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NASA NTRS1992

Stochastic stability properties of jump linear systems

Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented.

Feng, Xiangbo↗

NASA NTRS1992

Advanced aeroservoelastic stabilization techniques for hypersonic flight vehicles

Advanced high performance vehicles, including Single-Stage-To-Orbit (SSTO) hypersonic flight vehicles, that are statically unstable, require higher bandwidth flight control systems to compensate for the instability resulting in interactions between the flight control system, the engine/propulsion dynamics, and the low frequency structural modes. Military specifications, such as MIL-F-9490D and MIL-F-87242, tend to limit treatment of structural modes to conventional gain stabilization techniques. The conventional gain stabilization techniques, however, introduce low frequency effective time delays which can be troublesome from a flying qualities standpoint. These time delays can be alleviated by appropriate blending of gain and phase stabilization techniques (referred to as Hybrid Phase Stabilization or HPS) for the low frequency structural modes. The potential of using HPS for compensating structural mode interaction was previously explored. It was shown that effective time delay was significantly reduced with the use of HPS; however, the HPS design was seen to have greater residual response than a conventional gain stablized design. Additional work performed to advance and refine the HPS design procedure, to further develop residual response metrics as a basis for alternative structural stability specifications, and to develop strategies for validating HPS design and specification concepts in manned simulation is presented. Stabilization design sensitivity to structural uncertainties and aircraft-centered requirements are also assessed.

Chan, Samuel Y.↗

NASA NTRS1993

Active stabilization to prevent surge in centrifugal compression systems

This report documents an experimental and analytical study of the active stabilization of surge in a centrifugal engine. The aims of the research were to extend the operating range of a compressor as far as possible and to establish the theoretical framework for the active stabilization of surge from both an aerodynamic stability and a control theoretic perspective. In particular, much attention was paid to understanding the physical limitations of active stabilization and how they are influenced by control system design parameters. Previously developed linear models of actively stabilized compressors were extended to include such nonlinear phenomena as bounded actuation, bandwidth limits, and robustness criteria. This model was then used to systematically quantify the influence of sensor-actuator selection on system performance. Five different actuation schemes were considered along with four different sensors. Sensor-actuator choice was shown to have a profound effect on the performance of the stabilized compressor. The optimum choice was not unique, but rather shown to be a strong function of some of the non-dimensional parameters which characterize the compression system dynamics. Specifically, the utility of the concepts were shown to depend on the system compliance to inertia ratio ('B' parameter) and the local slope of the compressor speedline. In general, the most effective arrangements are ones in which the actuator is most closely coupled to the compressor, such as a close-coupled bleed valve inlet jet, rather than elsewhere in the flow train, such as a fuel flow modulator. The analytical model was used to explore the influence of control system bandwidth on control effectiveness. The relevant reference frequency was shown to be the compression system's Helmholtz frequency rather than the surge frequency. The analysis shows that control bandwidths of three to ten times the Helmholtz frequency are required for larger increases in the compressor flow range. This has important implications for implementation in gas turbine engines since the Helmholtz frequencies can be over 100 Hz, making actuator design extremely challenging.

Epstein, Alan H.↗

NASA NTRS1993

Attitude stabilization of a rigid spacecraft using gas jet actuators operating in a failure mode

The attitude stabilization of a rigid spacecraft using control torques supplied by gas jet actuators about only two of its principal axes is considered. First, the case where the uncontrolled principal axis of the spacecraft is not an axis of symmetry is considered. In this case, the complete spacecraft dynamics are small time locally controllable. However, the spacecraft cannot be asymptotically stabilized to an equilibrium attitude using time-invariant continuous feedback. A discontinuous stabilizing feedback control strategy is constructed which stabilizes the spacecraft to an equilibrium attitude. Next, the case where the uncontrolled principal axis of the spacecraft is an axis of symmetry is considered. In this case, the complete spacecraft dynamics are not even accessible. However, the spacecraft dynamics are strongly accessible and small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized to an equilibrium attitude using time-invariant continuous feedback, but again a discontinuous stabilizing feedback control strategy is constructed. In both cases, the discontinuous feedback controllers are constructed by switching between one of several feedback functions.

