The research aims at modeling and analyzing the interactions among functional process variables (FPVs) for process control in semiconductor manufacturing. Interaction is a universal phenomenon and different interaction patterns among system components might characterize the system conditions. To monitor and control the system, process variables are normally collected for observation which could vary with time and present in a functional form. These FPVs interact with each other and contain rich information regarding the process conditions. As an example in one of the semiconductor manufacturing processes, changes of interactions among FPVs like temperature and coefficient of friction (COF) might characterize different process conditions. This dissertation systematically developed a methodology to study interaction among FPVs through statistical and physical modeling. Three main topics are discussed in this dissertation: (1) Interaction patterns of FPVs under varying process conditions are studied both through experiments and statistical approaches. A method based on functional canonical correlation analysis (FCCA) is employed to extract the interaction patterns between FPVs and experiments of wafer polishing processes are conducted to verify the patterns of FPVs under varying process conditions. (2) Interaction among FPVs is further studied based on physics for process condition diagnosis. A mathematical model based on nonlinear dynamics is developed to study the strength of interaction and their directionalities, and advanced statistical control charts followed by this nonlinear dynamics model are established for process monitoring. (3) Complex interaction structures among multiple FPVs are analyzed based on nonlinear dynamics for a better understanding of process mechanism. An approach with extended nonlinear dynamics model is proposed to characterize process conditions, and combined engineering knowledge, complex interaction structure patterns are concluded accordingly for interpretation of process mechanism. The main contribution of this dissertation is to propose a novel methodology based on nonlinear dynamics, which could investigate interactions between components of systems and provide physical understanding of process mechanism for process monitoring and diagnosis. Through studies on interaction among FPVs in semiconductor manufacturing, this research provides guidance for improvement of manufacturing processes. Not limited to manufacturing, the developed methodology can be applied to other areas such as healthcare delivery.

Successful development of mechatronic systems requires a combination of targeted hardware and software design. The compact rescue robot (CRR), a quadruped pneumatically-actuated walking robot that seeks to use the benefits garnered from pneumatic power, is a prime example of such a system. This thesis discusses the development and testing of a simulation that will aid in further design and development of the CRR by enabling users to examine the impacts of pneumatic actuation on a walking robot. However, development of an entirely new dynamic simulation specific to the system is not practical. Instead, the simulation combines a MATLAB/Simulink actuator simulation with a readily available C++ dynamics library. This multi-platform approach results in additional incurred challenges due to the transfer of data between the platforms. As a result, the system developed here is designed in the fashion that provides the best balance of realistic behavior, model integrity, and practicality. An analytically derived actuator model is developed using classical fluid circuit modeling together with nonlinear area and pressure curves to model the valve and a Stribeck-Tanh model to characterize the effects of friction on the cylinder. The valve model is designed in Simulink and validated on a single degree-of-freedom test rig. This actuator model is then interfaced with SrLib, a dynamics library that computes dynamics of the robot and interactions with the environment, and validated through comparisons with a CRR prototype. Conclusions are focused on the final composition of the simulation, its performance and limitations, and the benefits it offers to the system as a whole.