Institute for Systems Research Technical Reports

Permanent URI for this collectionhttp://hdl.handle.net/1903/4376

This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.

Browse

Author: search.filters.author.Krishnaprasad, Perinkulam S.Subject: search.filters.subject.nonlinear systems

Search Results

Now showing 1 - 10 of 26
  • Thumbnail Image
    Item
    Computing Balanced Realizations for Nonlinear Systems
    (2000) Newman, Andrew J.; Krishnaprasad, Perinkulam S.; Krishnaprasad, Perinkulam S.; ISR; CDCSS
    This paper addresses the problem of computability pertaining to the Scherpen(1994) theory and procedure for balancing of nonlinear systems. In contrastto Moore's (1981) balancing method for linear systems, the Scherpen procedurefor nonlinear balancing is not immediately amenable to computationalimplementation. For example, the controllability energy function correspondsto the value function for a nonlinear optimal control problem. Also, theMorse-Palais lemma guarantees the existence of a local coordinatetransformation under which the controllability energy function takes acanonical quadratic form, but provides no constructive procedure for obtainingit. Thus, tools have not yet appeared for computing balanced realizations fornonlinear systems, and the procedure has not yet been applied as a tool formodel reduction.

    First, we consider the problem of computing the controllability energyfunction without numerically solving the family of optimal control problems,or the associated Hamilton-Jacobi-Bellman equation, implied in its definition.Stochastically excited systems play a major role in our methodology. Wepresent a stochastic method for computing an estimate of the controllabilityfunction, and show that in certain situations the method provides an exactsolution. The procedure is tested on applications via Monte-Carlo experiments.

    Then, we address the problem of numerically determining a Morse transformationfor a function with non-degenerate critical point at 0. We develop analgorithm for computing the desired nonlinear transformation and estimatingthe neighborhood on which the transformed controllability function isquadratic.

    In the literature, examples of applied nonlinear balancing have been limited topseudo-balancing of 2-dimensional gradient systems and noting that in the caseof linear systems the energy functions approach reduces to the usual setting ofgramians. We apply our approach to numerically derive, for the first time,balanced representations of nonlinear state-space models. In particular, wepresent applications to a forced damped pendulum system and a forced dampeddouble pendulum system.

    The research and scientific content in this material has been published in theProceedings of the 14th International Symposium on Mathematical Theory of Networks and Systems, Perpignan, France, June 19-23, 2000.
  • Thumbnail Image
    Item
    Analysis of a complex activator-inhibitor equation
    (1999) Justh, Eric W.; Krishnaprasad, Perinkulam S.; ISR; CDCSS
    Basic properties of solutions and a Lyapunov functionalare presented for a complex activator-inhibitor equation witha cubic nonlinearity.Potential applications include control of coupled-oscillator arrays(for quasi-optical power combining and phased-array antennas),and control of MEMS actuator arrays (for micro-positioning small items).

    (This work to appear in Proc. 1999 American Control Conference.)

  • Thumbnail Image
    Item
    Control Problems of Hydrodynamic Type
    (1998) Krishnaprasad, Perinkulam S.; Manikonda, Vikram; ISR; CDCSS
    It has been known for some time that the classical work of Kirchhoff, Love,and Birkhoff on rigid bodies in incompressible, irrotational flows provideseffective models for treating control problems for underwater vehicles.This has also led to a better appreciation of the dynamics of suchsystems. In this paper, we develop results based on geometric mechanics andcenter manifold theory to solve controllability and stabilization questionsfor a class of under-actuated left invariant mechanical systems on Liegroups that include approximate models of underwater vehicles and surfacevehicles. We also provide numerical evidence to capture the globalproperties of certain interesting feedback laws.