Krishnan, Hariharan↗

NASA NTRS1991

Effect of heat release on the stability of compressible reacting mixing layer

Reacting free shear layers are of fundamental importance in many industrial systems including gas turbine combustors and rockets. Efficient propulsion systems are essential for air breathing supersonic ramjets in the high Mach number range. A limiting factor in these engines is the time for fuel and oxidizer to mix in the combustion chamber; for fast mixing, the flow must be vigorously turbulent which requires the laminar flow to be unstable. Understanding the stability characteristics of compressible reacting free shear layers is, therefore, very important and may allow one to control the flow. Low speed shear layers are highly unstable but, as chemical reaction and compressibility effects tend to stabilize them, it is important to investigate the stability of high speed reacting mixing layers. The latter consists of two fluid streams containing fuel and oxidizer respectively, and the conclusions are expected to apply, with quantitative modifications, to other shear flows, e.g., jets. Since low speed reacting cases have been studied earlier, we concentrate on the effects of Mach number and heat release. We are primarily interested in solving the stability problem over a large range of Mach number and heat release. In order to understand the effect of the heat release on the stability of this flow, one must first study the characteristics of the non-reacting flow. Inviscid theory is a reliable guide for understanding stability of compressible shear flows at moderate and large Reynolds numbers and is the basis for this work.

Shin, Dong-Shin↗

NASA NTRS1952

Longitudinal Stability and Control Characteristics from a Flight Investigation of a Cruciform Canard Missile Configuration Having an Exposed Wing-canard Area Ratio of 16:1

A flight investigation has been made to determine the longitudinal stability and control characteristics of a 60 0 delta-wing-canard missile configuration with an exposed wing-canard area ratio of 16:1. The results presented include the longitudinal stability derivatives, control effectiveness, and drag characteristics for a Mach number range of 0.75 to 1.80 and are compared with the results of a similar configuration having larger 6ontrols. Stability characteristics are also presented from the flights of an interdigitated canard configuration at a Mach number of 2.08 and a wing-body configuration at Mach numbers of 1.25 to 1.45. The stability derivatives varied gradually with Mach number with the exception of the damping-in-pitch derivative. Aerodynamic damping in pitch decreased to a minimum at a Mach number of 1.0 3, then increased to a peak value at a Mach number of 1.26 followed by a gradual decrease at higher Mach numbers. The aerodynamic-center location of the in-line canard configuration shifted rearward 13 percent of the mean aerodynamic chord at transonic speeds. The pitching-moment curve slope was 25 percent greater for the model having no canards than for the in-line configuration. No large effects of interdigitation were noted in the stability derivatives. Pitching effectiveness of the in-line configuration was maintained throughout the Mach number range. A comparison of the stability and control characteristics of two canard configurations having different area controls showed that decreasing the control area 44 percent decreased the pitching effectiveness proportionally, shifted the aerodynamic-center location rearward 9 to 14 percent of the mean aerodynamic chord, and reduced the total hinge moments required for 10 trimmed flight about 50 percent at transonic speeds.

Moul, Martin T↗

NASA NTRS1994

Measurement of the frequency stability of responders in aircraft

Measurement on an aircraft orbit, such as a satellite launching orbit, is made by the responder in the aircraft along with several remote track stations on the ground. During the launching, the system is required to have precise time synchronization and frequency accuracy. At the same time, accurate measurement of aircraft velocity requires high frequency stability of the system. However, atomic frequency standards in the ground stations supply time and frequency reference standard with excellent long term and short term frequency stability for the above-mentioned goals. The stability of responder is also an important factor affecting the performance of the system and there are more requirements for the corresponding time/frequency measurements. In the system, the responders do not use continuous wave (CW) but narrow pulse modulated wave; consequently, the characterization theory of their stability is more complicated and the measurement technique is more difficult for pulsed wave than that for CW. A systematic characterization theory of the frequency stability for pulsed wave is demonstrated and the measuring methods are discussed. The measurement systems, which have been set up in Beijing Institute of Radio Metrology and Measurement (BIRMM) and can be used to test the frequency stability of pulse coherent responders in time domain and frequency domain with high sensitivity and accuracy, are described. Using these measurement systems, successful measurements for the responders were made with which the satellite launching orbits were precisely obtained and tracked.

Liu, Xiaofan↗

NASA NTRS1996

Robust Stabilization of Uncertain Systems Based on Energy Dissipation Concepts

Robust stability conditions obtained through generalization of the notion of energy dissipation in physical systems are discussed in this report. Linear time-invariant (LTI) systems which dissipate energy corresponding to quadratic power functions are characterized in the time-domain and the frequency-domain, in terms of linear matrix inequalities (LMls) and algebraic Riccati equations (ARE's). A novel characterization of strictly dissipative LTI systems is introduced in this report. Sufficient conditions in terms of dissipativity and strict dissipativity are presented for (1) stability of the feedback interconnection of dissipative LTI systems, (2) stability of dissipative LTI systems with memoryless feedback nonlinearities, and (3) quadratic stability of uncertain linear systems. It is demonstrated that the framework of dissipative LTI systems investigated in this report unifies and extends small gain, passivity, and sector conditions for stability. Techniques for selecting power functions for characterization of uncertain plants and robust controller synthesis based on these stability results are introduced. A spring-mass-damper example is used to illustrate the application of these methods for robust controller synthesis.

