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Method of learning identification from single set of input/output data formulated. Recursive and nonrecursive techniques used to estimate Markov parameters in state-space format.
System-identification methods compose a mathematical model, or series of models, from measurements of inputs and outputs of dynamic systems. The extracted models allow the characterization of the response of the overall aircraft or component subsystem behavior, such as actuators and on-board signal processing algorithms. This paper discusses the use of frequency-domain system-identification methods for the development and integration of aircraft flight-control systems. The extraction and analysis of models of varying complexity from nonparametric frequency-responses to transfer-functions and high-order state-space representations is illustrated using the Comprehensive Identification from FrEquency Responses (CIFER) system-identification facility. Results are presented for test data of numerous flight and simulation programs at the Ames Research Center including rotorcraft, fixed-wing aircraft, advanced short takeoff and vertical landing (ASTOVL), vertical/short takeoff and landing (V/STOL), tiltrotor aircraft, and rotor experiments in the wind tunnel. Excellent system characterization and dynamic response prediction is achieved for this wide class of systems. Examples illustrate the role of system-identification technology in providing an integrated flow of dynamic response data around the entire life-cycle of aircraft development from initial specifications, through simulation and bench testing, and into flight-test optimization.
This paper deals with the multipoint Cauer matrix continued-fraction expansion (MCFE) for model reduction of linear multi-input multi-output (MIMO) systems with various numbers of inputs and outputs. A salient feature of the proposed MCFE approach to model reduction of MIMO systems with square transfer matrices is its equivalence to the matrix Pade approximation approach. The Cauer second form of the ordinary MCFE for a square transfer function matrix is generalized in this paper to a multipoint and nonsquare-matrix version. An interesting connection of the multipoint Cauer MCFE method to the multipoint matrix Pade approximation method is established. Also, algorithms for obtaining the reduced-degree matrix-fraction descriptions and reduced-dimensional state-space models from a transfer function matrix via the multipoint Cauer MCFE algorithm are presented. Practical advantages of using the multipoint Cauer MCFE are discussed and a numerical example is provided to illustrate the algorithms.
A two-control volume is employed for honeycomb-stator/smooth-rotor seals, with a conventional control-volume used for the through flow and a 'capacitance accumulator' model for the honeycomb cells. The control volume for the honeycomb cells is shown to cause a dramatic reduction in the effective acoustic velocity of the main flow, dropping the lowest acoustic frequency into the frequency range of interest for rotordynamics. In these circumstances, the impedance functions for the seals can not be modeled with conventional (frequency-independent) stiffness, damping, and mass coefficients. More general transfer functions are required to account for the reaction forces, and calculated here as a lead-lag term for the direct force function and a lag term for the cross-coupled function. These first order functions are simple compared to transfer functions for magnetic bearings or foundations, For synchronous response to imbalance, they can be approximated by running-speed-dependent stiffness and damping coefficients in conventional rotordynamic codes. Correct predictions for stability and transient response will require more general algorithms, pressumably using a state-space format.
Design for prevention of aeroelastic instability (that is, the critical speeds leading to aeroelastic instability lie outside the operating range) is an integral part of the wing design process. Availability of the sensitivity derivatives of the various critical speeds with respect to shape parameters of the wing could be very useful to a designer in the initial design phase, when several design changes are made and the shape of the final configuration is not yet frozen. These derivatives are also indispensable for a gradient-based optimization with aeroelastic constraints. In this study, flutter characteristic of a typical section in subsonic compressible flow is examined using a state-space unsteady aerodynamic representation. The sensitivity of the flutter speed of the typical section with respect to its mass and stiffness parameters, namely, mass ratio, static unbalance, radius of gyration, bending frequency, and torsional frequency is calculated analytically. A strip theory formulation is newly developed to represent the unsteady aerodynamic forces on a wing. This is coupled with an equivalent plate structural model and solved as an eigenvalue problem to determine the critical speed of the wing. Flutter analysis of the wing is also carried out using a lifting-surface subsonic kernel function aerodynamic theory (FAST) and an equivalent plate structural model. Finite element modeling of the wing is done using NASTRAN so that wing structures made of spars and ribs and top and bottom wing skins could be analyzed. The free vibration modes of the wing obtained from NASTRAN are input into FAST to compute the flutter speed. An equivalent plate model which incorporates first-order shear deformation theory is then examined so it can be used to model thick wings, where shear deformations are important. The sensitivity of natural frequencies to changes in shape parameters is obtained using ADIFOR. A simple optimization effort is made towards obtaining a minimum weight design of the wing, subject to flutter constraints, lift requirement constraints for level flight and side constraints on the planform parameters of the wing using the IMSL subroutine NCONG, which uses successive quadratic programming.
