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Plotting digital simulation errors for a spring-mass-damper system and using these error curves to select type of integration, feedback update method, and number of samples per cycle at resonance reduces excessive number of samples per cycle and unnecessary iterations.
Slosh dynamics particularly in high gravity regime is of high interest to the NASA Human Landing Systems program, which aims to return humans to the Moon. This paper reexamines the commonly accepted equivalence between pendulum and mass-spring-damper mechanical analogies, demonstrating the differences through simulations and their impact on design and analysis. This study re-derives equations of motion for these mechanical models including mass-spring-damper (MSD) and pendulum by relaxing simplifying assumptions that had been typically applied to large launch vehicles and may be violated for lunar and planetary landing applications. The newly derived equations uncovers potential modeling gaps when applying the pendulum and MSD models, and the need for additional considerations in their application. Finally, the newly derived equations are validated using MathWorks® Simscape™ Multibody™ dynamics toolbox simulation.
Robust stabilization of uncertain systems has been extensively investigated and the stability test for the whole set of uncertain parameters has been reduced to a finite number of test points, four points for the characteristic polynomial with independent coefficients. As a result the robust stability margin can be determined using a reasonable amount of computation. It is impossible to apply the results of the test to a practical system as the coefficients of the characteristic polynomial for a physical system are usually functions of uncertain parameters. However, many physical systems may be represented by a second-order mass-spring-damper system with a special multilinear form in its characteristic polynomial. This paper investigates second-order mass-spring-damper systems and the reduction of the number of test points. It is shown that such a system with arbritrary compensators always has a multilinear characteristic polynomial. It is also shown that a line in the two-dimensional parameter space forms the boundary after the mapping of a multilinear characteristic polynomial and this interior extreme line forms a conic curve in the complex plane. The boundary of uncertain domain for a multilinear polynomial with two uncertainty parameters can be determined analytically using this curve, and the four sides image of a square of the uncertain parameter. Therefore, the stability margin may be determined by checking the intersections of the boundary with the zero point. A similar procedure can be used for second-order systems with more than two uncertainty parameters when parameter optimization is used in determining the boundary.
The focus is on a noise control method which considers aircraft fuselages lined with panels alternately tuned to frequencies above and below the frequency that must be attenuated. An interior noise reduction called alternate resonance tuning (ART) is described both theoretically and experimentally. Problems dealing with tuning single paneled wall structures for optimum noise reduction using the ART methodology are presented, and three theoretical problems are analyzed. The first analysis is a three dimensional, full acoustic solution for tuning a panel wall composed of repeating sections with four different panel tunings within that section, where the panels are modeled as idealized spring-mass-damper systems. The second analysis is a two dimensional, full acoustic solution for a panel geometry influenced by the effect of a propagating external pressure field such as that which might be associated with propeller passage by a fuselage. To reduce the analysis complexity, idealized spring-mass-damper panels are again employed. The final theoretical analysis presents the general four panel problem with real panel sections, where the effect of higher structural modes is discussed. Results from an experimental program highlight real applications of the ART concept and show the effectiveness of the tuning on real structures.
This paper presents a novel method to design decentralized controllers for large complex flexible structures by using the idea of joint decoupling. Decoupling of joint degrees of freedom from the interior degrees of freedom is achieved by setting the joint actuator commands to cancel the internal forces exerting on the joint degrees of freedom. By doing so, the interactions between substructures are eliminated. The global structure control design problem is then decomposed into several substructure control design problems. Control commands for interior actuators are set to be localized state feedback using decentralized observers for state estimation. The proposed decentralized controllers can operate successfully at the individual substructure level as well as at the global structure level. Not only control design but also control implementation is decentralized. A two-component mass-spring-damper system is used as an example to demonstrate the proposed method.
The rotational stability of a dual-spin satellite consisting of a main body and a symmetric rotor, both spinning about a common axis, is investigated. The main body is equipped with a spring-mass damper, while a partially filled viscous ring damper is mounted on the rapidly spinning rotor. The effect of fluid motion on the rotational stability of the satellite is calculated, considering the fluid as a single particle moving in a tube with viscous damping. Time constants are obtained by solving approximate equations of motion for the nutation-synchronous and the spin-synchronous modes, and the results are found to agree well with the numerical integrations of the exact equations. A limit cycle may exist for some configurations; the nutation angle tends to increase in such cases.