Gupta, Sandeep↗

NASA NTRS1999

Influence of Buoyant Convection on the Stability of Enclosed Laminar Flames

Enclosed diffusion flames are commonly found in practical combustion systems, such as the power-plant combustor, gas turbine combustor, and jet engine after-burner. In these systems, fuel is injected into a duct with a co-flowing or cross-flowing air stream. In combustors, this flame is anchored at the burner (i.e., fuel jet inlet) unless adverse conditions cause the flame to lift off or blow out. Investigations of burner stability study the lift off, reattachment, and blow out of the flame. There have been numerous studies of flame stability. Relatively few studies have investigated the stability of flames with an oxidizer co-flow, compared with the number of studies on (nearly) free jet diffusion flames. The air flow around the fuel jet can significantly alter the lift off, reattachment and blow out of the jet diffusion flame. In normal gravity, however, the effects of the air flow on flame stability are often complicated by the presence of buoyant convection. A comparison of normal-gravity and microgravity flames can provide clear indication of the influence of forced and buoyant flows on the flame stability. The overall goal of the Enclosed Laminar Flames (ELF) research, described at the following URL site: http://zeta.lerc.nasa.gov/expr/elf.htm, is to improve our understanding of the effects of buoyant convection on the structure and stability of co-flow diffusion flames.

Brooker, John E.↗

NASA NTRS1998

Sufficient Conditions for the Stability of a Lur'e System With Two Nonzero Inputs Based on Lyapunovs Direct Method

The Lur'e problem is a famous problem in nonlinear control theory. The analysis of this system is usually restricted to Lur'e systems in which the external input is zero. One form of this problem involves the stability analysis of the Lur'e system with two nonzero inputs. The stability analysis of this type of system is traditionally performed based on L stability theory. The objective of this paper is to present sufficient conditions for the stability of this system based on Lyapunov's direct method. This is a conceptually simpler approach to the existing analysis based on L stability theory and it provides some additional information about the stability of the system.

Adetona, Olawale↗

NASA NTRS1996

Effects of vestibular loss on head stabilization in response to head and body perturbations

Control of head position during postural responses is important to facilitate both the interpretation of vestibular signals and the stabilization of gaze. In these experiments, we compared head stabilization for two different postural tasks: 1) in response to perturbations at the head, and 2) in response to perturbations induced at the support surface, which perturb both body and head position. To determine whether normal vestibular function is necessary for head stabilization in these two tasks, responses to forward and backward mechanical perturbations of the head and body were compared for 13 normal subjects and 4 patients with profound bilateral vestibular loss (two with vestibular loss in adulthood and two in infancy). Normal subjects showed little neck muscle activity for body perturbations, but large, early activations in both neck extensors and flexors for head perturbations. In contrast, vestibular patients showed excessive neck muscle activation for body perturbations and reduced or absent neck muscle activity for head perturbations. Patients with vestibular loss in adulthood also showed increased head acceleration in response to both head and body perturbations, but patients with vestibular loss in infancy showed more normal head accelerations. For body perturbations, the differences in head acceleration between patients and normals were greater for later head acceleration peaks, indicating poor head control during the execution of the postural response. Trunk angle changes were also higher in the patients for forward body perturbations, indicating that poorer control of trunk position could have contributed to their poorer head stabilization. These results indicate that the vestibular system plays an important role in head and trunk stabilization for both head and body perturbations. However, the more normal head accelerations of the patients with infant vestibular loss also indicate that other mechanisms, possibly involving neck reflexes, can at least partially substitute for the vestibular system to provide head and trunk stabilization.

NASA Discipline Neuroscience↗

NASA NTRS1948

Measurements of the Lateral and Directional Stability and Control Characteristics of a P-51H Airplane (AAF No. 44-64164)

Flight tests of a P-51H airplane with two different vertical-tail assemblies were made to determine lateral and directional stability and control characteristics. The airplane had satisfactory directional stability in the landing, approach, and wave-off conditions with either tail. In the power-on clean and glide conditions, however, the airplane had weak directional stability with the original tail. The production tail, which had a 7-inch fin extension and a shorter span rudder, improved the directional stability in the power-on clean and glide conditions, but the stability was still weak in the power-on clean condition. Increased altitude in either case caused a slight decrease in the stability. The rudder-trim-force change with speed with either vertical-tail assembly was high. The general aileron control characteristics were satisfactory but the aileron effectiveness failed to meet the Army handling-qualities requirements.