Since the early 1990s the Aeroflightdynamics Directorate at the Ames Research Center has been conducting tests on isolated hingeless rotors in hover and forward flight. The primary objective is to generate a database on aeroelastic stability in trimmed flight for torsionally soft rotors at realistic tip speeds. The rotor test model has four soft inplane blades of NACA 0012 airfoil section with low torsional stiffness. The collective pitch and shaft tilt are set prior to each test run, and then the rotor is trimmed in the following sense: the longitudinal and lateral cyclic pitch controls are adjusted through a swashplate to minimize the 1/rev flapping moment at the 12 percent radial station. In hover, the database comprises lag regressive-mode damping with pitch variations. In forward flight the database comprises cyclic pitch controls, root flap moment and lag regressive-mode damping with advance ratio, shaft angle and pitch variations. This report presents the predictions and their correlation with the database. A modal analysis is used, in which nonrotating modes in flap bending, lag bending and torsion are computed from the measured blade mass and stiffness distributions. The airfoil aerodynamics is represented by the ONERA dynamic stall models of lift, drag and pitching moment, and the wake dynamics is represented by a state-space wake model. The trim analysis of finding, the cyclic controls and the corresponding, periodic responses is based on periodic shooting with damped Newton iteration; the Floquet transition matrix (FTM) comes out as a byproduct. The stabillty analysis of finding the frequencies and damping levels is based on the eigenvalue-eigenvector analysis of the FTM. All the structural and aerodynamic states are included from modeling to trim analysis. A major finding is that dynamic wake dramatically improves the correlation for the lateral cyclic pitch control. Overall, the correlation is fairly good.
Flutter analysis of a wing is performed in compressible flow using state-space representation of the unsteady aerodynamic behavior. Three different expressions are used to incorporate corrections due to the finite-span effects of the wing in estimating the lift-curve slope. The structural formulation is based on a Rayleigh-Pitz technique with Chebyshev polynomials used for the wing deflections. The aeroelastic equations are solved as an eigen-value problem to determine the flutter speed of the wing. The flutter speeds are found to be higher in these cases, when compared to that obtained without accounting for the finite-span effects. The derivatives of the flutter speed with respect to the shape parameters, namely: aspect ratio, area, taper ratio and sweep angle, are calculated analytically. The shape sensitivity derivatives give a linear approximation to the flutter speed curves over a range of values of the shape parameter which is perturbed. Flutter and sensitivity calculations are performed on a wing using a lifting-surface unsteady aerodynamic theory using modules from a system of programs called FAST.
This paper presents the results of modeling and system identification efforts on the NASA Large-Angle Magnetic Suspension Test Fixture (LAMSTF). The LAMSTF consists of a cylindrical permanent magnet which is levitated above a planar array of five electromagnets mounted in a circular configuration. The analytical model is first developed and open-loop characteristics are described. The system is shown to be highly unstable and requires feedback control in order to apply system identification. Limitations on modeling accuracy due to the effect of eddy-currents on the system are discussed. An algorithm is derived to identify a state-space model for the system from input/output data acquired during closed-loop operation. The algorithm is tested on both the baseline system and a perturbed system which has an increased presence of eddy currents. It is found that for the baseline system the analytic model adequately captures the dynamics, although the identified model improves the simulation accuracy. For the system perturbed by additional unmodeled eddy-currents the analytic model is no longer adequate and a higher-order model, determined through system identification, is required to accurately predict the system's time response.
