When you write your statement of purpose, here are some things to consider (in no particular order).
Obviously, you will only include a few items from this list in your statement of purpose. Basically, you are trying to communicate that you can and will succeed in graduate school and what research you are interested in.
Below are several statements of purpose that I wrote at different times for different things. This first one I wrote early in the fall semester of my senior year.
As long as I can remember, I have wondered what things were made of and why one material was used, as opposed to another, for a given application. When I was about eleven years old this curiosity drove me to look up "metal" in our encyclopedia. The entry was cross referenced to about thirty other entries in the encyclopedia for different metals. I then spent the afternoon poring over everything from antimony to zinc. I was particularly fascinated by the way that iron could be made into pig iron, stainless steel, carbon steel or any other number of alloys simply by varying the processing conditions and the additives used. It seemed to me that an alloy had been formulated for every different application imaginable and I began to wonder if there were other alloys and materials that could be made stronger, lighter and better.
As a senior in the chemical engineering program at Michigan State University, this same curiosity is with still me, but has been formalized somewhat by both my class work and my employment at a National Science Foundation Research Center contained within M.S.U.'s Composite Materials and Structures Center (CMSC). The research experience that I have gained at the CMSC has confirmed my lifelong ambition to earn a PhD and become a university professor. I am interested in investigating further the materials processing aspect of chemical engineering. Specifically, I want to research how processing conditions affect the properties of advanced materials, such as optically or electrically active polymers, ceramic-polymer mixtures, or "ferrocene" polymers.
The satisfaction in engineering for me is the application of science to the problems of everyday life. Advanced materials have tremendous potential for enhancing our lives and I look forward to furthering their development.
I was unsatisfied with this statement of purpose, particularly the bit about, "when I was eleven..." The statement of purpose evolved over the semester. The final statement was much changed.
As a senior in the chemical engineering program at Michigan State University, I have enjoyed a unique opportunity to participate, as an undergraduate, in graduate research at MSU's Composite Materials and Structures Center (CMSC), a National Science Foundation Research Center. In the spring semester of my sophomore year, I used a pilot mold to manufacture polymer composite plaques which I prepared for short beam shear, tensile and zero degree flexural tests.
During my junior year, I worked on determining the diffusion coefficients for the matrix resin into the fiber sizing films using a microdielectric technique. This measurement allowed prediction the time required to develop optimum interphase properties. I developed the experimental procedure, measurement protocol and computer models for the process. I then documented the results in a paper that was the basis for both a journal article and a chapter in my supervising graduate student's dissertation.
This year I have been working independently. I have begun to develop microdielectrometry as a tool for determining resin/sizing compatibility in situ, which allows one to determine compatibility from a sample of the sized fiber, without needing a liquid sample of the fiber sizing itself. This important development would allow an industry using composite materials, without access to the proprietary information of the sizing/matrix composition, to control their fiber/matrix interphase empirically.
This experience at the CMSC, more than anything else, has confirmed my desire to become a university professor and research scientist. I want to research how processing conditions affect the properties of advanced materials, such as optically or electrically active polymers, ceramic-polymer mixtures, or "ferrocene" polymers. I am also interested in investigating the optimization of advanced process control schemes.
The satisfaction in engineering for me is the application of science to the problems of everyday life. Both of these disciplines have tremendous potential for enhancing the world we live in and I look forward to furthering their development.
As I alluded earlier, statements of purpose evolve. In my first year of graduate studies I applied for several fellowships. Since I knew now what research I wanted to do I wrote a more specific essay. Polymers were out, chemical process control was in.
Chemical engineers design, construct, and operate chemical processes. Whether these processes are as simple as a cooling jacket on a reactor, or as complex as an entire chemical plant, they require process control technology to insure that they operate safely, efficiently, and cost effectively.
Although off-the-shelf hardware and software are routinely applied to the control of processes with a limited number of inputs and outputs, their application to large scale chemical processes has been severely limited. This is because traditional control techniques, when applied to large scale processes, have too much on-line computational load and tend to produce nonsensical results due to numerical inaccuracies which arise from the large scale, poorly conditioned nature of these processes. Limited input-output data exacerbates the difficulty in controlling these processes, since models developed from these data will be inaccurate. Linear control design techniques are not applicable, due to nonlinearities and the wide range of operating conditions which commonly occur in chemical processes, and to limitations on the control equipment and process operating conditions. For these reasons, the analysis and control of large scale processes are among the most important, challenging, and interesting problems in process systems theory and control. This motivates my research in the development of both analysis tools and controller design strategies for large scale nonlinear systems.
I will develop improved theoretical tools for analyzing the stability and performance of large scale nonlinear systems with model uncertainties. These general analysis tools would allow quantitative comparisons between different control algorithms so that rational decisions can be made regarding which approach is most appropriate in a particular application. For example, since the difference in cost between control systems can be substantial, the cost of implementing, maintaining, and commissioning different control systems could be explored for a variety of plant designs. The analysis tools would also allow comparison of different plant designs in terms of their ability to achieve performance specifications.
Addressing constraints when making decisions on plant design and actuator/sensor selections is important because limitations on control equipment and process operating conditions can have a significant impact on these decisions. These tools would also allow calculation of optimal control equipment and sensor type, location, and number to provide the required performance using a given controller design method with full consideration of the capital, installation, and maintenance costs of sensors and actuators.
The general stability and performance analysis tools will be developed using absolute stability theory to bound the magnitude and slope of the nonlinearities. The framework of linear matrix inequalities will be used for formulation of the optimization-based approach. Next, model structure will be exploited for wide classes of processes using circulant, singular value, and Toeplitz matrix theories to improve numerical conditioning and reduce computational expense.
I will also develop a general optimization-based method for designing control systems for large scale processes which takes nonlinearity and model inaccuracy into account thereby integrating design of the control system with the design of the plant. The performance requirements will be quantified in the objective function, and the optimum will be over all future control actions. The algorithm will handle a variety of uncertainty structures and multiple performance requirements in a transparent manner.
This year I am taking graduate courses in core chemical engineering subjects to provide a strong foundation in physics-based modeling of large scale process systems, and courses in matrix theory, optimization theory (linear and nonlinear programming), and other applied mathematics to complement my graduate control courses. The control courses I will take over the next few years will include large scale systems theory, identification and adaptive control, nonlinear control, and stochastic optimal control.