Nonlinear natural control of an experimental beam
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Meirovitch, L.↗
Engineering topics
Montgomery, R. C.
Publications and source records attributed to Montgomery, R. C..
Space Shuttle separate-surface control-system study
A control system concept is presented that produces proportional control of yaw moment for the space shuttle from early entry to Mach 2 with only software modifications of the vehicle. It uses separate deflections of the inboard and outboard elevon surfaces and is evaluated, by determining the maximum static yawing moment available by considering the deflection limits of the elevon surfaces. A proportional moment slightly in excess of that produced by the most effective reaction control system (RCS) jet for yaw control can be obtained. In addition to the static moment study, a control law is designed which is intended to produce desired flying qualities.
Brown, L. W.↗
Identification of the dynamics of a two-dimensional grid structure using least square lattice filters
The basic theory of least square lattice filters and their use in identification of structural dynamics systems is summarized. Thereafter, this theory is applied to a two-dimensional grid structure made of overlapping bars. Previously, this theory has been applied to an integral beam. System identification results are presented for both simulated and experimental tests and they are compared with those predicted using finite element modelling. The lattice filtering approach works well for simulated data based on finite element modelling. However, considerable discrepancy exists between estimates obtained from experimental data and the finite element analysis. It is believed that this discrepancy is the result of inadequacies in the finite element modelling to represent the damped motion of the laboratory apparatus.
Montgomery, R. C.↗
Identification of the dynamics of a two-dimensional grid structure using least square lattice filters
It is doubtful whether the dynamics of large space structures (LSS) can be predicted well enough for control system design applications. Hence, dynamic modeling from on-orbit measurements followed by a modification of the control system is of interest, taking into account the utilization of adaptive control concepts. The present paper is concerned with the model determination phase of the adaptive control problem. Using spectral decoupling to determine mode shapes, mode frequency and damping data can be obtained with the aid of an equation error parameter identification method. This method employs a second-order auto-regressive moving average (ARMA) model to represent the natural mode amplitudes. The discussed procedure involves an extension of the application of the least square lattice filter in system identification to a nonintegral, two-dimensional grid structure made of overlapping bars.
Montgomery, R. C.↗
Identification of structural dynamics systems using least-square lattice filters
Previously cited in issue 19, no. 2987, Accession no. A82-38965
Sundararajan, N.↗
Adaptive control of a flexible beam using least square lattice filters
This paper presents an indirect adaptive control scheme for the control of flexible structures using recursive least square lattice filters. The identification scheme uses lattice filters which provide an on-line estimate of the number of modes, mode shapes and modal amplitudes. These modes are coupled and a transformation to decouple them in order to obtain the natural modes is presented. The decoupled modal amplitude time series are then used in an equation error identification scheme to identify the model parameters in an autoregressive moving average (ARMA) form. The control is based on modal pole placement scheme with the objective of vibration suppression. The control gains are calculated based on the identified ARMA parameters. Before using the identified parameters for control, detailed testing and validation procedures are carried out on the identified parameters. The full adaptive control scheme is demonstrated using the simulation for the 12 foot free-free beam apparatus at NASA Langley Research Center.
Sundararajan, N.↗
Experimental implementation of parameter adaptive control on a free-free beam
A method for identifying modal parameters has been integrated with a modal control scheme and implemented on an experimental beam at the NASA Langley Research Center. This work is the culmination of several studies to develop adaptive control schemes for large flexible spacecraft. The identification scheme is an equation-error technique which generates modal frequency and damping estimates on-line from a set of distributed displacement measurements. The control law is a modal pole placement technique with the objective of vibration suppression. Integration of the identification and control schemes is achieved through a series of tests which validate the identified parameters before they are used for control gain updating. Results using a low order controller show that control gains can be updated in real time based on the validated parameters to improve the performance of the closed loop system. Important factors in the implementation are the test criterion and the a priori assumption of mode shapes.
Williams, J. P.↗
Results of studies at Langley Research Center on the control of large space systems
A control moment gyro, an integrated power/attitude control system, and distributed adaptive control are discussed.
Montgomery, R. C.↗
Nonlinear control of an experimental beam by IMSC
Results are reported from an experiment designed to control the vibratory motion of a beam at NASA, Langley Research Center. The experimental setup consists of a free-free uniform beam acted upon by four electromagnetic force actuators, with the motion being measured by nine displacement sensors. The entire assembly is linked to a CDC Cyber 175 computer which permits on-line real-time computation of the control forces. The control scheme is based on Independent Modal-Space Control (IMSC), whereby the modal forces are computed using a nonlinear, on-off control law. The actuator forces are then synthesized using a linear transformation, resulting in quantized forces. The sensors data is processed by modal filters. It is observed that the controls designed on the basis of the IMSC method are very effective in suppressing the vibratory motion of the beam, even though there is about a 50 percent differene between the actual and the analytically computed frequencies.
Meirovitch, L.↗
Experiments using least square lattice filters for the identification of structural dynamics
An approach for identifying the dynamics of large space structures is applied to a free-free beam. In this approach the system's order is determined on-line, along with mode shapes, using recursive lattice filters which provide a least square estimate of the measurement data. The mode shapes determined are orthonormal in the space of the measurements and, hence, are not the natural modes of the structure. To determine the natural modes of the structure, a method based on the fast Fourier transform is used on the outputs of the lattice filter. These natural modes are used to obtain the modal amplitude time series which provides the input data for an output error parameter identification scheme that identifies the ARMA parameters of the difference equation model of the modes. the approach is applied to both simulated and experimental data.