Kraft, Christopher C., Jr.↗

NASA NTRS1951

Investigation of the Low-Speed Stability and Control Characteristics of a 1/10-Scale Model of the Douglas XF4D-1 Airplane in the Langley Free-Flight Tunnel TED No. NACA DE 349

An investigation of the low-speed, power-off stability and control characteristics of a 1/10-scale model of the Douglas XF4D-1 airplane has been made in the Langley free-flight tunnel. The model was flown with leading-edge slats retracted and extended over a lift-coefficient range from 0.5 to the stall. Only relatively low-altitude conditions were simulated and no attempt was made to determine the effect on the stability characteristics of freeing the controls. The longitudinal stability and control characteristics of the model were satisfactory for all conditions investigated except near the stall with slats extended, where the model had a slight nosing-up tendency. The lateral stability and control characteristics of the model were considered satisfactory for all conditions investigated except near the stall with slats retracted, where a change in sign of the static- directional-stability parameter Cn(sub beta) caused the model to be directionally divergent. The addition of an extension to the top of the vertical tail did not increase Cn(sub beta) enough to eliminate the directional divergence of the model, but a large increase in Cn(sub beta) that was obtainable by artificial means appeared to eliminate the divergence and flights near the stall could be made. Artificially increasing the stability derivative-Cn(sub r) (yawing moment due to yawing) and Cn(sub p) (yawing moment due to rolling) had little effect on the divergence for the range of these parameters investigated. Calculations indicate that the damping of the lateral oscillation of the airplane with slats retracted or extended will be satisfactory at sea level but will be only marginally satisfactory at 40,000 feet.

Johnson, Joseph L.↗

NASA NTRS1995

Concept Designed and Developed for Distortion- Tolerant, High-Stability Engine Control

Engine Control Future aircraft turbine engines, both commercial and military, must be able to successfully accommodate expected increased levels of steady-state and dynamic engine-face distortion. Advanced tactical aircraft are likely to use thrust vectoring to enhance their maneuverability. As a result, the engines will see more extreme aircraft angles-of-attack and sideslip levels than are currently encountered with present-day aircraft. Also, the mixed-compression inlets needed for the High Speed Civil Transport will likely encounter disturbances similar to those seen by tactical aircraft, in addition to planar pulse, inlet buzz, and high distortion levels at low flight speed and off-design operation. The current approach of incorporating a sufficient component design stall margin to tolerate these increased levels of distortion would significantly reduce performance. The objective of the High Stability Engine Control (HISTEC) program is to design, develop, and flight demonstrate an advanced, high-stability, integrated engine-control system that uses measurement-based, real-time estimates of distortion to enhance engine stability. The resulting distortion-tolerant control reduces the required design stall margin, with a corresponding increase in performance and decrease in fuel burn. The HISTEC concept has been designed and developed, and the software implementing the concept has successfully accommodated time-varying distortion. The NASA Lewis Research Center is currently overseeing the development and validation of the hardware and software necessary to flight test the HISTEC concept. HISTEC is a contracted effort with Pratt & Whitney of West Palm Beach, Florida. The HISTEC approach includes two major systems: A Distortion Estimation System (DES) and Stability Management Control (SMC). DES is an aircraft-mounted, high-speed processor that estimates the amount and type of distortion present and its effect on the engine. It uses high-response pressure measurements at the engine face to calculate indicators of the type and extent of distortion in real time. From these indicators, DES determines the effects of distortion on the propulsion systems and the corresponding engine match point necessary to accommodate it. DES output consists of fan and compressor pressure ratio trim commands that are passed to the SMC. In addition, DES uses maneuver information, consisting of angle-of-attack and sideslip from the flight control, to anticipate high inlet distortion conditions. The SMC, which is contained in the engine-mounted, Improved Digital Electronic Engine Control (IDEEC), includes advanced control laws to directly control the fan and compressor transient operating line (pressure ratio). These advanced control laws, with a multivariable design, have the potential for higher bandwidth and the resulting more precise control of engine match. The ability to measure and assess the distortion effects in real time coupled with a high-response controller improves engine stability at high levels of distortion. The software algorithms implementing DES have been designed, developed, and demonstrated, and integration testing of the DES and SMC software has been completed. The results show that the HISTEC system will be able to sense inlet distortion, determine the effect on engine stability, and accommodate distortion by maintaining an adequate margin for engine surge. The Pratt &Whitney Comprehensive Engine Diagnostic Unit was chosen as the DES processor. An instrumented inlet case for sensing distortion was designed and fabricated. HISTEC is scheduled for flight test on the ACTIVE F-15 aircraft at the NASA Dryden Flight Research Center in Edwards, California, in late 1996.

