Results for “Dynamical Systems” — Page 75

NASA NTRS2006

Nonlinear consider covariance analysis using a sigma-point filter formulation

The research reported here extends the mathematical formulation of nonlinear, sigma-point estimators to enable consider covariance analysis for dynamical systems. This paper presents a novel sigma-point consider filter algorithm, for consider-parameterized nonlinear estimation, following the unscented Kalman filter (UKF) variation on the sigma-point filter formulation, which requires no partial derivatives of dynamics models or measurement models with respect to the parameter list. It is shown that, consistent with the attributes of sigma-point estimators, a consider-parameterized sigma-point estimator can be developed entirely without requiring the derivation of any partial-derivative matrices related to the dynamical system, the measurements, or the considered parameters, which appears to be an advantage over the formulation of a linear-theory sequential consider estimator. It is also demonstrated that a consider covariance analysis performed with this 'partial-derivative-free' formulation yields equivalent results to the linear-theory consider filter, for purely linear problems.

covariance↗

DOE OSTI2013

Final Report. Analysis and Reduction of Complex Networks Under Uncertainty

The project was a collaborative effort among MIT, Sandia National Laboratories (local PI Dr. Habib Najm), the University of Southern California (local PI Prof. Roger Ghanem), and The Johns Hopkins University (local PI Prof. Omar Knio, now at Duke University). Our focus was the analysis and reduction of large-scale dynamical systems emerging from networks of interacting components. Such networks underlie myriad natural and engineered systems. Examples important to DOE include chemical models of energy conversion processes, and elements of national infrastructure—e.g., electric power grids. Time scales in chemical systems span orders of magnitude, while infrastructure networks feature both local and long-distance connectivity, with associated clusters of time scales. These systems also blend continuous and discrete behavior; examples include saturation phenomena in surface chemistry and catalysis, and switching in electrical networks. Reducing size and stiffness is essential to tractable and predictive simulation of these systems. Computational singular perturbation (CSP) has been effectively used to identify and decouple dynamics at disparate time scales in chemical systems, allowing reduction of model complexity and stiffness. In realistic settings, however, model reduction must contend with uncertainties, which are often greatest in large-scale systems most in need of reduction. Uncertainty is not limited to parameters; one must also address structural uncertainties—e.g., whether a link is present in a network—and the impact of random perturbations, e.g., fluctuating loads or sources. Research under this project developed new methods for the analysis and reduction of complex multiscale networks under uncertainty, by combining computational singular perturbation (CSP) with probabilistic uncertainty quantification. CSP yields asymptotic approximations of reduceddimensionality “slow manifolds” on which a multiscale dynamical system evolves. Introducing uncertainty in this context raised fundamentally new issues, e.g., how is the topology of slow manifolds transformed by parametric uncertainty? How to construct dynamical models on these uncertain manifolds? To address these questions, we used stochastic spectral polynomial chaos (PC) methods to reformulate uncertain network models and analyzed them using CSP in probabilistic terms. Finding uncertain manifolds involved the solution of stochastic eigenvalue problems, facilitated by projection onto PC bases. These problems motivated us to explore the spectral properties stochastic Galerkin systems. We also introduced novel methods for rank-reduction in stochastic eigensystems—transformations of a uncertain dynamical system that lead to lower storage and solution complexity. These technical accomplishments are detailed below. This report focuses on the MIT portion of the joint project.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Evolution of Robustness in Growing Random Networks

Networks are widely used to model the interaction between individual dynamic systems. In many instances, the total number of units and interaction coupling are not fixed in time, and instead constantly evolve. In networks, this means that the number of nodes and edges both change over time. Various properties of coupled dynamic systems, such as their robustness against noise, essentially depend on the structure of the interaction network. Therefore, it is of considerable interest to predict how these properties are affected when the network grows as well as their relationship to the growth mechanism. Here, we focus on the time evolution of a network’s Kirchhoff index. We derive closed-form expressions for its variation in various scenarios, including the addition of both edges and nodes. For the latter case, we investigate the evolution where single nodes with one or two edges connecting to existing nodes are added recursively to a network. In both cases, we derive the relations between the properties of the nodes to which the new node connects along with the global evolution of network robustness. In particular, we show how different scalings of the Kirchhoff index can be obtained as a function of the number of nodes. We illustrate and confirm this theory via numerical simulations of randomly growing networks.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2014