Attitude control and various structural aspects of NASA's permanent manned Space Station are discussed in the framework of design flexibility, obsolescence as a deterent to a long operational life, modularity, and autonomy. Among the variable factors of specific importance, consideration is given to internal factors, such as inertial variations (up to 400 percent), center of mass movements (up to 28 m), and shifts in modal characteristics, as well as to external torque shifts associated with aerodynamic moments and gravity gradients. The compatibility among multiple-user requirements is also considered. As the Station is a low-orbit spacecraft, its attitude will be greatly affected by the inhomogeneity of the atmosphere, placing a priority on the attitude control techniques. A combination of passive (spring-mass-damper suspension systems) and active (sensor/disturbance-canceling device) systems are expected to be used.
Model problem development and analysis continues with the Alternate Resonance Tuning (ART) concept. The various topics described are presently at different stages of completion: investigation of the effectiveness of the ART concept under an external propagating pressure field associated with propeller passage by the fuselage; analysis of ART performance with a double panel wall mounted in a flexible frame model; development of a data fitting scheme using a branch analysis with a Newton-Raphson scheme in multiple dimensions to determine values of critical parameters in the actual experimental apparatus; and investigation of the ART effect with real panels as opposed to the spring-mass-damper systems currently used in much of the theory.
An asymptotic LQG design synthesis technique is described which explicitly includes a class of structured plant uncertainties by viewing plant parameter variations as an internal feedback loop. A direct structural relationship between this class of parameter uncertainties and the weighting matrices in the design of the LQG compensator is exploited by an asymptotic procedure in which either the regulator or the filter become insensitive to parameter variations. This asymptotic approach represents a generalization of the LQG/LTR technique. Controllers designed by this new LQG method and LQG/LTR are compared by application to a mass-spring-damper system which approximates the dynamics of flexible structures. For both colocated and noncolocated sensors and actuators configurations, the LQG/LTR design is extremely sensitive to parameter variations whereas the new LQG design allows considerably improved parameter robustness.
A stability analysis for robot manipulators under the influence of external forces is presented. Several control objectives are considered: rejecting the external force as a source of disturbance, complying to the external force as a generalized mass-spring-damper system, and actively controlling the external force when a dynamic model for the environment is available. An explanation of instability is given for the case in which the environment has flexibility and the gains are inappropriately chosen. When the environment is stiff in the force control subspace, robust stability can be achieved via the integral force feedback.
A decentralized control design method is presented for large complex flexible structures by using the idea of joint decoupling. The derivation is based on a coupled substructure state-space model, which is obtained from enforcing conditions of interface compatibility and equilibrium to the substructure state-space models. It is shown that by restricting the control law to be localized state feedback and by setting the joint actuator input commands to decouple joint 'degrees of freedom' (dof) from interior dof, the global structure control design problem can be decomposed into several substructure control design problems. The substructure control gains and substructure observers are designed based on modified substructure state-space models. The controllers produced by the proposed method can operate successfully at the individual substructure level as well as at the global structure level. Therefore, not only control design but also control implementation is decentralized. Stability and performance requirement of the closed-loop system can be achieved by using any existing state feedback control design method. A two-component mass-spring damper system and a three-truss structure are used as examples to demonstrate the proposed method.
Robust stability conditions obtained through generalization of the notion of energy dissipation in physical systems are discussed in this report. Linear time-invariant (LTI) systems which dissipate energy corresponding to quadratic power functions are characterized in the time-domain and the frequency-domain, in terms of linear matrix inequalities (LMls) and algebraic Riccati equations (ARE's). A novel characterization of strictly dissipative LTI systems is introduced in this report. Sufficient conditions in terms of dissipativity and strict dissipativity are presented for (1) stability of the feedback interconnection of dissipative LTI systems, (2) stability of dissipative LTI systems with memoryless feedback nonlinearities, and (3) quadratic stability of uncertain linear systems. It is demonstrated that the framework of dissipative LTI systems investigated in this report unifies and extends small gain, passivity, and sector conditions for stability. Techniques for selecting power functions for characterization of uncertain plants and robust controller synthesis based on these stability results are introduced. A spring-mass-damper example is used to illustrate the application of these methods for robust controller synthesis.
The free-piston Stirling convertor end-to-end modeling effort at NASA Glenn Research Center (GRC) has produced a software-based test bed in which free-piston Stirling convertors can be simulated and evaluated. The simulation model includes all the components of the convertor - the Stirling cycle engine, linear alternator, controller, and load. This paper is concerned with controllers. It discusses three controllers that have been studied using this model. Case motion has been added to the model recently so that effects of differences between convertor components can be simulated and ameliorative control engineering techniques can be developed. One concern when applying a system comprised of interconnected mass-spring-damper components is to prevent operation in any but the intended mode. The design mode is the only desired mode of operation, but all other modes are considered in controller design.