Source record↗

NASA NTRS2004

The Stability of Two Connected Pendant Drops

The stability of an equilibrium system of two drops suspended from circular holes is examined. The drop surfaces are disconnected surfaces of a connected liquid body. For holes of equal radii and identical pendant drops axisymmetric perturbations are always the most dangerous. The stability region for two identical drops differs considerably from that for a single drop. Loss of stability leads to a transition from a critical system of identical drops to a stable system of axisymmetric non-identical. This system of non-identical drops reaches its own stability limit (to isochoric or non-isochoric paturbations). For non-identical drops, loss of stability results in dripping or streaming from the holes. Critical volumes for non-identical drops have been calculated as functions of the Bond number, B. For unequal hole radii, stability regions have been constructed for a set of hole radius, K. The dependence of critical volumes on K and B is analyzed.

Slobozhanin, Lev A.↗

NASA NTRS2006

Stability Limits of a PD Controller for a Flywheel Supported on Rigid Rotor and Magnetic Bearings

Active magnetic bearings are used to provide a long-life, low-loss suspension of a high-speed flywheel rotor. This paper describes a modeling effort used to understand the stability boundaries of the PD controller used to control the active magnetic bearings on a high speed test rig. Limits of stability are described in terms of allowable stiffness and damping values which result in stable levitation of the nonrotating rig. Small signal stability limits for the system is defined as a nongrowth in vibration amplitude of a small disturbance. A simple mass-force model was analyzed. The force resulting from the magnetic bearing was linearized to include negative displacement stiffness and a current stiffness. The current stiffness was then used in a PD controller. The phase lag of the control loop was modeled by a simple time delay. The stability limits and the associated vibration frequencies were measured and compared to the theoretical values. The results show a region on stiffness versus damping plot that have the same qualitative tendencies as experimental measurements. The resulting stability model was then extended to a flywheel system. The rotor dynamics of the flywheel was modeled using a rigid rotor supported on magnetic bearings. The equations of motion were written for the center of mass and a small angle linearization of the rotations about the center of mass. The stability limits and the associated vibration frequencies were found as a function of nondimensional magnetic bearing stiffness and damping and nondimensional parameters of flywheel speed and time delay.

Kascak, Albert F.↗

NASA NTRS2008

Changes in Head Stability Control in Response to a Lateral Perturbation while Walking in Older Adults

Falling is a main contributor of injury in older adults. The decline in sensory systems associated with aging limits information needed to successfully compensate for unexpected perturbations. Therefore, sensory changes result in older adults having problems maintaining balance stability when experiencing an unexpected lateral perturbation (e.g. slip) in the environment. The goal of this study was to determine head stability movement strategies used by older adults when experiencing an unexpected lateral perturbation during walking. A total of 16 healthy adults, aged 66-81 years, walked across a foam pathway 6 times. One piece of the foam pathway covered a movable platform that translated to the left when the subject stepped on the foam. Three trials were randomized in which the platform shifted. Angular rate sensors were placed on the center of mass for the head and trunk segments to collect head and trunk movement in all three planes of motion. The predominant movement strategies for maintaining head stability were determined from the results of the cross-correlation analyses between the head and trunk segments. The Chi square test of independence was used to evaluate the movement pattern distributions of head-trunk coordination during perturbed and non-perturbed walking. When perturbed, head stabilization was significantly challenged in the yaw and roll planes of motion. Subjects demonstrated a movement pattern of the head leading the trunk in an effort to stabilize the head. The older adult subjects used this head stabilization movement pattern to compensate for sensory changes when experiencing the unexpected lateral perturbation.

Buccello, Regina R.↗

NASA NTRS2009

Application of Bounded Linear Stability Analysis Method for Metrics-Driven Adaptive Control

This paper presents the application of Bounded Linear Stability Analysis (BLSA) method for metrics-driven adaptive control. The bounded linear stability analysis method is used for analyzing stability of adaptive control models, without linearizing the adaptive laws. Metrics-driven adaptive control introduces a notion that adaptation should be driven by some stability metrics to achieve robustness. By the application of bounded linear stability analysis method the adaptive gain is adjusted during the adaptation in order to meet certain phase margin requirements. Analysis of metrics-driven adaptive control is evaluated for a second order system that represents a pitch attitude control of a generic transport aircraft. The analysis shows that the system with the metrics-conforming variable adaptive gain becomes more robust to unmodeled dynamics or time delay. The effect of analysis time-window for BLSA is also evaluated in order to meet the stability margin criteria.

Bakhtiari-Nejad, Maryam↗