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At least 55 records · Page 3

The reduced order model problem in distributed parameter systems adaptive identification and control

The basic assumption that a large space structure can be decoupled preceding the application of reduced order active control was considered and alternative solutions to the control of such structures (in contrast to the strict modal control) were investigated. The transfer function matrix from the actuators to the sensors was deemed to be a reasonable candidate. More refined models from multivariable systems theory were studied and recent results in the multivariable control field were compared with respect to theoretical deficiencies and likely problems in application to large space structures.

Johnson, C. R., Jr.↗

A method for high order linear system reduction and nonlinear system simplification

Least-squares-type algorithms for reducing the order of linear systems in the frequency domain and simplifying nonlinear systems in time domain are developed and demonstrated. The possible model structures are represented as nodes in a tree, and costs along the branches are assigned using the repeated-Gram-Schmidt orthogonalization procedure of Desrochers and Saridis (1980), permitting identification of the optimal n-term model by searching the tree to depth n, with no need for parameter identification. The efficiency and flexibility of the algorithms is shown in applications to the eighth-order linear system studied by Hsia (1972), a three-state eight-nonlinear-term aircraft-dynamics problem, and the related linear-controller problem (Garrard and Jordan, 1977).

Desrochers, A. A.↗

Using integrals of the state transition matrix for efficient transient-response computations

An iterative technique for the computation of lower-order state systems with poles at the origin (such as aircraft lateral dynamics) or with time-polynomial inputs is developed and demonstrated. The integrated input or output signals are computed using the integrals of the state transition matrix, thus reducing the system order and computation time. In an application to the lateral response of a DC-8 aircraft (Grunwald, 1981), this method required only 7824 multiplication or addition operations (at fourth order) to achieve the accuracy obtained in 15,012 operations by a conventional sixth-order computation.

Grunwald, A. J.↗

State reduction for semi-Markov reliability models

Semi-Markov processes have proved to be an effective and convenient tool to construct models of systems that achieve reliability by redundancy and reconfiguration. These models are able to depict complex system architectures and to capture the dynamics of fault arrival and system recovery. A disadvantage of this approach is that the models can be extremely large, which poses both a model construction and a computational problem. Techniques are needed to reduce the model size. Because these systems are used in critical applications where failure can be expensive, there must be an analytically derived bound for the error produced by the model reduction technique. Automatic model generation programs have been written to help the reliability analyst produce models of complex systems. Because of the importance of these programs, the model reduction technique needs to be precise and easily implemented. This paper presents a model reduction technique called trimming that can be applied to a popular class of systems. An error bound for the trimming procedure is derived that uses readily available system parameters. The trimming procedure is precisely described and appears easy to implement in a model generation program.

Reduced order systems↗

Elevation control system model for the DSS 13 antenna

In order to meet the requirements for precision pointing of 34-m antennas, adequate control design and simulation software have to be developed along with a detailed description of the supporting analytical tools. This article describes a control system model for the elevation drive of the DSS 13 antenna. The model allows one to simulate elevation dynamics, cross-coupled dynamics in azimuth and elevation, and RF pointing error. A modal state-space model of the antenna structure was obtained from its finite-element model with a free rotating tipping structure. Model reduction techniques were applied separately for the antenna model and rate-loop model, thereby reducing the system order to one-third of the original one while preserving its dynamic properties. Extensive simulation results illustrate properties of the model.

Gawronski, W.↗

Mechanical Testing of PMCs under Simulated Rapid Heat-Up Propulsion Environments: In-Plane Compressive Behavior - II

Carbon fiber thermoset polymer matrix composites (PMC) with high temperature polyimide based in-situ polymerized monomer reactant (PMR) resin has been used for some time in applications which can see temperatures up to 550 F. Currently, graphite fiber PMR based composites are used in several aircraft engine components including the outer bypass duct for the GE F-404, exit flaps for the P&W F-100-229, and the core cowl for the GE/Snecma CF6-80A3. Newer formulations, including PMR-II-50 are being investigated as potential weight reduction replacements of various metallic components in next generation high performance propulsion rocket engines that can see temperatures which exceed 550 F. Extensive FEM thermal modeling indicates that these components are exposed to rapid heat-up rates (up to -200 F/sec) and to a maximum temperature of around 600 F. Even though the predicted maximum part temperatures were within the capability of PW-II-50, the rapid heat-up causes significant through-thickness thermal gradients in the composite part and even more unstable states when combined with moisture. Designing composite parts for such extreme service environments will require accurate measurement of intrinsic and transient mechanical properties and the hygrothermal performance of these materials under more realistic use conditions. The mechanical properties of polymers degrade when exposed to elevated temperatures even in the absence of gaseous oxygen. Accurate mechanical characterization of the material is necessary in order to reduce system weight while providing sufficient factors of safety. Historically, the testing of PMCs at elevated temperatures has been plagued by the antagonism between two factors. First, moisture has been shown to profoundly affect the mechanical response of these materials at temperatures above their glass transition temperature while concurrently lowering the material's Tg. Moisture phenomena is due to one or a combination of three effects, i.e., plastization of polymeric material by water, the internal pressure generated by the volatilization of water at elevated temperatures, and hydrolytic chemical decomposition. However, moisture is lost from the material at increasing rates as temperature increases. Second, because PMCs are good thermal insulators, when they are externally heated at even mild rates large thermal gradients can develop within the material. At temperatures where a material property changes rapidly with temperature the presence of a large thermal gradient is unacceptable for intrinsic property characterization purposes. Therefore, long hold times are required to establish isothermal conditions. However, in the service environments high-heating-rates, high temperatures, high-loading rates are simultaneous present along with residual moisture. In order to capture the effects of moisture on the material, holding at- temperature until isothermal conditions are reached is unacceptable particularly in materials with small physical dimensions. Thus, the effects due to moisture on the composite's mechanical characteristics, ie., their so-called analog response, may be instructive. One approach employed in this program was rapid heat-up (approx. 200 F/sec.) and loading of both dry and wet in-plane compressive specimens to examine the effects of moisture on this resin dominated mechanical property of the material.