Statistical Mechanics of Turbulent Dynamos

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Shebalin, John V.↗

NASA NTRS2014

MHD Turbulence and Magnetic Dynamos

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Shebalin, John V↗

DOE OSTI2016

Structural transitions and hysteresis in clump- and stripe-forming systems under dynamic compression

In using numerical simulations, we study the dynamical evolution of particles interacting via competing long-range repulsion and short-range attraction in two dimensions. The particles are compressed using a time-dependent quasi-one dimensional trough potential that controls the local density, causing the system to undergo a series of structural phase transitions from a low density clump lattice to stripes, voids, and a high density uniform state. The compression proceeds via slow elastic motion that is interrupted with avalanche-like bursts of activity as the system collapses to progressively higher densities via plastic rearrangements. The plastic events vary in magnitude from small rearrangements of particles, including the formation of quadrupole-like defects, to large-scale vorticity and structural phase transitions. In the dense uniform phase, the system compresses through row reduction transitions mediated by a disorder-order process. We also characterize the rearrangement events by measuring changes in the potential energy, the fraction of sixfold coordinated particles, the local density, and the velocity distribution. At high confinements, we find power law scaling of the velocity distribution during row reduction transitions. We observe hysteresis under a reversal of the compression when relatively few plastic rearrangements occur. The decompressing system exhibits distinct phase morphologies, and the phase transitions occur at lower compression forces as the system expands compared to when it is compressed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2013

Finite groups and quantum physics

Concepts of quantum theory are considered from the constructive 'finite' point of view. The introduction of a continuum or other actual infinities in physics destroys constructiveness without any need for them in describing empirical observations. It is shown that quantum behavior is a natural consequence of symmetries of dynamical systems. The underlying reason is that it is impossible in principle to trace the identity of indistinguishable objects in their evolution-only information about invariant statements and values concerning such objects is available. General mathematical arguments indicate that any quantum dynamics is reducible to a sequence of permutations. Quantum phenomena, such as interference, arise in invariant subspaces of permutation representations of the symmetry group of a dynamical system. Observable quantities can be expressed in terms of permutation invariants. It is shown that nonconstructive number systems, such as complex numbers, are not needed for describing quantum phenomena. It is sufficient to employ cyclotomic numbers-a minimal extension of natural numbers that is appropriate for quantum mechanics. The use of finite groups in physics, which underlies the present approach, has an additional motivation. Numerous experiments and observations in the particle physics suggest the importance of finite groups of relatively small orders in some fundamental processes. The origin of these groups is unclear within the currently accepted theories-in particular, within the Standard Model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Analysis of chaotic dynamic regimes using series of interburst intervals

The problem of reconstruction of dynamic systems in the presence of noise using series of interburst intervals is solved. It is shown that the reconstruction procedure can be applied to strongly nonlinear noisy oscillatory processes. The results make it possible to generalize the method for analysis of dynamic systems with respect to recovery time to a wide variety of neuron oscillators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Aggregation of Inverter-Based Resources for Modeling and Simulation

In order to conduct system dynamic studies, it is necessary to have dynamic models of both inverter and plant levels. Detailed and aggregated modeling approaches are two essential options. The detailed modeling method involves capturing the dynamic characteristics of each individual device (e.g., wind turbine or PV array), as well as their interconnections. However, as the scale of the IBR plant increases, the complexity and computation time required for detailed modeling also increase. On the other hand, aggregated modeling offers a more efficient way of representing large-scale IBRs in power system dynamic studies. This approach involves aggregating a large number of wind turbines, PV arrays, inverters, and/or plant controllers into one or a smaller number of equivalent models. In order to analyze the impact of a high-level IBR penetration in power systems, it is important to develop accurate and computationally efficient models for both the detailed and aggregated methods.