An ongoing program exists to investigate and develop magnetic suspension technologies and modelling techniques at NASA Langley Research Center. Presently, there is a laboratory-scale large air-gap suspension system capable of five degree-of-freedom (DOF) control that is operational and a six DOF system that is under development. Those systems levitate a cylindrical element containing a permanent magnet core above a planar array of electromagnets, which are used for levitation and control purposes. In order to evaluate various control approaches with those systems, the Generic Real-Time State-Space Controller (GRTSSC) software package was developed. That control software package allows the user to implement multiple control methods and allows for varied input/output commands. The development of the control algorithm is presented. The desired functionality of the software is discussed, including the ability to inject noise on sensor inputs and/or actuator outputs. Various limitations, common issues, and trade-offs are discussed including data format precision; the drawbacks of using either Direct Memory Access (DMA), interrupts, or program control techniques for data acquisition; and platform dependent concerns related to the portability of the software, such as memory addressing formats. Efforts to minimize overall controller loop-rate and a comparison of achievable controller sample rates are discussed. The implementation of a modular code structure is presented. The format for the controller input data file and the noise information file is presented. Controller input vector information is available for post-processing by mathematical analysis software such as MATLAB1.
In this thesis linear, dynamic, multivariable state-space models for three joints of the ground-based Hydraulic Manipulator Test Bed (HMTB) are identified. HMTB, housed at the NASA Langley Research Center, is a ground-based version of the Dexterous Orbital Servicing System (DOSS), a representative space station manipulator. The dynamic models of the HMTB manipulator will first be estimated by applying nonparametric identification methods to determine each joint's response characteristics using various input excitations. These excitations include sum of sinusoids, pseudorandom binary sequences (PRBS), bipolar ramping pulses, and chirp input signals. Next, two different parametric system identification techniques will be applied to identify the best dynamical description of the joints. The manipulator is localized about a representative space station orbital replacement unit (ORU) task allowing the use of linear system identification methods. Comparisons, observations, and results of both parametric system identification techniques are discussed. The thesis concludes by proposing a model reference control system to aid in astronaut ground tests. This approach would allow the identified models to mimic on-orbit dynamic characteristics of the actual flight manipulator thus providing astronauts with realistic on-orbit responses to perform space station tasks in a ground-based environment.
An algorithm is presented for identifying a state-space model of linear stochastic systems operating under known feedback controller. In this algorithm, only the reference input and output of closed-loop data are required. No feedback signal needs to be recorded. The overall closed-loop system dynamics is first identified. Then a recursive formulation is derived to compute the open-loop plant dynamics from the identified closed-loop system dynamics and known feedback controller dynamics. The controller can be a dynamic or constant-gain full-state feedback controller. Numerical simulations and test data of a highly unstable large-gap magnetic suspension system are presented to demonstrate the feasibility of this indirect identification method.
Several new computational algorithms are presented to compute the deadbeat predictive control law. The first algorithm makes use of a multi-step-ahead output prediction to compute the control law without explicitly calculating the controllability matrix. The system identification must be performed first and then the predictive control law is designed. The second algorithm uses the input and output data directly to compute the feedback law. It combines the system identification and the predictive control law into one formulation. The third algorithm uses an observable-canonical form realization to design the predictive controller. The relationship between all three algorithms is established through the use of the state-space representation. All algorithms are applicable to multi-input, multi-output systems with disturbance inputs. In addition to the feedback terms, feed forward terms may also be added for disturbance inputs if they are measurable. Although the feedforward terms do not influence the stability of the closed-loop feedback law, they enhance the performance of the controlled system.
