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The major accomplishments of this research are: (1) the refinement and documentation of a multi-input, multi-output modal parameter estimation algorithm which is applicable to general linear, time-invariant dynamic systems; (2) the development and testing of an unsymmetric block-Lanzcos algorithm for reduced-order modeling of linear systems with arbitrary damping; and (3) the development of a control-structure-interaction (CSI) test facility.
As modal testing techniques have improved in recent years, the demands placed on the accuracy of modal test results have increased. This paper describes a new multi-input, multi-output modal parameter estimation algorithm suitable for the identification of reduced-order models of structures. The method described is a frequency-domain method based on excitation and response spectra. The principal features of the algorithm are: (1) applicability to general linear, time-invariant systems, (2) direct use of multiple input and multiple response data, (3) identification of reduced-order models with minimum user interaction through the use of two automatic model-reduction techniques, (4) identification of a consistent set of modal parameters through the use of numerically stable least-squares techniques, and (5) complete user documentation.
A classification of all the compensators that stabilize a given general plant in a linear, time-invariant multi-input, multi-output feedback system is developed. This classification, along with the associated necessary and sufficient conditions for stability of the feedback system, is achieved through the introduction of a new parameterization, referred to as R-Parameterization, which is a dual of the familiar Q-Parameterization. The classification is made to the stability conditions of the compensators and the plant by themselves; and necessary and sufficient conditions are based on the stability of Q and R themselves.
The authors treat the robust stability issue using the characteristic polynomial, for two different cases: first in coefficient space with respect to perturbations in the coefficient of the characteristic polynomial; and then for a control system containing perturbed parameters in the transfer function description of the plant. In coefficient space, a simple expression is first given for the l-(squared) stability margin for both the monic and nonmonic cases. Following this, a method is given to find the l(infinity) margin, and the method is extended to reveal much larger stability regions. In parameter space the authors consider all single-input (multi-output) or single-output (multi-input) systems with a fixed controller and a plant described by a set of transfer functions which are ratios of polynomials with variable coefficients. A procedure is presented to calculate the radius of the largest stability ball in the space of these variable parameters. The calculation serves as a stability margin for the control system. The formulas that result are quasi-closed-form expressions for the stability margin and are computationally efficient.
A new approach for the eigenvalue assignment of linear, first-order, time-invariant systems using output feedback is developed. The approach can assign the maximum allowable number of closed-loop eigenvalues through output feedback provided that the system is fully controllable and observable, and both the input influence and output influence matrices are full rank. First, a collection of bases for the space of attainable closed-loop eigenvectors is generated using the Singular Value Decomposition or QR Decomposition techniques. Then, an algorithm based on subspace intersections is developed and used to compute the corresponding coefficients of the bases, and the required output feedback gain matrix. Moreover, the additional freedom provided by the multi-inputs and multi-outputs beyond the eigenvalue assignment is characterized for possible exploitation. A numerical example is given to demonstrate the viability of the proposed approach.
Future space manipulators may need translational base motion to expand the access region of a manipulator. An experiment was conducted to demonstrate slewing of flexible structures with coupled rotational and translational axes while simultaneously suppressing vibrational motion during the maneuver. In the experiment, a flexible steel beam carried by a translational cart was maneuvered by an active controller to perform position-control tasks. Experimental results are presented to show how the flexibility of the steel beam influences the multi-input multi-output feedback controller.
Control theory design package offers engineer full range of subroutines to manipulate and solve Linear-Quadratic-Gaussian types of problems. ORACLS is rigorous tool, intended for multi-input and multi-output dynamic systems in both continuous and discrete form. Written in FORTRAN.
A description of the advanced structures/control integrated experiment (ASCIE) experimental setup, a generic test bed for several essential technologies was presented. In particular its multi-input, multi-output, non-collocated control system and its complex structural dynamics, characteristic of large segmented systems make it an ideal test bed for Control-Structure Interaction (CSI) experiments. The high accuracy of its measurement system will make it possible to investigate the dynamics of microvibrations and its implication for the CSI phenomenon.
The theory of polynomial matrices plays a key role in the design and analysis of multi-input multi-output control and communications systems using frequency domain methods. Examples include coprime factorizations of transfer functions, cannonical realizations from matrix fraction descriptions, and the transfer function design of feedback compensators. Typically, such problems abstract in a natural way to the need to solve systems of Diophantine equations or systems of linear equations over polynomials. These and other problems involving polynomial matrices can in turn be reduced to polynomial matrix triangularization procedures, a result which is not surprising given the importance of matrix triangularization techniques in numerical linear algebra. Matrices with entries from a field and Gaussian elimination play a fundamental role in understanding the triangularization process. In the case of polynomial matrices, matrices with entries from a ring for which Gaussian elimination is not defined and triangularization is accomplished by what is quite properly called Euclidean elimination. Unfortunately, the numerical stability and sensitivity issues which accompany floating point approaches to Euclidean elimination are not very well understood. New algorithms are presented which circumvent entirely such numerical issues through the use of exact, symbolic methods in computer algebra. The use of such error-free algorithms guarantees that the results are accurate to within the precision of the model data--the best that can be hoped for. Care must be taken in the design of such algorithms due to the phenomenon of intermediate expressions swell.
The notion of controller partitioning is described. Conditions are developed under which the input/output behavior of a multi-input multi-output centralized controller can be exactly matched by two separate subsystem controllers interconnected through output crossfeed. A systematic method is developed for determining a controller partitioning which best approximates the input/output behavior of the centralized controller for the general case when the exact matching conditions are not satisfied. The controller partitioning procedure is demonstrated for a centralized integrated flight/propulsion controller designed in a previous study.