14 SOLAR ENERGY↗

DOE OSTI2014

Analysis of the Space Propulsion System Problem Using RAVEN

This paper presents the solution of the space propulsion problem using a PRA code currently under development at Idaho National Laboratory (INL). RAVEN (Reactor Analysis and Virtual control ENviroment) is a multi-purpose Probabilistic Risk Assessment (PRA) software framework that allows dispatching different functionalities. It is designed to derive and actuate the control logic required to simulate the plant control system and operator actions (guided procedures) and to perform both Monte- Carlo sampling of random distributed events and Event Tree based analysis. In order to facilitate the input/output handling, a Graphical User Interface (GUI) and a post-processing data-mining module are available. RAVEN allows also to interface with several numerical codes such as RELAP5 and RELAP-7 and ad-hoc system simulators. For the space propulsion system problem, an ad-hoc simulator has been developed and written in python language and then interfaced to RAVEN. Such simulator fully models both deterministic (e.g., system dynamics and interactions between system components) and stochastic behaviors (i.e., failures of components/systems such as distribution lines and thrusters). Stochastic analysis is performed using random sampling based methodologies (i.e., Monte-Carlo). Such analysis is accomplished to determine both the reliability of the space propulsion system and to propagate the uncertainties associated to a specific set of parameters. As also indicated in the scope of the benchmark problem, the results generated by the stochastic analysis are used to generate risk-informed insights such as conditions under witch different strategy can be followed.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Study of possible chaotic, quasi-periodic and periodic structures in quantum dusty plasma

Existence of chaotic, quasi-periodic, and periodic structures of dust-ion acoustic waves is studied in quantum dusty plasmas through dynamical system approach. A system of coupled differential equations is derived from the fluid model and subsequently, variational matrix is obtained. The characteristic equation is obtained at the equilibrium point, and the behavior of nonlinear waves is studied numerically using Runge-Kutta method. The behavior of the dynamical system changes significantly when any of plasma parameters, such as the dust concentration parameter, temperature ratio, or the quantum diffraction parameter, is varied. The change of the characteristic of solution of the system is extensively studied. It is found that the system changes its behavior from chaotic pattern to limit cycle behavior.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1975

Hybrid computer methods for direct functional optimization

Control and trajectory optimization involves the minimization of a performance index (PI) of integral form where some optimal control law exists in a dynamic system. In this paper, a hybrid minicomputer with an adaptive random-search algorithm implements an iterative search for the optimal control. The search assumes that some initial control is randomly perturbed and a fast analog computer generates respective PI from the analog response of the dynamic system. An improved PI informs the digital computer to utilize the perturbed control as a basis for the next iteration; otherwise a new perturbation replaces the old perturbation in the next iteration. The search terminates when no further improvements occur.

Andrews, M.↗

NASA NTRS1996

Application of Consider Covariance to the Extended Kalman Filter

The extended Kalman filter (EKF) is the basis for many applications of filtering theory to real-time problems where estimates of the state of a dynamical system are to be computed based upon some set of observations. The form of the EKF may vary somewhat from one application to another, but the fundamental principles are typically unchanged among these various applications. As is the case in many filtering applications, models of the dynamical system (differential equations describing the state variables) and models of the relationship between the observations and the state variables are created. These models typically employ a set of constants whose values are established my means of theory or experimental procedure. Since the estimates of the state are formed assuming that the models are perfect, any modeling errors will affect the accuracy of the computed estimates. Note that the modeling errors may be errors of commission (errors in terms included in the model) or omission (errors in terms excluded from the model). Consequently, it becomes imperative when evaluating the performance of real-time filters to evaluate the effect of modeling errors on the estimates of the state.