This paper highlights some of the results and issues associated with estimating models to evaluate control law design methods and design criteria for advanced high performance aircraft. Experimental fighter aircraft such as the NASA-High Alpha Research Vehicle (HARV) have the capability to maneuver at very high angles of attack where nonlinear aerodynamics often predominate. HARV is an experimental F/A-18, configured with thrust vectoring and conformal actuated nose strakes. Identifying closed-loop models for this type of aircraft can be made difficult by nonlinearities and high order characteristics of the system. In this paper, only lateral-directional axes are considered since the lateral-directional control law was specifically designed to produce classical airplane responses normally expected with low-order, rigid-body systems. Evaluation of the control design methodology was made using low-order equivalent systems determined from flight and simulation. This allowed comparison of the closed-loop rigid-body dynamics achieved in flight with that designed in simulation. In flight, the On Board Excitation System was used to apply optimal inputs to lateral stick and pedals at five angles at attack : 5, 20, 30, 45, and 60 degrees. Data analysis and closed-loop model identification were done using frequency domain maximum likelihood. The structure of identified models was a linear state-space model reflecting classical 4th-order airplane dynamics. Input time delays associated with the high-order controller and aircraft system were accounted for in data preprocessing. A comparison of flight estimated models with small perturbation linear design models highlighted nonlinearities in the system and indicated that the closed-loop rigid-body dynamics were sensitive to input amplitudes at 20 and 30 degrees angle of attack.
The fault detection process is modelled as a disturbance attenuation problem. The solution to this problem is found via differential game theory, leading to an H(sub infinity) filter which bounds the transmission of all exogenous signals save the fault to be detected. For a general class of linear systems which includes some time-varying systems, it is shown that this transmission bound can be taken to zero by simultaneously bringing the sensor noise weighting to zero. Thus, in the limit, a complete transmission block can he achieved, making the game filter into a fault detection filter. When we specialize this result to time-invariant system, it is found that the detection filter attained in the limit is identical to the well known Beard-Jones Fault Detection Filter. That is, all fault inputs other than the one to be detected (the "nuisance faults") are restricted to an invariant subspace which is unobservable to a projection on the output. For time-invariant systems, it is also shown that in the limit, the order of the state-space and the game filter can be reduced by factoring out the invariant subspace. The result is a lower dimensional filter which can observe only the fault to be detected. A reduced-order filter can also he generated for time-varying systems, though the computational overhead may be intensive. An example given at the end of the paper demonstrates the effectiveness of the filter as a tool for fault detection and identification.
A linear state-space system will be said to be estimable if in estimating its state from its output the posterior error covariance matrix is strictly smaller than the prior covariance matrix. It will be said to be regulable if the quadratic cost of state feedback control is strictly smaller than the cost when no feedback is used. Estimability and regulability are shown to be dual properties, equivalent to the nonreducibility of the Kalman filter and of the optimal linear quadratic regulator, respectively.
We discuss how to describe the Markov chain underlying a generalized stochastic Petri net using Kronecker operators on smaller matrices. We extend previous approaches by allowing both an extensive type of marking-dependent behavior for the transitions and the presence of immediate synchronizations. The derivation of the results is thoroughly formalized, including the use of Kronecker operators in the treatment of the vanishing markings and the computation of impulse-based reward measures. We use our techniques to analyze a model whose solution using conventional methods would fail because of the state-space explosion. In the conclusion, we point out ideas to parallelize our approach.
An improved state-space analysis of the CMOS static RAM cell is presented. Introducing theconcept of the dividing line, the critical charge for heavy-ion-induced upset of memory cells can becalculated considering symmetrical as well as asymmetrical capacitive loads. From the criticalcharge, the upset-rate per bit-day for static RAMs can be estimated.
This invention provides a method and apparatus for determining a precise switching sequence for the power switching elements of electric power delivery systems of the on-off switching type and which enables extremely fast transient response, precise regulation and highly stable operation. The control utilizes the values of the power delivery system power handling network components, a desired output characteristic, a system timing parameter, and the externally imposed operating conditions to determine where steady state operations should be in order to yield desired output characteristics for the given system specifications. The actual state of the power delivery system is continuously monitored and compared to a state-space boundary which is derived from the desired equilibrium condition, and from the information obtained from this comparison, the system is moved to the desired equilibrium condition in one cycle of switching control. Since the controller continuously monitors the power delivery system's externally imposed operating conditions, a change in the conditions is immediately sensed and a new equilibrium condition is determined and achieved, again in a single cycle of switching control.