Clark J. Radcliffe

Global Active Noise Control of a One-Dimensional Acoustic Duct Using a Feedback Controller

The active noise control of a one-dimensional hard-walled duct with a partially dissipative boundary condition is addressed. Previous techniques have attacked this problem by developing adaptive filters designed to cancel acoustic noise at a single measurement location. The work presented here applies modern, state space, control theory to globally reduce noise levels in a one-dimensional acoustic enclosure rather than at a single location. This global control requires only the addition of a single response measurement microphone and control speaker to the open-loop system

A natural modal expansion for the flexible robot arm problem via a self-adjoint formulation

The equations of motion of a flexible robot arm consist of a coupled partial differential equation describing the arms transverse vibrations and an ordinary differential equation describing the hubs rigid motion. Many researchers obtained a solution using a modal expansion based on the arms equation alone, which has erroneous eigenfunctions and eigenvalues. A novel method is presented for obtaining an equivalent but self-adjoint form for the problem. This self-adjoint form leads to a natural modal expansion, where the equations decouple. This method is used to show that the effect of the hub-arm model coupling depends exclusively on the hub-inertia-to-arm-mass ratio. The need for a self-adjoint form arises in many control applications. This is because, typically, the control design is based on approximate models, and in order to guarantee robust performance, a prior estimate of the approximation error is required. When a self-adjoint form is available, obtaining approximate modes and the associated error bounds becomes an easy task. >

Solutions to the Inverse LQR Problem With Application to Biological Systems Analysis

In this brief, we present a set of techniques for finding a cost function to the time-invariant linear quadratic regulator (LQR) problem in both continuous- and discrete-time cases. Our methodology is based on the solution to the inverse LQR problem, which can be stated as: does a given controller K describe the solution to a time-invariant LQR problem, and if so, what weights Q and R produce K as the optimal solution? Our motivation for investigating this problem is the analysis of motion goals in biological systems. We first describe an efficient linear matrix inequality (LMI) method for determining a solution to the general case of this inverse LQR problem when both the weighting matrices Q and R are unknown. Our first LMI-based formulation provides a unique solution when it is feasible. In addition, we propose a gradient-based, least-squares minimization method that can be applied to approximate a solution in cases when the LMIs are infeasible. This new method is very useful in practice since the estimated gain matrix K from the noisy experimental data could be perturbed by the estimation error, which may result in the infeasibility of the LMIs. We also provide an LMI minimization problem to find a good initial point for the minimization using the proposed gradient descent algorithm. We then provide a set of examples to illustrate how to apply our approaches to several different types of problems. An important result is the application of the technique to human subject posture control when seated on a moving robot. Results show that we can recover a cost function which may provide a useful insight on the human motor control goal.

Control of flexible structures with spillover using an augmented observer

Modern modal control methods for flexible structures have control and observation spillover that can degrade performance and reduce the stability margin of the closed-loop controlled structure. The sensor output is often filtered to reduce observation spillover, however, the filter introduces signal distortion and perturbs the closed-loop system eigenvalue locations. This perturbation can reduce the stability margin and jeopardize convergence of a deterministic observer. If the filter equations are not explicitly included in the observer design, then the separation principle between the controller and the observer states no longer holds when present in the unfiltered system. A new method is presented where the observer equations are augmented to include a first-order filter dynamics. The separation principle, controllability, and observability of the unfiltered system are invariant to the filter dynamics in this new method, resulting in no perturbation of controlled system eigenvalue locations. The filter cutoff frequency can be located even within the bandwidth of the system, thereby increasing the filter effectiveness in reducing observation spillover. Spillover-generated errors in closed-loop eigenvalues of these control methods are compared using a numerical example.

A compensated acoustic actuator for systems with strong dynamic pressure coupling

This study improves the performance of a previously developed acoustic actuator in the presence of an acoustic duct system with strong pressure coupling. The speaker dynamics and the acoustic duct dynamics are first modeled separately. The two sysrems are then coupled, and the resulting system is modeled. A velocity sensor is developed and used in feedback compensation. The resulting speaker system has minimal magnitude and phase variation over a 20-200 Hz bandwidth. These conclusions are verified through experimental results.