Stokes, Eric H.↗

Influences of joystick spring resistance on the execution of simple and complex positioning movements

To provide good proprioceptive feedback in a manual control device for a designation task, spring resistance of a joystick was optimized by adjustment of centering force and deflection nonlinearly with each other by using the psychophysical method of cross modality matching. Designation with zero and first order systems showed that the coarse adjustment was insensitive to stick and certain task parameters, although it was influenced by some biomechanical parameters and the anticipated demands of the final control positioning. Only the more difficult fine adjustment is sensitive to parameter alterations and therefore suitable for optimization attempts. The strong centering of the stick by a nonlinear degressive spring resistance facilitates fine adjustment. Through this, total adjustment time with the first order system is reduced by more than thirty percent, compared to a linear resistance. Tracking experiments affirm the usefulness and preference of nonlinear spring resistance.

Rothbauer, G.↗

Model reduction for discrete bilinear systems

A model reduction method for discrete bilinear systems is developed which matches q sets of Volterra and covariance parameters. These parameters are shown to represent both deterministic and stochastic attributes of the discrete bilinear system. A reduced order model which matches these q sets of parameters is defined to be a q-Volterra covariance equivalent realization (q-Volterra COVER). An algorithm is presented which constructs a class of q-Volterra COVERs parameterized by solutions to a Hermitian, quadratic, matrix equation. The algorithm is applied to a bilinear model of a robot manipulator.

King, A. M.↗

Modeling and simulations of the DSS 13 antenna control system

A model of the antenna control system for the azimuth and elevation axes of the Deep Space Station (DSS) 13 antenna is developed. This model is used for simulation of elevation and azimuth dynamics, cross-coupled dynamics, and radio-frequency pointing error due to both input commands and wind disturbances. This model also serves as a tool for the antenna controller design. A modal state-space model of the antenna structure was obtained from its finite-element model with a free-rotating tipping structure and alidade. Model reduction techniques applied separately for the antenna structure, elevation, and azimuth drives, and rate-loop model reduce the system order to one-third of that of the original, while preserving its significant dynamic properties. Extensive simulation results illustrate properties of the model.

Gawronski, W.↗

Discrete-time model reduction in limited frequency ranges

A mathematical formulation for model reduction of discrete time systems such that the reduced order model represents the system in a particular frequency range is discussed. The algorithm transforms the full order system into balanced coordinates using frequency weighted discrete controllability and observability grammians. In this form a criterion is derived to guide truncation of states based on their contribution to the frequency range of interest. Minimization of the criterion is accomplished without need for numerical optimization. Balancing requires the computation of discrete frequency weighted grammians. Close form solutions for the computation of frequency weighted grammians are developed. Numerical examples are discussed to demonstrate the algorithm.

Horta, Lucas G.↗

An unsymmetric Lanczos algorithm for damped structural dynamics systems

A one-sided, unsymmetric block Lanczos algorithm is proposed for the model reduction of structural dynamics systems with unsymmetric damping and/or stiffness matrices. The algorithm is a three-term iteration scheme, which transforms the system matrix into an almost skew-symmetric, block-tridiagonal form. The Lanczos reduced-order model is guaranteed to be stable if the full-order system is stable. For unstable systems, a shifting method is available. Also, the algorithm offers flexibility in the choice of starting vectors and thus can yield more accurate reduced-order models. A linear system example and a plane truss structure example are used to show the efficacy of the proposed method.