Sundararajan, N.↗
Structural control research and experiments at NASA/LaRC
The advances made in the area of structural dynamics and control using the flexible beam facility at the NASA Langley Research Center are surveyed. Spectral attention is given to the progress in adaptive control and reliability improvements using advanced control concepts. Both theoretical and experimental results are given to delineate the nature of the work being undertaken. With regard to adaptive control, emphasis is placed on parameter and system identification and on comparisons between competing on-line algorithms. In addition, results are presented for on-line modal control laws that are interfaced to a parameter identification scheme. This gives an on-line distributed adaptive control system. With regard to reliability, a design process is outlined that incorporates reliability over the design mission life.
Montgomery, R. C.↗
Parameter testing for lattice filter based adaptive modal control systems
For Large Space Structures (LSS), an adaptive control system is highly desirable. The present investigation is concerned with an 'indirect' adaptive control scheme wherein the system order, mode shapes, and modal amplitudes are estimated on-line using an identification scheme based on recursive, least-squares, lattice filters. Using the identified model parameters, a modal control law based on a pole-placement scheme with the objective of vibration suppression is employed. A method is presented for closed loop adaptive control of a flexible free-free beam. The adaptive control scheme consists of a two stage identification scheme working in series and a modal pole placement control scheme. The main conclusion from the current study is that the identified parameters cannot be directly used for controller design purposes.
Sundararajan, N.↗
Reliability considerations in the placement of control system components
This paper presents a methodology, along with applications to a grid type structure, for incorporating reliability considerations in the decision for actuator placement on large space structures. The method involves the minimization of a criterion that considers mission life and the reliability of the system components. It is assumed that the actuator gains are to be readjusted following failures, but their locations cannot be changed. The goal of the design is to suppress vibrations of the grid and the integral square of the grid modal amplitudes is used as a measure of performance of the control system. When reliability of the actuators is considered, a more pertinent measure is the expected value of the integral; that is, the sum of the squares of the modal amplitudes for each possible failure state considered, multiplied by the probability that the failure state will occur. For a given set of actuator locations, the optimal criterion may be graphed as a function of the ratio of the mean time to failure of the components and the design mission life or reservicing interval. The best location of the actuators is typically different for a short mission life than for a long one.
Montgomery, R. C.↗
Structural control research and experiments at NASA/LaRC
Research progress in the area of structural dynamics and control using the flexible beam facility at the NASA Langley Research Center is reviewed. Particular attention is placed on the progress in adaptive control and reliability improvements using advanced control concepts. Both theoretical and experimental results are given to indicate the nature of the work being undertaken. In the adaptive control area, emphasis is placed on parameter and system identification and in comparison of competing on-line algorithms. Also, results are presented for on-line modal control laws that are interfaced to a parameter identification scheme. This provides an on-line distributed adaptive control system. In the reliability area, a design process is outlined that incorporates reliability over the design mission life.
Montgomery, R. C.↗
Decoupling the structural modes estimated using recursive lattice filters
A method is presented for decoupling modal amplitudes generated by recursive least squares lattice filters. The proposed method, which involves transformation of basis functions obtained from lattice filters, is illustrated using a free-free beam simulation. The decoupled mode shape functions are required for the implementation of an adaptive control scheme for large space systems.
Sundararajan, N.↗
Adaptive identification for the dynamics of large space structures
A new approach for identifying the dynamics of large space structures using noisy measurements is presented. In this approach, a modal system description is avoided and, hence, the a priori specification of model order. Instead, the system's order is recursively determined on-line, along with its parameters, using recursive lattice filters which are widely used in adaptive signal processing. The order determination is carried out based on statistical hypothesis testing theory. The approach is illustrated for the problem of identifying the structural dynamic characteristics of a free-free beam. Results on the effectiveness and accuracy of the identification scheme with respect to noise levels, sampling rates, and data window sizes are presented
Sundararajan, N.↗
Simulation and testing of digital control on a flexible beam
Large space structures are expected to have control problems due to low stiffness and damping, and control laws for these structures must deal with shape and configuration control as well as attitude and orbit maintenance. In general, these control tasks must be accomplished without adversely interacting with the lightly damped and low frequency vibration modes of the structure. Modal control schemes have been proposed to deal with these problems. A discrete time parameter adaptive control scheme which uses modal control has been proposed by Montgomery and Johnson (1978). In the present investigation the method considered by Montgomery and Johnson is applied to a homogeneous free-free beam in both numerical simulation and laboratory experimentation. Mathematical modeling of the beam is treated in a manner expedient for digital simulation and control implementation.
Williams, J. P.↗
Least-squares sequential parameter and state estimation for large space structures
This paper presents the formulation of simultaneous state and parameter estimation problems for flexible structures in terms of least-squares minimization problems. The approach combines an on-line order determination algorithm, with least-squares algorithms for finding estimates of modal approximation functions, modal amplitudes, and modal parameters. The approach combines previous results on separable nonlinear least squares estimation with a regression analysis formulation of the state estimation problem. The technique makes use of sequential Householder transformations. This allows for sequential accumulation of matrices required during the identification process. The technique is used to identify the modal prameters of a flexible beam.
Thau, F. E.↗