Lundberg, John B.↗

NASA NTRS2007

Zero-Gravity Locomotion Simulators: New Ground-Based Analogs for Microgravity Exercise Simulation

Maintaining health and fitness in crewmembers during space missions is essential for preserving performance for mission-critical tasks. NASA's Exercise Countermeasures Project (ECP) provides space exploration exercise hardware and monitoring requirements that lead to devices that are reliable, meet medical, vehicle, and habitat constraints, and use minimal vehicle and crew resources. ECP will also develop and validate efficient exercise prescriptions that minimize daily time needed for completion of exercise yet maximize performance for mission activities. In meeting these mission goals, NASA Glenn Research Center (Cleveland, OH, USA), in collaboration with the Cleveland Clinic (Cleveland, Ohio, USA), has developed a suite of zero-gravity locomotion simulators and associated technologies to address the need for ground-based test analog capability for simulating in-flight (microgravity) and surface (partial-gravity) exercise to advance the health and safety of astronaut crews and the next generation of space explorers. Various research areas can be explored. These include improving crew comfort during exercise, and understanding joint kinematics and muscle activation pattern differences relative to external loading mechanisms. In addition, exercise protocol and hardware optimization can be investigated, along with characterizing system dynamic response and the physiological demand associated with advanced exercise device concepts and performance of critical mission tasks for Exploration class missions. Three zero-gravity locomotion simulators are currently in use and the research focus for each will be presented. All of the devices are based on a supine subject suspension system, which simulates a reduced gravity environment by completely or partially offloading the weight of the exercising test subject s body. A platform for mounting treadmill is positioned perpendicularly to the test subject. The Cleveland Clinic Zero-g Locomotion Simulator (ZLS) utilizes a pneumatic subject load device to apply a near constant gravity-replacement load to the test subject during exercise, and is currently used in conjunction with the General Clinical Research Center for evaluating exercise protocols using a bedrest analog. The enhanced ZLS (eZLS) at NASA Glenn Research Center features an offloaded treadmill that floats on a thin film of air and interfaces to a force reaction frame via variably-compliant isolators, or vibration isolation system. The isolators can be configured to simulate compliant interfaces to the vehicle, which affects mechanical loading to crewmembers during exercise, and has been used to validate system dynamic models for new countermeasures equipment designs, such as the second International Space Station treadmill slated for use in 2010. In the eZLS, the test subject and exercise device can be pitched at the appropriate angle for partial gravity simulations, such as lunar gravity (1/6th earth gravity). On both the eZLS and the NASA-Johnson Space Center standalone ZLS installed at the University of Texas Medical Branch in Galveston, Texas, USA, the subject's body weight relative to the treadmill is controlled via a linear motor subject load device (LM-SLD). The LM-SLD employs a force-feedback closed-loop control system to provide a relatively constant force to the test subject during locomotion, and is set and verified for subject safety prior to each session. Locomotion data were collected during parabolic flight and on the eZLS. The purpose was to determine the similarities and differences between locomotion in actual and simulated microgravity. Subjects attained greater amounts of hip flexion during walking and running during parabolic flight. During running, subjects had greater hip range of motion. Trunk motion was significantly less on the eZLS than during parabolic flight. Peak impact forces, loading rate, and impulse were greater on the eZLS than during parabolic while walking with a low external load (EL) and rning with a high EL. Activation timing differences existed between locations in all muscles except for the rectus femoris. The tibialis anterior and gluteus maximus were active for longer durations on the eZLS than in parabolic flight during walking. Ground reaction forces were greater with the LM-SLD than with bungees during eZLS locomotion. While the eZLS serves as a ground-based analog, researchers should be aware that subtle, but measurable, differences in kinematics and leg musculature activities exist between the environments. Aside from space applications, zero-gravity locomotion simulators may help medical researchers in the future with development of rehabilitative or therapeutic protocols for injured or ill patients. Zero-gravity locomotion simulators may be used as a ground-based test bed to support future missions for space exploration, and eventually may be used to simulate planetary locomotion in partial gravity environments, including the Moon and Mars. Figure: Zero-gravity Locomotion Simulator at the Cleveland Clinic, Cleveland, Ohio, USA

