Balanced Truncation Model Reduction of a Nonlinear Cable-Mass PDE System with Interior Damping

We consider model order reduction of a nonlinear cable-mass system modeled by a 1D wave equation with interior damping and dynamic boundary conditions. The system is driven by a time dependent forcing input to a linear mass-spring system at one boundary. The goal of the model reduction is to produce a low order model that produces an accurate approximation to the displacement and velocity of the mass in the nonlinear mass-spring system at the opposite boundary. We first prove that the linearized and nonlinear unforced systems are well-posed and exponentially stable under certain conditions on the damping parameters, and then consider a balanced truncation method to generate the reduced order model (ROM) of the nonlinear input-output system. Little is known about model reduction of nonlinear input-output systems, and so we present detailed numerical experiments concerning the performance of the nonlinear ROM. We find that the ROM is accurate for many different combinations of model parameters

A Comparison of Balanced Truncation Methods for Closed Loop Systems

Real-time control of a physical system necessitates controllers that are low order. In this paper, we compare two balanced truncation methods as a means of designing low order compensators for partial differential equation (PDE) systems. The first method is the application of balanced truncation to the compensator dynamics, rather than the state dynamics, as was done in cite{Skelton:1984}. The second method, LQG balanced truncation, applies the balancing technique to the Riccati operators obtained from a specific LQG design. We discuss snapshot-based algorithms for constructing the reduced order compensators and present numerical results for a two dimensional convection diffusion PDE system

A Proper Orthogonal Decomposition Approach to Approximate Balanced Truncation of Infinite Dimensional Linear Systems

We extend a method for approximate balanced reduced order model derivation for finite dimensional linear systems developed by Rowley (Int. J. Bifur. Chaos Appl. Sci. Eng. 15(3) (2005), pp. 997-1013) to infinite dimensional systems. The algorithm is related to standard balanced truncation, but includes aspects of the proper orthogonal decomposition in its computational approach. The method can be also applied to nonlinear systems. Numerical results are presented for a convection diffusion system

Balanced POD Algorithm for Robust Control Design for Linear Distributed Parameter Systems

A mathematical model of a physical system is never perfect; therefore, robust control laws are necessary for guaranteed stabilization of the nominal model and also nearby systems, including hopefully the actual physical system. We consider the computation of a robust control law for large-scale finite dimensional linear systems and a class of linear distributed parameter systems. The controller is robust with respect to left coprime factor perturbations of the nominal system. We present an algorithm based on balanced proper orthogonal decomposition to compute the nonstandard features of this robust control law. Numerical results are presented for a convection diffusion partial differential equation

Balanced Proper Orthogonal Decomposition for Model Reduction of Infinite Dimensional Linear Systems

In this paper, we extend a method for reduced order model derivation for finite dimensional systems developed by Rowley to infinite dimensional systems. The method is related to standard balanced truncation, but includes aspects of the proper orthogonal decomposition in its computational approach. The method is also applicable to nonlinear systems. The method is applied to a convection diffusion equation

Balanced POD for Linear PDE Robust Control Computations

A mathematical model of a physical system is never perfect; therefore, robust control laws are necessary for guaranteed stabilization of the nominal model and also nearby systems, including hopefully the actual physical system. We consider the computation of a robust control law for large-scale nite dimensional linear systems and a class of linear distributed parameter systems. The controller is robust with respect to left coprime factor perturbations of the nominal system. We present an algorithm based on balanced proper orthogonal decomposition to compute the nonstandard features of this robust control law. Convergence theory is given, and numerical results are presented for two partial di erential equation systems

A method of predicting variable speed rail corrugation growth using standard statistical moments

Wear-type rail corrugation is a significant problem in the railway transport industry. Some recent work has suggested that speed control can be used as an effective tool to minimize the rate of corrugation growth. This has brought about the need to model corrugation growth under variable passing speed. Variable speed rail corrugation growth modelling normally consists of either numerical simulation of a sequence of varied speed wheel passes or direct integration of a probabilistic passing speed distribution function; both of which are computationally expensive. This paper investigates the use of the statistical moments of the speed probability density function to greatly improve the computational speed of variable speed corrugation growth models and compares results of changing standard deviation and skewness to numerical integration models. It also identifies the effects of individual statistical moments on corrugation growth to provide better insight into control methods. The new modelling method correlated well with the numerical integration models for small standard deviations in speed (less than 10%) and highlighted a need to consider kurtosis in predicting the performance of speed control based corrugation mitigation schemes. For larger standard deviations in speed, higher than 4th order effects need to be considered

The visual orbits of the spectroscopic binaries HD 6118 and HD 27483 from the Palomar Testbed Interferometer

We present optical interferometric observations of two double-lined spectroscopic binaries, HD 6118 and HD 27483, taken with the Palomar Testbed Interferometer (PTI) in the K band. HD 6118 is one of the most eccentric spectroscopic binaries and HD 27483 a spectroscopic binary in the Hyades open cluster. The data collected with PTI in 2001-2002 allow us to determine astrometric orbits and when combined with the radial velocity measurements derive all physical parameters of the systems. The masses of the components are 2.65 +/- 0.27 M_Sun and 2.36 +/- 0.24 M_Sun for HD 6118 and 1.38 +/- 0.13 M_Sun and 1.39 +/- 0.13 M_Sun for HD 27483. The apparent semi-major axis of HD 27483 is only 1.2 mas making it the closest binary successfully observed with an optical interferometer.Comment: submitted to Ap

Feedback Control of a Bioinspired Plate-Beam System

In this paper we present a model for a plate-beam system to represent a bioinspired flexible wing. Using a Galerkin based finite element approximation to the system, we compute functional gains that can be used for sensor placement and show that a piezoceramic actuator on the beam can be used for camber contro

A Snapshot Algorithm for Linear Feedback Flow Control Design

The control of fluid flows has many applications. For micro air vehicles, integrated flow control designs could enhance flight stability by mitigating the effect of destabilizing air flows in their low Reynolds number regimes. However, computing model based feedback control designs can be challenging due to high dimensional discretized flow models. In this work, we investigate the use of a snapshot algorithm proposed in Ref. 1 to approximate the feedback gain operator for a linear incompressible unsteady flow problem on a bounded domain. The main component of the algorithm is obtaining solution snapshots of certain linear flow problems. Numerical results for the example flow problem show convergence of the feedback gains