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NASA NTRS1989

Absolute Stability And Hyperstability In Hilbert Space

Theorems on stabilities of feedback control systems proved. Paper presents recent developments regarding theorems of absolute stability and hyperstability of feedforward-and-feedback control system. Theorems applied in analysis of nonlinear, adaptive, and robust control. Extended to provide sufficient conditions for stability in system including nonlinear feedback subsystem and linear time-invariant (LTI) feedforward subsystem, state space of which is Hilbert space, and input and output spaces having finite numbers of dimensions. (In case of absolute stability, feedback subsystem memoryless and possibly time varying. For hyperstability, feedback system dynamical system.)

Wen, John Ting-Yung↗

NASA NTRS1988

Survey of Army/NASA rotorcraft aeroelastic stability research

Theoretical and experimental developments in the aeroelastic and aeromechanical stability of helicopters and tilt-rotor aircraft are addressed. Included are the underlying nonlinear structural mechanics of slender rotating beams, necessary for accurate modeling of elastic cantilever rotor blades, and the development of dynamic inflow, an unsteady aerodynamic theory for low frequency aeroelastic stability applications. Analytical treatment of isolated rotor stability in hover and forward flight, coupled rotor-fuselage stability are considered. Results of parametric investigations of system behavior are presented, and correlations between theoretical results and experimental data from small- and large-scale wind tunnel and flight testing are discussed.

Ormiston, Robert A.↗

NASA NTRS1989

Inviscid spatial stability of a compressible mixing layer. Part 3: Effect of thermodynamics

The results of a comprehensive comparative study of the inviscid spatial stability of a parallel compressible mixing layer using various models for the mean flow are reported. The models are: (1) the hyperbolic tangent profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; (2) the Lock profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; and (3) the similarity solution for the coupled velocity and temperature equations using the Sutherland viscosity temperature relation and arbitrary but constant Prandtl number. The purpose was to determine the sensitivity of the stability characteristics of the compressible mixing layer to the assumed thermodynamic properties of the fluid. It is shown that the quantative features of the stability characteristics are quite similiar for all models but that there are quantitative differences resulting from the difference in the thermodynamic models. In particular, it is shown that the stability characteristics are sensitive to the value of the Prandtl number.

Jackson, T. L.↗

NASA NTRS1989

Stabilized fiber-optic frequency distribution system

A technique for stabilizing reference frequencies transmitted over fiber-optic cable in a frequency distribution system is discussed. The distribution system utilizes fiber-optic cable as the transmission medium to distribute precise reference signals from a frequency standard to remote users. The stability goal of the distribution system is to transmit a 100-MHz signal over a 22-km fiber-optic cable and maintain a stability of 1 part in 10(17) for 1000-second averaging times. Active stabilization of the link is required to reduce phase variations produced by environmental effects, and is achieved by transmitting the reference signal from the frequency standard to the remote unit and then reflecting back to the reference unit over the same optical fiber. By comparing the phase of the transmitted and reflected signals at the reference unit, phase variations of the remote signal can be measured. An error voltage derived from the phase difference between the two signals is used to add correction phase.

Primas, L. E.↗

NASA NTRS1989

Stability boundaries for aircraft with unstable lateral-directional dynamics and control saturation

Aircraft that do not possess inherent (aerodynamic) stability must rely on closed-loop control systems for stable operation. Because there are limits on the deflections of an aircraft's control surfaces, the region of stable operation also is bounded. These boundaries are investigated for a lateral-directional example in which vertical fin size is inadequate to provide directional stability and where aileron and rudder deflections are subject to saturation. Fourth-order models are used in this study, with flight control logic based on minimum-control-energy linear-quadratic-regulatory theory. It is found that the stability boundaries can be described by unstable limit cycles surrounding stable equilibrium points. Variations in regions of stability with gain levels and command inputs are illustrated. Current results suggest guidelines for permissible limits on the open-loop instability of an aircraft's lateral-directional modes.

Shrivastava, Prakash C.↗

NASA NTRS1989

Control and stabilization of decentralized systems

Proceeding from the problem posed by the need to stabilize the motion of two helicopters maneuvering a single load, a methodology is developed for the stabilization of classes of decentralized systems based on a more algebraic approach, which involves the external symmetries of decentralized systems. Stabilizing local-feedback laws are derived for any class of decentralized systems having a semisimple algebra of symmetries; the helicopter twin-lift problem, as well as certain problems involving the stabilization of discretizations of distributed parameter problems, have just such algebras of symmetries.

Byrnes, Christopher I.↗

NASA NTRS1989

Stability and performance tradeoffs in bi-lateral telemanipulation

Kinesthetic force feedback provides measurable increase in remote manipulation system performance. Intensive computation time requirements or operation under conditions of time delay can cause serious stability problems in control-system design. Here, a simplified linear analysis of this stability problem is presented for the forward-flow generalized architecture, applying the hybrid two-port representation to express the loop gain of the traditional master-slave architecture, which can be subjected to similar analysis. The hybrid two-port representation is also used to express the effects on the fidelity of manipulation or feel of one design approach used to stabilize the forward-flow architecture. The results suggest that, when local force feedback at the slave side is used to reduce manipulator stability problems, a price is paid in terms of telemanipulation fidelity.

