SEMIANNUAL STATUS REPORT NO. 1 <TO THE< NATIONAL AERONAUTICS AND SPACE ADMINISTRATION, MAR. 1 - SEPT. 1, 1962 <AN ADAPTIVE MODEL FOR NONLINEAR PROCESS IDENTIFICATION<
Adaptive model for nonlinear process identification
NONLINEARITY↗
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Results for “model identification”
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System identification for modeling for control of flexible structures
The major components of a design and operational flight strategy for flexible structure control systems are presented. In this strategy an initial distributed parameter control design is developed and implemented from available ground test data and on-orbit identification using sophisticated modeling and synthesis techniques. The reliability of this high performance controller is directly linked to the accuracy of the parameters on which the design is based. Because uncertainties inevitably grow without system monitoring, maintaining the control system requires an active on-line system identification function to supply parameter updates and covariance information. Control laws can then be modified to improve performance when the error envelopes are decreased. In terms of system safety and stability the covariance information is of equal importance as the parameter values themselves. If the on-line system ID function detects an increase in parameter error covariances, then corresponding adjustments must be made in the control laws to increase robustness. If the error covariances exceed some threshold, an autonomous calibration sequence could be initiated to restore the error enveloped to an acceptable level.
Mettler, Edward↗
System identification and model reduction using modulating function techniques
Weighted least squares (WLS) and adaptive weighted least squares (AWLS) algorithms are initiated for continuous-time system identification using Fourier type modulating function techniques. Two stochastic signal models are examined using the mean square properties of the stochastic calculus: an equation error signal model with white noise residuals, and a more realistic white measurement noise signal model. The covariance matrices in each model are shown to be banded and sparse, and a joint likelihood cost function is developed which links the real and imaginary parts of the modulated quantities. The superior performance of above algorithms is demonstrated by comparing them with the LS/MFT and popular predicting error method (PEM) through 200 Monte Carlo simulations. A model reduction problem is formulated with the AWLS/MFT algorithm, and comparisons are made via six examples with a variety of model reduction techniques, including the well-known balanced realization method. Here the AWLS/MFT algorithm manifests higher accuracy in almost all cases, and exhibits its unique flexibility and versatility. Armed with this model reduction, the AWLS/MFT algorithm is extended into MIMO transfer function system identification problems. The impact due to the discrepancy in bandwidths and gains among subsystem is explored through five examples. Finally, as a comprehensive application, the stability derivatives of the longitudinal and lateral dynamics of an F-18 aircraft are identified using physical flight data provided by NASA. A pole-constrained SIMO and MIMO AWLS/MFT algorithm is devised and analyzed. Monte Carlo simulations illustrate its high-noise rejecting properties. Utilizing the flight data, comparisons among different MFT algorithms are tabulated and the AWLS is found to be strongly favored in almost all facets.
Shen, Yan↗
Comparison of Five System Identification Algorithms for Rotorcraft Higher Harmonic Control
This report presents an analysis and performance comparison of five system identification algorithms. The methods are presented in the context of identifying a frequency-domain transfer matrix for the higher harmonic control (HHC) of helicopter vibration. The five system identification algorithms include three previously proposed methods: (1) the weighted-least- squares-error approach (in moving-block format), (2) the Kalman filter method, and (3) the least-mean-squares (LMS) filter method. In addition there are two new ones: (4) a generalized Kalman filter method and (5) a generalized LMS filter method. The generalized Kalman filter method and the generalized LMS filter method were derived as extensions of the classic methods to permit identification by using more than one measurement per identification cycle. Simulation results are presented for conditions ranging from the ideal case of a stationary transfer matrix and no measurement noise to the more complex cases involving both measurement noise and transfer-matrix variation. Both open-loop identification and closed- loop identification were simulated. Closed-loop mode identification was more challenging than open-loop identification because of the decreasing signal-to-noise ratio as the vibration became reduced. The closed-loop simulation considered both local-model identification, with measured vibration feedback and global-model identification with feedback of the identified uncontrolled vibration. The algorithms were evaluated in terms of their accuracy, stability, convergence properties, computation speeds, and relative ease of implementation.
Jacklin, Stephen A.↗
Indirect M-MRAC for Systems with Time Varying Parameters and Bounded Disturbances
The paper presents a prediction-identification model based adaptive control method for uncertain systems with time varying parameters in the presence of bounded external disturbances. The method guarantees desired tracking performance for the system s state and input signals. This is achieved by feeding back the state prediction error to the identification model. It is shown that the desired closed-loop properties are obtained with fast adaptation when the error feedback gain is selected proportional to the square root of the adaptation rate. The theoretical findings are confirmed via a simulation example.
Stepanyan, Vahram↗
Modeling and identification of SCOLE
Vector differential equations for distributed structures; discretization (in space) of distributed structures; and parameter identification for the Spacecraft Control Laboratory Experiment (SCOLE) are examined.