Perusek, Gail P.↗

DOE OSTI2019

Decentralized Carrier Interleaving in Cascaded Multilevel DC-AC Converters: Preprint

Cascaded dc-ac converters with interleaved carriers are commonly used in applications where elevated voltages and low-distortion multilevel waveforms are needed. Example applications include modular multilevel converters and solid-state transformers. In such systems, carrier interleaving is generally achieved via communication among the stacked converters or a centralized controller. Due to the large number of converters in such a system, existing approaches entail significant wiring complexity and communication may limit resilience to failures. In this paper, we introduce a control strategy which achieves communication-free carrier interleaving among series-connected converters. The proposed controller is embedded within each converter control loop and only requires measurements available at each set of converter terminals. We formulate a dynamic system model and show that the system converges to the interleaved condition irrespective of the number of converters in the stack. After outlining a practical method for digital implementation, experiments are shown on a hardware-in-the-loop setup.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1995

Lyapunov exponents from CHUA's circuit time series using artificial neural networks

In this paper we present the general problem of identifying if a nonlinear dynamic system has a chaotic behavior. If the answer is positive the system will be sensitive to small perturbations in the initial conditions which will imply that there is a chaotic attractor in its state space. A particular problem would be that of identifying a chaotic oscillator. We present an example of three well known different chaotic oscillators where we have knowledge of the equations that govern the dynamical systems and from there we can obtain the corresponding time series. In a similar example we assume that we only know the time series and, finally, in another example we have to take measurements in the Chua's circuit to obtain sample points of the time series. With the knowledge about the time series the phase plane portraits are plotted and from them, by visual inspection, it is concluded whether or not the system is chaotic. This method has the problem of uncertainty and subjectivity and for that reason a different approach is needed. A quantitative approach is the computation of the Lyapunov exponents. We describe several methods for obtaining them and apply a little known method of artificial neural networks to the different examples mentioned above. We end the paper discussing the importance of the Lyapunov exponents in the interpretation of the dynamic behavior of biological neurons and biological neural networks.

Gonzalez, J. Jesus↗

NASA NTRS1988

High-speed data acquisition for the Princeton University Dynamic Model Track

Real time analysis of data can reduce the time involved in exploring dynamic systems. The failure of the data acquisition system at the Princeton Dynamic Model Track prompted its replacement with a real time data acquisition system. Data can be obtained from an experiment and analyzed during and immediately following a data run. The new system employs high speed analog to digital conversion and a small computer to collect data. Sampling rates of 1000 hertz over 44 channels (44,000 words/sec) are obtainable. The data can be accessed as it enters the computer's environment where it may be displayed or stored for later processing. The system was tested on a helicopter rotor steep descent experiment. The data collected compares with previous data from a similar experiment.

Demko, Michael G.↗

NASA NTRS1991

Performance and stability of telemanipulators using bilateral impedance control

A new method of control for telemanipulators called bilateral impedance control is investigated. This new method differs from previous approaches in that interaction forces are used as the communication signals between the master and slave robots. The new control architecture has several advantages: (1) It allows the master robot and the slave robot to be stabilized independently without becoming involved in the overall system dynamics; (2) It permits the system designers to arbitrarily specify desired performance characteristics such as the force and position ratios between the master and slave; (3) The impedance at both ends of the telerobotic system can be modulated to suit the requirements of the task. The main goals of the research are to characterize the performance and stability of the new control architecture. The dynamics of the telerobotic system are described by a bond graph model that illustrates how energy is transformed, stored, and dissipated. Performance can be completely described by a set of three independent parameters. These parameters are fundamentally related to the structure of the H matrix that regulates the communication of force signals within the system. Stability is analyzed with two mathematical techniques: the Small Gain Theorem and the Multivariable Nyquist Criterion. The theoretical predictions for performance and stability are experimentally verified by implementing the new control architecture on a multidegree of freedom telemanipulator.

Moore, Christopher Lane↗