Hannaford, Blake↗

NASA NTRS1989

Curvature effects on the stability of three-dimensional laminar boundary layers

The linear stability equations for compressible, three-dimensional laminar boundary layer flow are derived in an orthogonal curvilinear coordinate system. The system of equations is solved using a finite difference scheme in order to study the effects of streamline and surface curvature and compressibility on the stability of the flow past a swept wing. It is known that convex surface curvature can have a stabilizing effect on the laminar boundary layer. Conversely, concave surface curvature can be destabilizing. The magnitude of these effects for swept wings is determined. Results indicate that amplification rates and hence, N-factors, for the flow over the convex upper surface of a swept wing can be reduced by about 15 to 45 percent when curvature effects are included in the linear stability analysis. The results of the calculations show that concave curvature destabilizes crossflow type disturbances with a significant increase in amplification rate. In addition, comparisons are made with some experimental results on a swept concave-convex surface. Calculated velocity vector plots show good agreement with observed disturbances in the laminar boundary layer over the concave surface.

Collier, F. S., Jr.↗

NASA NTRS1989

Effect of control surface mass unbalance on the stability of a closed-loop active control system

The effects on stability of inertial forces arising from closed-loop activation of mass-unbalanced control surfaces are studied analytically using inertial energy approach, similar to the aerodynamic energy approach used for flutter suppression. The limitations of a single control surface like a leading-edge (LE) control or a trailing-edge (TE) control are demonstrated and compared to the superior combined LE-TE mass unbalanced system. It is shown that a spanwise section for sensor location can be determined which ensures minimum sensitivity to the mode shapes of the aircraft. It is shown that an LE control exhibits compatibility between inertial stabilization and aerodynamic stabilization, and that a TE control lacks such compatibility. The results of the present work should prove valuable, both for the purpose of flutter suppression using mass unbalanced control surfaces, or for the stabilization of structural modes of large space structures by means of inertial forces.

Nissim, E.↗

NASA NTRS1990

Effects of forebody geometry on subsonic boundary-layer stability

As part of an effort to develop computational techniques for design of natural laminar flow fuselages, a computational study was made of the effect of forebody geometry on laminar boundary layer stability on axisymmetric body shapes. The effects of nose radius on the stability of the incompressible laminar boundary layer was computationally investigated using linear stability theory for body length Reynolds numbers representative of small and medium-sized airplanes. The steepness of the pressure gradient and the value of the minimum pressure (both functions of fineness ratio) govern the stability of laminar flow possible on an axisymmetric body at a given Reynolds number. It was found that to keep the laminar boundary layer stable for extended lengths, it is important to have a small nose radius. However, nose shapes with extremely small nose radii produce large pressure peaks at off-design angles of attack and can produce vortices which would adversely affect transition.

Dodbele, Simha S.↗

NASA NTRS1988

Aeroelastic effects on stability and control of hingeless rotor helicopters

The combined effect of torsional flexibility and offset of the aerodynamic center relative to the elastic axis on the stability and control of a hingeless rotor helicopter in forward flight is studied in this paper. The aeroelastic model of the blade is based on fully coupled flap-lag-torsion equations of motion, which include kinematic nonlinearities due to moderate deflections. The equations are discretized using a finite element Galerkin method in space, and a classical Galerkin method in time. The vehicle trim calculations are coupled to the blade aeroelastic response calculations. Quasilinearization is used to compute aeroelastic stability. Reducing torsional stiffness and moving the elastic axis ahead of the aerodynamic center strongly stabilizes the phugoid mode without reducing control sensitivity. Aeroelastic stability calculations must accompany flight dynamics calculations to prevent aeroelastic instabilities that might easily go undetected.

Celi, Roberto↗

NASA NTRS1990

Power and stability limitations of resonant tunneling diodes

Stability criteria for resonant tunneling diodes are investigated. Details of how extrinsic elements, such as series inductance and parallel capacitance, affect the stability are presented. A GaAs/AlAs/InGaAs/AlAs/GaAs double-barrier diode is investigated, showing the effect of different modes of low-frequency oscillation and the extrinsic circuit required for stabilization. The effect of device stabilization on high-frequency power generation is described. The main conclusions of the paper are: (1) stable resonant tunneling diode operation is difficult to obtain, and (2) the circuit and device conditions required for stable operation greatly reduce the amount of power that can be produced by these devices.