Meirovitch, L.↗
Physical model-set identification for robust control of flexible structures
An approach to dynamic system identification is presented taking into account the goal of enhancing robust control performance of flexible structures. Identification techniques are derived which take advantage of the physics of structural dynamics and can provide realistic bounds for all potential parameter uncertainties. The developed approach includes input optimization which distributes excitation energy in such a way that the influence of residual uncertainties on robust control performance is reduced.
Karlov, Valeri I.↗
Identification of modeled ocean plumes in Greenland gyre ERS-1 SAR data
Oceanic convective plumes modeled with a thermobaric large-eddy simulation and driven by conditions similar to those of the Greenland Sea are compared to observations from ERS-1 Synthetic Aperture Radar (SAR) data from the Greenland Sea for the winter of 1992. In both form and size the two representations are seen to compare favorably. The plume-filled area of the SAR image occupies a region about 20 km by 90 km at the ice edge of the open water in 'Nordbukta', the large seasonal ice retreat, in the 'Odden' ice protuberance in the southern Greenland gyre. In the SAR data the plumes appear to be ice covered while the convective-return areas are open.
Carsey, Frank D.↗
The Identification and Modeling of Visual Cue Usage in Manual Control Task Experiments
Many fields of endeavor require humans to conduct manual control tasks while viewing a perspective scene. Manual control refers to tasks in which continuous, or nearly continuous, control adjustments are required. Examples include flying an aircraft, driving a car, and riding a bicycle. Perspective scenes can arise through natural viewing of the world, simulation of a scene (as in flight simulators), or through imaging devices (such as the cameras on an unmanned aerospace vehicle). Designers frequently have some degree of control over the content and characteristics of a perspective scene; airport designers can choose runway markings, vehicle designers can influence the size and shape of windows, as well as the location of the pilot, and simulator database designers can choose scene complexity and content. Little theoretical framework exists to help designers determine the answers to questions related to perspective scene content. An empirical approach is most commonly used to determine optimum perspective scene configurations. The goal of the research effort described in this dissertation has been to provide a tool for modeling the characteristics of human operators conducting manual control tasks with perspective-scene viewing. This is done for the purpose of providing an algorithmic, as opposed to empirical, method for analyzing the effects of changing perspective scene content for closed-loop manual control tasks.
Sweet, Barbara Townsend↗
Estimation of Unsteady Aerodynamic Models from Dynamic Wind Tunnel Data
Demanding aerodynamic modelling requirements for military and civilian aircraft have motivated researchers to improve computational and experimental techniques and to pursue closer collaboration in these areas. Model identification and validation techniques are key components for this research. This paper presents mathematical model structures and identification techniques that have been used successfully to model more general aerodynamic behaviours in single-degree-of-freedom dynamic testing. Model parameters, characterizing aerodynamic properties, are estimated using linear and nonlinear regression methods in both time and frequency domains. Steps in identification including model structure determination, parameter estimation, and model validation, are addressed in this paper with examples using data from one-degree-of-freedom dynamic wind tunnel and water tunnel experiments. These techniques offer a methodology for expanding the utility of computational methods in application to flight dynamics, stability, and control problems. Since flight test is not always an option for early model validation, time history comparisons are commonly made between computational and experimental results and model adequacy is inferred by corroborating results. An extension is offered to this conventional approach where more general model parameter estimates and their standard errors are compared.
Murphy, Patrick↗
Modeling, estimation and identification methods for static shape determination of flexible structures
This paper outlines methods for modeling, identification and estimation for static determination of flexible structures. The shape estimation schemes are based on structural models specified by (possibly interconnected) elliptic partial differential equations. The identification techniques provide approximate knowledge of parameters in elliptic systems. The techniques are based on the method of maximum-likelihood that finds parameter values such that the likelihood functional associated with the system model is maximized. The estimation methods are obtained by means of a function-space approach that seeks to obtain the conditional mean of the state given the data and a white noise characterization of model errors. The solutions are obtained in a batch-processing mode in which all the data is processed simultaneously. After methods for computing the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the related estimation error is conducted. In addition to outlining the above theoretical results, the paper presents typical flexible structure simulations illustrating performance of the shape determination methods.
Rodriguez, G.↗
A DIGITAL ORTHOGONAL MODEL FOR NONLINEAR PROCESSES WITH TWOLEVEL INPUTS
Identification & model construction of nonlinear systems with two-level inputs & finite settling times
ADAPTIVE CONTROL↗
Identification of propulsion systems
This paper presents a tutorial on the use of model identification techniques for the identification of propulsion system models. These models are important for control design, simulation, parameter estimation, and fault detection. Propulsion system identification is defined in the context of the classical description of identification as a four step process that is unique because of special considerations of data and error sources. Propulsion system models are described along with the dependence of system operation on the environment. Propulsion system simulation approaches are discussed as well as approaches to propulsion system identification with examples for both air breathing and rocket systems.