Su, Tzu-Jeng↗

Component model reduction via the projection and assembly method

The problem of acquiring a simple but sufficiently accurate model of a dynamic system is made more difficult when the dynamic system of interest is a multibody system comprised of several components. A low order system model may be created by reducing the order of the component models and making use of various available multibody dynamics programs to assemble them into a system model. The difficulty is in choosing the reduced order component models to meet system level requirements. The projection and assembly method, proposed originally by Eke, solves this difficulty by forming the full order system model, performing model reduction at the the system level using system level requirements, and then projecting the desired modes onto the components for component level model reduction. The projection and assembly method is analyzed to show the conditions under which the desired modes are captured exactly; to the numerical precision of the algorithm.

Bernard, Douglas E.↗

A hierarchy for modeling high speed propulsion systems

General research efforts on reduced order propulsion models for control systems design are overviewed. Methods for modeling high speed propulsion systems are discussed including internal flow propulsion systems that do not contain rotating machinery, such as inlets, ramjets, and scramjets. The discussion is separated into four areas: (1) computational fluid dynamics models for the entire nonlinear system or high order nonlinear models; (2) high order linearized models derived from fundamental physics; (3) low order linear models obtained from the other high order models; and (4) low order nonlinear models (order here refers to the number of dynamic states). Included in the discussion are any special considerations based on the relevant control system designs. The methods discussed are for the quasi-one-dimensional Euler equations of gasdynamic flow. The essential nonlinear features represented are large amplitude nonlinear waves, including moving normal shocks, hammershocks, simple subsonic combustion via heat addition, temperature dependent gases, detonations, and thermal choking. The report also contains a comprehensive list of papers and theses generated by this grant.

Hartley, Tom T.↗

A hierarchy for modeling high speed propulsion systems

General research efforts on reduced order propulsion models for control systems design are overviewed. Methods for modeling high speed propulsion systems are discussed including internal flow propulsion systems that do not contain rotating machinery such as inlets, ramjets, and scramjets. The discussion is separated into four sections: (1) computational fluid dynamics model for the entire nonlinear system or high order nonlinear models; (2) high order linearized model derived from fundamental physics; (3) low order linear models obtained from other high order models; and (4) low order nonlinear models. Included are special considerations on any relevant control system designs. The methods discussed are for the quasi-one dimensional Euler equations of gasdynamic flow. The essential nonlinear features represented are large amplitude nonlinear waves, moving normal shocks, hammershocks, subsonic combustion via heat addition, temperature dependent gases, detonation, and thermal choking.

Hartley, Tom T.↗

Space power system design and development from an economic point of view

The concept of a satellite solar power system offers a feasible, but unproven, long-range energy alternative. While the basic physics of these systems is understood, many developments are necessary in order to reduce the system cost to the point of being cost-competitive with alternative energy sources. Thus, a substantial technology advancement and verification program, plus test and demonstration satellite programs are necessary before a full-scale satellite can be designed and built. It is important to properly identify those elements of the technology that should be subject to development efforts, the goals of the corresponding development programs and the appropriate funding levels and schedules. Systems studies and designs play a major role in rationally formulating a development program. This paper uses an economic approach to place these studies into a framework for formulating a viable satellite solar power system development plan.

Hazelrigg, G. A., Jr.↗

Sliding regimes on slow manifolds of systems with fast actuators

In this article the slow manifold of a system with actuator parasitics is used as a sliding surface on which a Variable Structure Controller recovers the qualitative properties of the reduced order, closed loop system obtained from an ideal actuator-based feedback controller design. Illustrative examples are presented, where (1) the simplicity of reduced order singular perturbation design methods; and (2) the robustness of Variable Structure sliding modes, are advantageously combined.

Sira-Ramirez, Hebertt↗

Nonlinear analysis of rotor-bearing systems using component mode synthesis

The method of component mode synthesis is developed to determine the forced response of nonlinear, multishaft, rotor-bearing systems. The formulation allows for simulation of system response due to blade loss, distributed unbalance, base shock, maneuver loads, and specified fixed frame forces. The motion of each rotating component of the system is described by superposing constraint modes associated with boundary coordinates and constrained precessional modes associated with internal coordinates. The precessional modes are truncated for each component and the reduced component equations are assembled with the nonlinear supports and interconnections to form a set of nonlinear system equations of reduced order. These equations are then numerically integrated to obtain the system response. A computer program, which is presently restricted to single shaft systems, has been written and results are presented for transient system response associated with blade loss dynamics with squeeze film dampers, and with interference rubs.

Nelson, H. D.↗

Bounding filters in the presence of inexactly known parameters.

Optimum bounding filters are derived for a specific version (steady state time-invariant with scalar observations) of the Kalman-Bucy filtering problem with inexactly known system parameters and for the Wiener filtering problem with inexactly known spectral densities. The designed filter obtains a bound on the actual error covariance which is not known, and it also prevents apparent divergence. Conditions are derived for the design of the optimum bounding filter within a permissible class of solutions; this turns out to be the min-max mean-square error filter for an extended class of solutions. The bounding filter can be of lower order than the original system, and a technique is devised for reducing the order of the filtering system and concurrently obtaining a figure of merit for its performance.

Nahi, N. E.↗