An Eigenvalue Based Acoustic Impedance Measurement Technique

The method employs a one-dimensional tube or duct with excitation at one end and an unknown acoustic impedance at the termination end. Microphones placed in the tube are then employed to measure the frequency response of the system. This method uses fixed instrumentation. This technique calculates the acoustic impedance from measured duct eigenvalues

A Nyquist stability criterion for distributed parameter systems

A Nyquist graphical stability criterion is developed for distributed parameter, possible unstable, single-loop systems. Practical conditions are presented for existence, uniqueness, causality, and asymptotic or exponential stability of the closed-loop impulse response. The hypotheses are given for the transfer function only and do not require any knowledge of its time-domain impulse response. >

Reliability of assessing trunk motor control using position and force tracking and stabilization tasks

System-based methods have been applied to assess trunk motor control in people with and without back pain, although the reliability of these methods has yet to be established. Therefore, the goal of this study was to quantify within- and between-day reliability using systems-based methods involving position and force tracking and stabilization tasks. Ten healthy subjects performed six tasks, involving tracking and stabilizing of trunk angular position in the sagittal plane, and trunk flexion and extension force. Tracking tasks involved following a one-dimensional, time-varying input signal displayed on a screen by changing trunk position (position tracking) or trunk force (force tracking). Stabilization tasks involved maintaining a constant trunk position (position stabilization) or constant trunk force (force stabilization) while a sagittal plane disturbance input was applied to the pelvis using a robotic platform. Time and frequency domain assessments of error (root mean square and H2 norm, respectively) were computed for each task on two separate days. Intra-class correlation coefficients (ICC) for error and coefficients of multiple correlations (CMC) for frequency response curves were used to quantify reliability of each task. Reliability for all tasks was excellent (between-day ICC≥0.8 and CMC>0.75, within-day CMC>0.85). Therefore, position and force control tasks used to assess trunk motor control can be deemed reliable.

Decomposing one‐dimensional acoustic pressure response into propagating and standing waves

Few actual sound fields are representative of ideal acoustic pressure responses and ideal boundary conditions, such as those nearly found in anechoic or reverberant rooms. Normally encountered enclosures have complicated responses that are difficult to relate to a boundary condition that is inbetween these two ideal extremes. Yet, the propagating‐ and standing‐wave responses associated with absorptive and reflective boundary conditions seen in the ideal cases are fundamental bases to understand these more complicated problems. An analytical method is developed to decompose a one‐dimensional acoustic pressure response associated with a specified partially absorptive boundary condition into an equivalent summation of propagating and standing waves usually associated with absorptive and reflective boundary conditions, respectively. The propagating‐ and standing‐wave responses are scaled and shifted in phase by factors that are dependent on the boundary absorptivity and frequency, but are independent of the s...

Networked Assembly of Mechatronic Linear Physical System Models

Engineering design is evolving into a global activity. Globally distributed design requires efficient global distribution of models of dynamic physical systems through computer networks. These models must describe the external input-output behavior of the electrical, mechanical, fluid, and thermal dynamics of engineering systems. An efficient system model assembly method is then required to assemble these component system models into a model of a yet higher-level dynamic system. Done recursively, these higher-level system models become possible components for yet higher-level analytical models composed of external model equations in the same standardized format as that of the lowest level components. Real-time, automated exchange, and assembly of engineering dynamic models over a global network requires four characteristics. The models exchanged must have a unique standard format so that they can be exchanged and assembled by an automated process. The exchange of model information must be executed in a single-query transmission to minimize network load. The models must describe only external behavior to protect internal model details. Finally, the assembly process must be recursive so that the transfer and assembly processes do not change with the level of the model exchanged or assembled. This paper will introduce the modular modeling method (MMM), a modeling strategy that satisfies these requirements. The MMM distributes and assembles linear dynamic physical system models with a dynamic matrix representation. Using the MMM method, dynamic models of complex assemblies can be built and distributed while hiding the topology and characteristics of their dynamic subassemblies.