Institute for Systems Research Technical Reports

Previous and concurrent research in the modeling of magnetostrictive actuators and the related area of electrostrictive actuators have produced models that are of low order and reproduce their quasi-static response reasonably well. But the main interest in using these and other smart actuators is at a high frequency -- for producing large displacements with mechanical rectification, producing sonar signals etc. The well known limitation of smart actuators that are based on electro-magneto-thermo-elastic behaviors of smart materials is the complex, input-rate dependent, hysteretic behavior of the latter.

The model proposed in this dissertation is a bulk model and describes the behaviour of a magnetostrictive actuator by a system with 4 states. We develop this model using phenomenological arguments following the work done by Jiles and Atherton for describing bulk ferromagnetic hysteresis. The model accounts for magnetic hysteresis; eddy current effects; magneto-elastic effects; inertial effects; and mechanical damping. We show rigorously that the system with the intial state at the origin has a periodic orbit as its $Omega$ limit set. For the bulk ferromagnetic hysteresis model - a simplification of the magnetostrictive model, we show that all trajectories starting within a certain set approach this limit set.

It is envisioned that the model will help application engineers to do simulation studies of structures with magnetostrictive actuators. Towards this end, an algorithm is proposed to identify the various parameters in the model.

In control applications, one may require the actuator to follow a certain trajectory. The complex rate dependent behaviour of the actuator makes the design of a suitable control law a challenging one. As our system of equations do not model transient effects, they do not model the minor-loop closure property common to ferromagnetic materials. Therefore, the design of control laws making explicit use of the model (without modifications) is not possible.

A major reason to use model free approaches to control design is that magnetostrictive actuators seem to have slight variations in their behavior with time. Therefore, we tried to use a direct adaptive control methodology that uses features of our model. The system is now looked at as a relative degree two linear system with set-valued input nonlinearity. Extensions of Eugene Ryan's work on universal tracking for a relative degree one linear system and Morse's work on stablization for relative degree two linear systems were sought.

Experimental verification of our method confirmed our intuition about the model structure. Though the tracking results were not very satisfactory due to the presence of sensor noise, the experimental results, nevertheless validate our modeling effort.

This thesis examines how computational methods can be utilized to study the functionality of these systems. Building on past research, dynamic models for a human skeletal system pedaling a bicycle are used as a basis for examining various methods of implementing inputs that will control the cycling. Two models are used a three degree-of-freedom model implementing ideal torque inputs at the hip, knees, and feet, and a one degree-of-freedom model involving inputs at the hip and knee only. Both models are characterized by highly nonlinear dynamics, requiring the use of nonlinear analysis, optimization theory, and computational methods for examination. Control of the one degree- of-freedom model has been addressed in previous work; here, parameterization of the control and the process of learning it is examined. Next, control strategies for the more complex three degree-of-freedom model are developed. Finally, results for upright and recumbent cycling are compared using the three degree-of-freedom model.

We also provide a constructive procedure to build networks based on wavelet theory. Moreover, cognizant of the problems usually encountered in practical implementations of these ideas, we develop a heuristic methodology, inspired by similar work in the area of Radial Basis Function (RBF) networks (Moody & Darken, Platt), to build a network sequentially on-line as well as off-line.

We show some connections of our method to some existing methods such as Projection Pursuit Regression (Friedman), Hyper Basis Functions (Poggio & Girosi) and other methods that have been proposed in the literature on neural- networks as well as statistics. In particular, some classes of wavelets can also be derived from the regularization theoretical framework given by Poggio & Girosi.

Finally, we choose direct nonlinear adaptive control to demonstrate the utility of the network in the context of local learning. Stability analysis is carried out within a standard Lyapunov formulation. Simulation studies show the effectiveness of these methods. We compare and contrast these methods with some recent results obtained by other researchers using Back Propagation (Feed-Forward) Networks, and Gaussian Networks.

Motivating applications can be found in the theory of Markov decision processes in both its adaptive and non-adaptive formulations, and in the theory of Stochastic Approximations. The results complement available results from Potential Theory for Markov chains, and are therefore of independent interest.

The need for such a measurement system is discussed, and a review of several systems currently available for this purpose is provided. The theory upon which many of these optical system is based is introduced, and the theory is extended for application to the measurement system introduced in this work. The differences and advantages of the developed vision system, compared to other optical systems, are investigated. Particular attention is paid to the area-based nature of the new technique. The performance of a prototype vision system is considered, and the results of a factorial design are interpreted to determine the sensitivity of the system to six environmental and system configuration factors. A calibration curve, which relates the surface roughness of fifty aluminum workpieces to an optical roughness parameter, is developed to provide a method of determining surface roughness directly from optical measurements. A prototype of a second optical system is constructed to attach directly to a CNC milling machine, and the suitability of this system for use in a machining environment is investigated.

There are three stages of this work. In the first stage, a preliminary experimental study is performed to investigate some of the basic attributes of the vision system. While this study is fairly simple, it demonstrates the potential usefulness of the proposed system. In the second stage, a prototype vision system is designed and constructed, and a detailed factorial design is undertaken to develop an empirical model of the system output as a function of six factors related to the system configuration and environmental conditions. Several calibration curves are produced for relating the system output to a range of known surface roughnesses. In the third stage, a prototype system is integrated with a Computer Numerically Controlled (CNC) milling machine to investigate the feasibility of using the system in a true machining environment. The results indicate some of the advantages and limitations of the proposed system.