    (This work appears as an invited paper in the Proc. IFAC Sympo. on NonlinearControl Systems Design (NOLCOS'98), (1998), 1:139-144)

  • Thumbnail Image
    Item
    Nonlinear Model Reduction for RTCVD
    (1998) Newman, A.; Krishnaprasad, Perinkulam S.; Krishnaprasad, Perinkulam S.; ISR; CDCSS
    In this paper, we examine alternative methods for reducing thedimensionality of nonlinear dynamical system models arising incontrol of rapid thermal chemical vapor deposition (RTCVD) forsemiconductor manufacturing. We focus on model reduction forthe ordinary differential equation model describing heattransfer to, from, and within a semiconductor wafer in theRTCVD chamber. Two model reduction approaches are studied andcompared: the proper orthogonal decomposition and the method of balancing.This leads to a discussion of computational issues in the practicalimplementation of balancing for nonlinear systems.
  • Thumbnail Image
    Item
    A Model for a Thin Magnetostrictive Actuator
    (1998) Venkataraman, R.; Krishnaprasad, Perinkulam S.; ISR; CDCSS
    In this paper, we propose a model for dynamic magnetostrictive hysteresisin a thin rod actuator. We derive two equations that representmagnetic and mechanical dynamic equilibrium. Our model results from an application of the energy balance principle.It is a dynamic model as it accounts for inertial effects and mechanicaldissipation as the actuator deforms, and also eddy current lossesin the ferromagnetic material. We show rigorously that the model admits a periodic solution thatis asymptotically stable when a periodic forcing function is applied.(Proc. Conf. Information Sci. and Systems, Princeton, March 1998)
  • Thumbnail Image
    Item
    A Lyapunov Functional for the Cubic Nonlinearity Activator-Inhibitor Model Equation
    (1998) Justh, Eric W.; Krishnaprasad, Perinkulam S.; ISR; CDCSS
    The cubic nonlinearity activator-inhibitor model equation is a simpleexample of a pattern-forming system for which strong mathematical resultscan be obtained. Basic properties of solutions and the derivation ofa Lyapunov functional for the cubic nonlinearity model are presented.Potential applications include control of large MEMS actuator arrays.(In Proc. IEEE Conf. Decision and Control, December 16-18, 1998)
  • Thumbnail Image
    Item
    The Hybrid Motor Prototype: Design Details and Demonstration Results
    (1998) Venkataraman, R.; Dayawansa, Wijesuriya P.; Krishnaprasad, Perinkulam S.; ISR; CDCSS
    A novel hybrid rotary motor incorporating piezoelectric and magnetostrictive actuators has been designed and demonstrated. The novelty of this motor was the creation of an electrical resonant circuit, whereby reactive power requirement on the power source is reduced. It was envisioned that the motor would be suitable for low output speed, high torque applications because of its design. This report presents the constructional details of this motor and the results of the demonstration.
  • Thumbnail Image
    Item
    Characterization of an ETREMA MP 50/6 Magnetostrictive Actuator
    (1998) Venkataraman, R.; Rameau, J.; Krishnaprasad, Perinkulam S.; ISR; CDCSS
    This report presents the Displacement (Strain)-Current characteristic of an ETREMA MP 50/6 magnetostrictive actuator. This actuator is made of TERFENOL-D and displays giant magnetostriction. The displacement-current characteristic shows significant hysteresis behavior that depends on the rate at which the input is applied. Another important property of ferromagnetic hysteresis - the wiping out property, was also observed in the experiments.
  • Thumbnail Image
    Item
    Computation for Nonlinear Balancing
    (1998) Newman, Andrew J.; Krishnaprasad, Perinkulam S.; Krishnaprasad, Perinkulam S.; ISR; CDCSS
    We illustrate a computational approach to practicalnonlinear balancing via the forced damped pendulum example.
  • Thumbnail Image
    Item
    Convergence Analysis and Analog Circuit Applications for a Class of Networks of Nonlinear Coupled Oscillators
    (1996) Justh, Eric W.; Krishnaprasad, Perinkulam S.; Kub, Francis J.; ISR
    The physical motivation and rigorous proof of convergence for a particular network of nonlinear coupled oscillators are reviewed. Next, the network and convergence proof are generalized in several ways, to make the network more applicable to actual engineering problems. It is argued that such coupled oscillator circuits are more natural to implement in analog hardware than other types of dynamical equations because the signal levels tend to remain at sufficiently large values that effects of offsets and mismatch are minimized. Examples of how analog implementations of these networks are able to address actual control problems are given. The first example shows how a pair of coupled oscillators can be used to compensate for the feedback path phase shift in a complex LMS loop, and has potential application for analog adaptive antenna arrays or linear predictor circuits. The second example shows how a single oscillator circuit with feedback could be used for continuous wavelet transform applications. Finally, analog CMOS implementation of the coupled oscillator dynamics is briefly discussed.