Seth L. Lacy

Subspace identification with guaranteed stability using constrained optimization

In system identification, the true system is often known to be stable. However, due to finite sample constraints, modeling errors, plant disturbances and measurement noise, the identified model may be unstable. We present a constrained optimization method to ensure asymptotic stability of the identified model in the context of subspace identification methods. In subspace identification, we first obtain an estimate of the state sequence or extended observability matrix and then solve a least squares optimization problem to estimate the system parameters. To ensure asymptotic stability of the identified model, we write the least-squares optimization problem as a convex linear programming problem with mixed equality, quadratic, and positive-semidefinite constraints suitable for existing convex optimization codes such as SeDuMi. We present examples to illustrate the method and compare to existing approaches.

Identification of FIR Wiener systems with unknown, non-invertible, polynomial non-linearities

Wiener systems consist of a linear dynamic system whose output is measured through a static non-linearity. In this paper we study the identification of single-input single-output Wiener systems with finite impulse response dynamics and polynomial output non-linearities. Using multi-index notation, we solve a least squares problem to estimate products of the coefficients of the non-linearity and the impulse response of the linear system. We then consider four methods for extracting the coefficients of the non-linearity and impulse response: direct algebraic solution, singular value decomposition, multi-dimensional singular value decomposition and prediction error optimization.

Subspace identification for non-linear systems with measured-input non-linearities

This paper uses subspace methods to identify a class of multi-input multi-output discrete-time non-linear time-varying systems. Specifically, we identify systems that are non-linear in measured data and linear in unmeasured states. Numerical examples are presented to demonstrate the efficacy of the method.

Identification of Wiener Systems With Known Noninvertible Nonlinearities

In this paper we develop a method for identifying SISO Wiener-type nonlinear systems, that is, systems consisting of a linear dynamic system followed by a static nonlinearity. Unlike previous techniques developed for Wiener system identification, our approach allows the identification of systems with nonlinearities that are known but not necessarily invertible, continuous, differentiable, or analytic.

System identification of space structures

Large precision spacecraft present a challenging control problem. They are modally dense, have a very large frequency bandwidth over which disturbances can affect payload performance, and are lightly damped. The performance of passive vibration isolation systems is limited by the constraints of physics and mechanical components, particularly at low frequencies. This motivates the need for an active isolation system. High fidelity system models are required to obtain the high performance control. Developing these high fidelity system models of large space structures is a challenge for experiments, algorithms, and computational resources.

Adaptive control of a flexible membrane using acoustic excitation and optical sensing

Flexible membranes are envisioned as a key component of large, lightweight, space-based systems. This paper focuses on the problem of adaptive disturbance rejection, that is, the rejection of external disturbances with unknown spectral content. It describes the design and operation of a laboratory testbed involving a exible membrane with acoustic excitation and optical sensing. The ARMARKOV adaptive disturbance rejection algorithm is used to reject single- and dual-tone disturbances without knowledge of the disturbance spectrum and with limited modeling of the membrane dynamics.

FRF Correlation and Error Metrics for Plant Identification

In plant identification and modeling efforts, metrics are needed to quantitatively compare experimental data to model predictions. Quantitative metrics broadly fall into five categories: Performance Metrics; Correlation Metrics; Error Metrics; Data Quality Metrics; and Model Interpretation Metrics. This paper describes the utility of frequency response function (FRF) correlation and error metrics for plant identification based on response data collected from dynamic tests of complex space structures. Three correlation metrics and three error metrics are discussed. MIMO extensions to the correlation metrics are presented and their application is demonstrated on data collected from spacecraft- representative structures. (k U - matrix of left singular vectors associated with the non-zero singular values of the identified model complex response at frequency f(k) ) (k V - matrix of right singular vectors associated with the non-zero singular values of the identified model complex response at frequency f(k) ) ( ˆ k U - matrix of left singular vectors associated with the non-zero singular values of the measured complex response at frequency f(k) ) ( ˆ k V - matrix of right singular vectors associated with the non-zero singular values of the measured complex response at frequency f(k)

Identification of Wiener systems with known noninvertible nonlinearities

In this paper we develop a method for identifying Wiener-type nonlinear systems, that is, systems consisting of a linear dynamic system followed by a static nonlinearity. Unlike previous techniques developed for Wiener system identification, our approach allows the identification of systems with noninvertible, but known, nonlinearities.

Hysteretic systems and step-convergent semistability

Hysteresis is usually characterized as a memory-dependent relationship between inputs and outputs. While various operator models have been proposed, it is often convenient for engineering applications to approximate hysteretic behavior by means of finite-dimensional differential models. In the present paper we show that step-convergent semistable systems (that is, semistable systems with convergent step response) give rise to multiple-valued maps under quasi-static operation. By providing a connection between semistability and hysteresis, our goal is to provide a class of differential models for representing hysteretic behavior.

Characterization and Modeling of the Nonlinear Response of Ionic Polymer Actuators

Ionic polymers are compliant, low density materials that operate under low voltage levels as transducers. They can be used as both sensors and actuators for various applications, primarily those involving flexible structures. While some debate continues over the dominant physical mechanisms of actuation, several model forms have been proposed. The majority of these existing models are linear relationships between the applied potential and the strain generated. However, nonlinear characteristics have been observed in both the electrical and mechanical response of cantilever actuators, including harmonic distortion in the sinusoidal time response and a shifting frequency response for increased input levels. Characterization results indicate that the nonlinear mechanisms are dynamic, since they have dominance at low frequencies, but are essentially negligible as the excitation frequency increases. This research uses knowledge gained from the characterization results to develop a dynamic model that can predict the observed nonlinear behavior. The empirical model is constructed from input-output data collected using a Gaussian input current signal and is validated against the measured frequency response function and single-frequency sinusoidal responses. The basic model form has a dynamic nonlinearity on the input to an underlying nonlinear system.