Abstract The majority of literature on robust control assumes that a design model is available and that the uncertainty model bounds the actual variations about the nominal model. However, methods for generating accurate design models have not received as much attention in the literature. The influence of the level of accuracy of the uncertainty model on closed loop performance has received even less attention. The research reported herein is an initial step in applying and extending the concept of model validation to the problem of obtaining practical uncertainty models for robust control analysis and design applications. An extension of model validation called 'sequential validation' is presented and applied to a simple spring-mass-damper system to establish the feasibility of the approach and demonstrate the benefits of the new developments.
Cryocooler thermal and vibrational performance is determined, fundamentally, by the dynamic interactions between the mechanical system and the working fluid. This paper explores the effect of working-fluid characteristics on the mechanical response of the cooler. Experimental data collected from two coolers characterized under the Jet Propulsion Laboratory's extensive program of cryocooler testing and characterization show that a classical single-degree-of-freedom spring-mass-damper model does not capture the full frequency dependence of the mechanical response. The data from the two modes of cooler operation (slosh and head-to-head) are used to motivate the explanation that working-fluid characteristics dominate at high frequencies, and mechanical system characteristics dominate at lower frequencies. Operating temperature is shown to be a significant factor in determining resonance behavior. Finally, the discussion provides a framework within which resonate parameters and cooler characteristics can be extracted from the experimental data.
A dynamic model of a high-power Stirling convertor has been developed for space nuclear power systems modeling. The model is based on the Component Test Power Convertor (CTPC), a 12.5-kWe free-piston Stirling convertor. The model includes the fluid heat source, the Stirling convertor, output power and heat rejection. The Stirling convertor model includes the Stirling cycle thermodynamics, heat flow, mechanical mass-spring damper systems, and the linear alternator. The model was validated against test data. Both nonlinear and linear versions of the model were developed. The linear version algebraically couples two separate linear dynamic models; one model of the Stirling cycle and one model of the thermal system, through the pressure factors. Future possible uses of the Stirling system dynamic model are discussed. A pair of commercially available 1-kWe Stirling convertors is being purchased by NASA Glenn Research Center. The specifications of those convertors may eventually be incorporated into the dynamic model and analysis compared to the convertor test data. Subsequent potential testing could include integrating the convertors into a pumped liquid metal hot-end interface. This test would provide more data for comparison to the dynamic model analysis.
A dynamic model of a high-power Stirling convertor has been developed for space nuclear power systems modeling. The model is based on the Component Test Power Convertor (CTPC), a 12.5-kWe free-piston Stirling convertor. The model includes the fluid heat source, the Stirling convertor, output power, and heat rejection. The Stirling convertor model includes the Stirling cycle thermodynamics, heat flow, mechanical mass-spring damper systems, and the linear alternator. The model was validated against test data. Both nonlinear and linear versions of the model were developed. The linear version algebraically couples two separate linear dynamic models; one model of the Stirling cycle and one model of the thermal system, through the pressure factors. Future possible uses of the Stirling system dynamic model are discussed. A pair of commercially available 1-kWe Stirling convertors is being purchased by NASA Glenn Research Center. The specifications of those convertors may eventually be incorporated into the dynamic model and analysis compared to the convertor test data. Subsequent potential testing could include integrating the convertors into a pumped liquid metal hot-end interface. This test would provide more data for comparison to the dynamic model analysis.
Propellant slosh is a potential source of disturbance critical to the stability of space vehicle. The sloshing dynamics is typically represented by a mechanical model of spring mass damper. This mechanical model is then included in the equation of motion of the entire vehicle for Guidance, Navigation and Control analysis. The typical parameters required by the mechanical model include natural frequency of the sloshing, sloshing mass, sloshing mass center coordinates, and critical damping coefficient. During the 1960 s US space program, these parameters were either computed from analytical solution for simple geometry or by experimental testing for the sub-scaled configurations. The purpose of this work is to demonstrate the soundness of a CFD approach in modeling the detailed fluid dynamics of tank sloshing and the excellent accuracy in extracting mechanical properties for different tank configurations and at different fill levels. The validation studies included straight cylinder against analytical solution, and sub-scaled Centaur LOX and LH2 tanks with and without baffles against experimental results. This effort shows that CFD technology can provide accurate mechanical parameters for any tank configuration, and is especially valuable to the future design of propellant tanks, as there is no previous experimental data available for the same size and configuration.