter to be the variable, thus generating an entire family of bifurcation diagrams. Traditionally, therefore, bifurcation analysis of a multiparameter dynamical system involves solving a series of one-parameter problems of the following form: _ x f x; 1; j kj ; j 2; . . . ; m (2)

Key factors that affect the performance of flares against a heat-seeking air-to-air missile

Deploying flare decoys against heat-seeking threats involves various parameters such as flare timing, flare ejection velocity, direction of ejection and the number of flares used. In this study, an attempt has been made to identify the key parameters among these that impact the performance of flares the most. For this, engagement studies involving six-degrees-of-freedom models for an air-to-air heat-seeking missile and a fighter aircraft were carried out using the CADAC++ simulation environment. The effect of flare parameters was studied using their impact on missile envelopes. Studies show that the effectiveness of the flare decoys is a strong function of the flare timing and the number of flares used.

Analysis and modelling of septic shock microarray data using Singular Value Decomposition

Being a high throughput technique, enormous amounts of microarray data has been generated and there arises a need for more efficient techniques of analysis, in terms of speed and accuracy. Finding the differentially expressed genes based on just fold change and p-value might not extract all the vital biological signals that occur at a lower gene expression level. Besides this, numerous mathematical models have been generated to predict the clinical outcome from microarray data, while very few, if not none, aim at predicting the vital genes that are important in a disease progression. Such models help a basic researcher narrow down and concentrate on a promising set of genes which leads to the discovery of gene-based therapies. In this article, as a first objective, we have used the lesser known and used Singular Value Decomposition (SVD) technique to build a microarray data analysis tool that works with gene expression patterns and intrinsic structure of the data in an unsupervised manner. We have re-analysed a microarray data over the clinical course of Septic shock from Cazalis et al. (2014) and have shown that our proposed analysis provides additional information compared to the conventional method. As a second objective, we developed a novel mathematical model that predicts a set of vital genes in the disease progression that works by generating samples in the continuum between health and disease, using a simple normal-distribution-based random number generator. We also verify that most of the predicted genes are indeed related to septic shock.