Enrique Barbieri

An ultrasonic ranging system for structural vibration measurements

An ultrasonic ranging system (URS) that can be used to measure vibratory displacements in structures is described. A pair of ultrasonic transducers is used in a transmit-receive mode to acquire the motion of a point on a flexible structure. The structures oscillating motion modulates the phase angle between the transmitted and received acoustic signals. A simple phase detector and low-pass filter combination demodulate the phase signal, thus extracting information about the motion of the point on the structure. The results reported concentrate on some design issues of the URS and its use as a potential displacement measuring device for flexible structures. The URS accurately distinguished four vibration frequencies of a simple cantilevered aluminum beam, with the highest frequency near 50 Hz. >

A new minimum-time control law for a one-mode model of a flexible slewing structure

The construction of a minimum-time control law for a single-axis, undamped, one-mode model of a flexible slewing structure is described. The set of necessary and sufficient conditions for optimality is developed using phase-plane techniques, and is given in terms of the vibration frequencies and the rigid-body states. This effectively provides the switching hypersurface in four-dimensional space. The resulting control strategy can be implemented on line since no a priori computation of switching times is required. >

Sliding mode control of a heat equation with application to arc welding

This paper considers the use of sliding mode control to perform robotic welding. The arc welding model is considered as a distributed parameter system described by partial differential equations with unknown boundary conditions. Simulations with temperature distribution surface plots are also included.

Stability Analysis of a Class of Interconnected Systems

There exists a class of systems that is characterized by having a so called regular cellular structure or homogeneous interconnection. In this note, the bilateral Z-Transform is used to obtain a mathematical model parametrized by z and it is shown that properties of the system can be more easily investigated by a simple test applied to the parametrized model. The analysis is illustrate via three examples: the heat equation, the Euler-Bernoulli beam, and decentralized control of a countably infinite string of interconnected mass-spring-damper systems

On the infinite-horizon LQ tracker

Abstract The infinite-horizon tracking problem is considered in the linear-quadratic optimal control framework. Computationally, one term in the control signal is a constant gain, stabilizing, full-state feedback found by solving an algebraic Riccati equation; the second term involves a steady-state function vss(t) that solves an auxiliary, forced differential equation with unknown initial condition. In this article, a linear system of algebraic equations is derived to determine vss(0). Numerical examples are included to illustrate the result.

Rest-to-rest slewing of flexible structures in minimum time

The rest-to-rest slewing of flexible structures in minimum time is considered via phase-plane techniques. The trajectories are shown to exhibit a mirror-image symmetry in the phase plane. The advantage of this approach is that the switching control law can be expressed in terms of the rigid body states only, thereby resulting in a closed-loop strategy. Simulations are included for a one-bending model of a flexible slewing structure.<<ETX>>

Real-time Infinite Horizon Linear-Quadratic Tracking Controller for Vibration Quenching in Flexible Beams

It is well known that the infinite horizon linear-quadratic tracking problem does not have a solution in the strict sense because in general the performance index is infinite. Additional computational difficulties arise for applications where real-time computations are needed. However, for applications where the reference signal is generated by an asymptotically stable system, then the problem has an optimal solution. In the present paper a methodology that can be used to design real-time infinite horizon linear-quadratic tracking controllers for vibration quenching in flexible beams is presented. A numerical example is included to illustrate the effectiveness of the method.

Single-input/single-output transfer functions for a flexible slewing link

Truncated linear models based on constrained and unconstrained mode expansions for a flexible link with torque actuation at its hub led us to examine the behavior of the open-loop-zeros of five commonly used single-input single-output transfer functions. We arrive at new conclusions with regard to minimum- and non-minimum-phase zeros, and passivity of the transfer functions. The flexible-to-rigid inertia (FRI) ratio plays an important role in the determination of these characteristics. This article illustrates how the zero locations of some of the transfer functions are dramatically affected by the FRI ratio. We also investigate the performance of a hub angle, hub rate, and relative tip position static feedback controller based on a reduced-order constrained mode model when applied to both unconstrained and constrained mode models of the same dimension. Simulations indicate that the constrained model can be stable while the unconstrained model is not for high FRI ratios. Our findings can provide useful information to designers in cases where the controller is sensitive to the location of the plants zeros.

Small signal point-to-point tracking of a propellant mixer

The mixer described in this work is responsible for combining high pressure LH2 and GH2 to produce a hydrogen flow that meets certain thermodynamic properties before it is fed in to a test article. The desired properties are maintained by controlling the LH2 and GH2 flows. The mixer is modeled as a general multi-flow lumped volume for single constituent fluids using density and internal energy as states. A small-signal model is developed based on the nonlinear model and simulated including a table look-up feature of the fluid thermodynamic properties. Pulse disturbances are introduced to the valve positions and the quality of the linear model is ascertained by comparing its behavior against the nonlinear model simulations. Valve control strategies that simulate an operator-in-the-loop scenario are then explored demonstrating the need for automatic feedback control. Finally, classical optimal multi-output proportional/integral controllers are designed based on the linear model and applied to the nonlinear model with excellent results to track simultaneous, constant setpoint changes in desired exit flow, exit temperature, and mixer pressure, as well as to reject unmeasurable but bounded additive step perturbations in the valve positions.

Mathematical representation of fuzzy membership functions

The most commonly used membership function distributions in fuzzy controllers are evenly-spaced triangular and trapezoidal membership functions which allow simple traversal routines to fuzzify the input. Evenly-spaced membership distributions become very sensitive to inaccuracies in the fuzzy representation of the input. The paper proposes a membership function shape and distribution which makes the fuzzified input more robust to biases in the fuzzified input.<<ETX>>