Kidner, C.↗

NASA NTRS1989

Dynamic stability of unidirectional fiber-reinforced viscoelastic composite plates

This paper deals with a dynamic stability analysis of unidirectional fiber-reinforced composite viscoelastic plates subjected to compressive edge loads. The integrodifferential equations governing the stability problem are obtained by using, in conjunction with a Boltzmann hereditary constitutive law for a three-dimensional viscoelastic medium, a higher-order shear deformation theory of orthotropic plates. Such a theory incorporates transverse shear deformation, transverse normal stress, and rotatory inertia effects. The solution of the stability problem as considered within this paper concerns the determination of the critical in-plane edge loads yielding the asymptotic instability. Numerical applications, based on material properties derived within the framework of Aboudi's micromechanical model, are presented and pertinent conclusions concerning the nature of the loss of stability and the influence of various parameters are outlined.

Chandiramani, N. K.↗

NASA NTRS1991

Stability of a non-orthogonal stagnation flow to three dimensional disturbances

A similarity solution for a low Mach number nonorthogonal flow impinging on a hot or cold plate is presented. For the constant density case, it is known that the stagnation point shifts in the direction of the incoming flow and that this shift increases as the angle of attack decreases. When the effects of density variations are included, a critical plate temperature exists; above this temperature the stagnation point shifts away from the incoming stream as the angle is decreased. This flow field is believed to have application to the reattachment zone of certain separated flows or to a lifting body at a high angle of attack. Finally, the stability of this nonorthogonal flow to self similar, 3-D disturbances is examined. Stability properties of the flow are given as a function of the parameters of this study; ratio of the plate temperature to that of the outer potential flow and angle of attack. In particular, it is shown that the angle of attack can be scaled out by a suitable definition of an equivalent wavenumber and temporal growth rate, and the stability problem for the nonorthogonal case is identical to the stability problem for the orthogonal case.

Lasseigne, D. G.↗

NASA NTRS1991

Nonlinear stability and control study of highly maneuverable high performance aircraft

The purpose was to develop and apply new nonlinear system methodologies to the stability analysis and adaptive control of high angle of attack (alpha) aircraft such as the F-18. Considerable progress is documented on nonlinear adaptive control and associated model development, identification, and simulation. The analysis considered linear and nonlinear, longitudinal, high alpha aircraft dynamics with varying degrees of approximation dependent on the purpose. In all cases, angle of attack or pitch rate was controlled primarily by a horizontal stabilizer. In most cases studied, a linear adaptive controller provided sufficient stability. However, it has been demonstrated by simulation of a simplified nonlinear model that certain large rapid maneuvers were not readily stabilized by the investigated linear adaptive control, but were controlled instead by means of a nonlinear time-series based adaptive control.

Mohler, R. R.↗

NASA NTRS1990

Stability analysis of multigrid acceleration methods for the solution of partial differential equations

A calculation is made of the stability of various relaxation schemes for the numerical solution of partial differential equations. A multigrid acceleration method is introduced, and its effects on stability are explored. A detailed stability analysis of a simple case is carried out and verified by numerical experiment. It is shown that the use of multigrids can speed convergence by several orders of magnitude without adversely affecting stability.

Fay, John F.↗

NASA NTRS1991

Inviscid spatial stability of a compressible mixing layer. III - Effect of thermodynamics

The results of a comprehensive comparative study of the inviscid spatial stability of a parallel compressible mixing layer using various models for the mean flow are reported. The models are: (1) the hyperbolic tangent profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; (2) the Lock profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; and (3) the similarity solution for the coupled velocity and temperature equations using the Sutherland viscosity temperature relation and arbitrary but constant Prandtl number. The purpose was to determine the sensitivity of the stability characteristics of the compressible mixing layer to the assumed thermodynamic properties of the fluid. It is shown that the quantitative features of the stability characteristics are quite similar for all models but that there are quantitative differences resulting from the difference in the thermodynamic models. In particular, it is shown that the stability characteristics are sensitive to the value of the Prandtl number.

Jackson, T. L.↗

NASA NTRS1991

Performance and stability of telemanipulators using bilateral impedance control

A new method of control for telemanipulators called bilateral impedance control is investigated. This new method differs from previous approaches in that interaction forces are used as the communication signals between the master and slave robots. The new control architecture has several advantages: (1) It allows the master robot and the slave robot to be stabilized independently without becoming involved in the overall system dynamics; (2) It permits the system designers to arbitrarily specify desired performance characteristics such as the force and position ratios between the master and slave; (3) The impedance at both ends of the telerobotic system can be modulated to suit the requirements of the task. The main goals of the research are to characterize the performance and stability of the new control architecture. The dynamics of the telerobotic system are described by a bond graph model that illustrates how energy is transformed, stored, and dissipated. Performance can be completely described by a set of three independent parameters. These parameters are fundamentally related to the structure of the H matrix that regulates the communication of force signals within the system. Stability is analyzed with two mathematical techniques: the Small Gain Theorem and the Multivariable Nyquist Criterion. The theoretical predictions for performance and stability are experimentally verified by implementing the new control architecture on a multidegree of freedom telemanipulator.

Moore, Christopher Lane↗