The component technologies were developed required for an advanced control moment gyro (CMG) type of slewing actuator for large payloads. The key component of the CMG is a large-angle magnetic suspension (LAMS). The LAMS combines the functions of the gimbal structure, torque motors, and rotor bearings of a CMG. The LAMS uses a single superconducting source coil and an array of cryoresistive control coils to produce a specific output torque more than an order of magnitude greater than conventional devices. The designed and tested LAMS system is based around an available superconducting solenoid, an array of twelve room-temperature normal control coils, and a multi-input, multi-output control system. The control laws were demonstrated for stabilizing and controlling the LAMS system.
A design strategy which integrates model reduction by modal cost analysis and a multiobjective controller design is proposed. The necessary modeling and control algorithms are easily programmed in Matlab standard software. Hence, this method is very practical for controller design for large space structures. The design algorithm also solves the very important problem of tuning multiple loop controllers (multi-input, multi-output, or MIMO). Instead of the single gain change that is used in standard root locus and gain and phase margin theories, this method tunes multiple loop controllers from low to high gain in a systematic way in the design procedure. This design strategy is applied to NASA's Mini-Mast system.
This program demonstrated the technical feasibility of constructing large-stroke magnetic suspensions that can meet the active vibration isolation requirements of Space Station. These requirements include: (1) strokes over 1 cm in all directions, (2) actuator bandwidths over 100 Hz, (3) isolator roll-off frequencies below 10(exp -2) Hertz, and (4) force capability over 1 Newton in all axes. The 100 Hz actuator bandwidth allows the suspension to reject any direct force disturbances that act on the microgravity experiment, for example forces created by cable connections. The low isolator roll-off frequency and large stroke allow the magnetic suspension to isolate the microgravity experiment from Space Station vibrations above the roll-off frequency. The capability to meet these requirements was demonstrated by designing, constructing and testing a six-degree-of-freedom, prototype magnetic suspension system that featured high-performance, Lorentz-force actuators and full multi-input, multi-output control. This prototype suspension is designed to isolate large orbiter locker experiments under typical spacecraft constraints of size, weight, and power. Suspension in the full six-degrees-of-freedom was successfully demonstrated in this program while using a gravity-force unload mechanism to simulate a space environment. The prototype isolator is capable of space-based isolation service with relatively minor modification. The use of advanced, nonlinear control algorithms were investigated on a specially designed single-degree-of-freedom testbed. This low acceleration test facility simulates the Space Station vibration isolation problem in a single horizontal axis with low-friction, air-slide support. This allowed testing at the desired microgravity levels, without the gravity bias effects that are seen in a full six-degrees-of-freedom suspension. Precision components were used to reduce residual accelerations to microgravity levels so that the effects of sensor, actuator, and electronic noise could be evaluated. During the Phase 2 program, this testbed was used to demonstrate the advantages of nonlinear control algorithms to provide increased vibration isolation performance.
Quantitative Feedback Theory describes a frequency-domain technique for the design of multi-input, multi-output control systems which meet time or frequency domain performance criteria when specified uncertainty exists in the linear description of the vehicle dynamics. Quantitative Feedback Theory is applied to the design of the longitudinal flight control system for a linear uncertain model of the AH-64 rotorcraft. In this model, the uncertainty is assigned, and is assumed to be attributable to actual uncertainty in the dynamic model and to the changes in the vehicle aerodynamic characteristics which occur near hover. The model includes an approximation to the rotor and actuator dynamics. The design example indicates the manner in which handling qualities criteria may be incorporated into the design of realistic rotorcraft control systems in which significant uncertainty exists in the vehicle model.
A multi-input multi-output system identification technique is used to obtain linearized point models of the Space Shuttle Main Engine (SSME) at five different operating conditions (power levels) from the engine firing data. This study demonstrates that the open-loop dynamics of the SSME can be successfully modeled from the engine firing data. The identified linear models may be used for fault detection studies and control system design and development.
This paper derives algorithms for identifying autoregressive models, with external input, of multi-input multi-output systems from data using a fast transversal filter or a least-squares lattice filter. The autoregressive models including external inputs are used to identify state-space models and the corresponding observer/Kalman filter gains of the system. The derivation is an extension of scalar autoregressive model approaches, modified to cope with multivariables, external inputs and an extra direct-influence term. Comparisons between the fast transversal filter, the least-squares lattice filter and the classical least-squares method are made in terms of complexity, computational cost and practical applications issues. A numerical example is included to illustrate the approach.
This paper demonstrates a new system identification approach of using Lanczos coordinates in place of modal coordinates. Identified experimental Lanczos vectors can be directly used in many structural dynamics analysis applications. A multi-input, multi-output frequency-domain technique was used to extract system matrices and an unsymmetric block Lanczos algorithm was used to reduce the order of the experimental model. A cantilever beam example showed promising results, indicating that a new system identification approach using Lanczos coordinates is worthy of further study.
The control of structures for vibration suppression is discussed in the context of using smart materials and structures. Here the use of smart structures refers to using embedded piezoelectric devices as both control actuators and sensors. Using embedded sensors and actuators allows great improvements in performance over traditional structures (both passive and active) for vibration suppression. The application of smart structures to three experimental flexible structures is presented. The first is a flexible beam, the second is a flexible beam undergoing slewing motion, the third is a ribbed antenna. A simple model of a piezoelectric actuator/sensor is presented. The equations of motion for each structure is presented. The control issues considered as those associated with multi-input, multi-output control, PID control and LQR control implementation. A modern control analysis illustrates the usefulness of smart structures for vibration suppression.