Merrill, Walter↗
Similarity Metrics for Closed Loop Dynamic Systems
To what extent and in what ways can two closed-loop dynamic systems be said to be "similar?" This question arises in a wide range of dynamic systems modeling and control system design applications. For example, bounds on error models are fundamental to the controller optimization with modern control design methods. Metrics such as the structured singular value are direct measures of the degree to which properties such as stability or performance are maintained in the presence of specified uncertainties or variations in the plant model. Similarly, controls-related areas such as system identification, model reduction, and experimental model validation employ measures of similarity between multiple realizations of a dynamic system. Each area has its tools and approaches, with each tool more or less suited for one application or the other. Similarity in the context of closed-loop model validation via flight test is subtly different from error measures in the typical controls oriented application. Whereas similarity in a robust control context relates to plant variation and the attendant affect on stability and performance, in this context similarity metrics are sought that assess the relevance of a dynamic system test for the purpose of validating the stability and performance of a "similar" dynamic system. Similarity in the context of system identification is much more relevant than are robust control analogies in that errors between one dynamic system (the test article) and another (the nominal "design" model) are sought for the purpose of bounding the validity of a model for control design and analysis. Yet system identification typically involves open-loop plant models which are independent of the control system (with the exception of limited developments in closed-loop system identification which is nonetheless focused on obtaining open-loop plant models from closed-loop data). Moreover the objectives of system identification are not the same as a flight test and hence system identification error metrics are not directly relevant. In applications such as launch vehicles where the open loop plant is unstable it is similarity of the closed-loop system dynamics of a flight test that are relevant.
Whorton, Mark S.↗
Aero-Propulsive Modeling for eVTOL Aircraft Using Wind Tunnel Testing with Multisine Inputs
A novel approach for modeling the aero-propulsive characteristics of an electric vertical takeoff and landing (eVTOL) aircraft was developed and demonstrated in wind tunnel testing. The approach was applied to the NASA LA-8 tandem tilt-wing eVTOL aircraft, using an efficient, hybrid experiment design composed of a static I-optimal response surface design for slowly-varying test variables, and dynamic orthogonal phase-optimized multisine excitations for the control surfaces and electric propulsors. Both the static and dynamic experiment designs were executed simultaneously to collect informative data for model identification. Statistically-weighted multivariate orthogonal function modeling was used to combine local modeling results computed in the frequency domain using data collected with dynamic excitations operating on the control effectors to form an aggregate aero-propulsive model. The final identified model exhibited good predictive capability when compared to validation data acquired separately from the data used to develop the model. The required test time using these new techniques was reduced by at least a factor of five compared to previous static wind tunnel testing for the LA-8 aircraft, while providing more informative data, greater parameterization flexibility, and high-quality models.
system identification↗
Modeling of Longitudinal Unsteady Aerodynamics of a Wing-Tail Combination
Aerodynamic equations for the longitudinal motion of an aircraft with a horizontal tail were developed. In this development emphasis was given on obtaining model structure suitable for model identification from experimental data. The resulting aerodynamic models included unsteady effects in the form of linear indicial functions. These functions represented responses in the lift on the wing and tail alone, and interference between those two lifting surfaces. The effect of the wing on the tail was formulated for two different expressions concerning the downwash angle at the tail. The first expression used the Cowley-Glauert approximation known-as "lag-in-downwash," the second took into account growth of the wing circulation and delay in the development of the lift on the tail. Both approaches were demonstrated in two examples using the geometry of a fighter aircraft and a large transport. It was shown that the differences in the two downwash formulations would increase for an aircraft with long tail arm performing low-speed, rapid maneuvers.
Klein, Vladislav↗
A survey of AFFDL parameter estimation efforts and future plans
An overview is presented of the applications of parameter estimation methods to the following areas of interest at the Air Force Flight Dynamics Laboratory (AFFDL): (1) conventional stability and control parameter estimation of rigid aircraft; (2) extension to elastic aircraft; (3) extension to stall/spin aerodynamics of rigid aircraft with a nonlinear model; (4) application to the pilot model identification; and (5) correlation of wind tunnel, drop model and flight test data. Only well-documented algorithms are used with modification to the model as required for the specific application. The genesis of each problem and other background information are discussed which enumerate the algorithms and explain how this information is used to improve existing operational aircraft characteristics as well as specify design criteria for future USAF aerospace vehicles.
Eckholdt, D. C.↗
Flight-Test Validation and Flying Qualities Evaluation of a Rotorcraft UAV Flight Control System
This paper presents a process of design and flight-test validation and flying qualities evaluation of a flight control system for a rotorcraft-based unmanned aerial vehicle (RUAV). The keystone of this process is an accurate flight-dynamic model of the aircraft, derived by using system identification modeling. The model captures the most relevant dynamic features of our unmanned rotorcraft, and explicitly accounts for the presence of a stabilizer bar. Using the identified model we were able to determine the performance margins of our original control system and identify limiting factors. The performance limitations were addressed and the attitude control system was 0ptimize.d for different three performance levels: slow, medium, fast. The optimized control laws will be implemented in our RUAV. We will first determine the validity of our control design approach by flight test validating our optimized controllers. Subsequently, we will fly a series of maneuvers with the three optimized controllers to determine the level of flying qualities that can be attained. The outcome enable us to draw important conclusions on the flying qualities requirements for small-scale RUAVs.
Mettler, Bernard↗