Micro-cantilevers have revolutionized microscopy in the past decade. Ingenious ways of using them have been deviced to probe and manipulate material at very small scale. Research made possible by such structures is the reason for numerous articles in reputed journals such as Science and Nature. They have found widespread use in diverse areas such as biology (DNA strands have been manipulated using micro-cantilevers) and semiconductor processing. Some of the recent research which utilize micro-cantilevers are in the areas of nano-machining and electron spin detection.
Inspite of the importance of control design for such systems, a systematic study of the role of controllers has been neglected. The proposed project will perform such a study where the primary objective is to obtain control-oriented models for micro-cantilever based devices, and the utilization of such models to design and implement controllers. Based on such models a methodology to assess the limits of performance of such a device will be developed. Initial research has indicated that vast advances can be made by such a study.
For effective design of controllers for such systems a good understanding of the underlying physical principles is required. There are novel phenomena which affect the performance adversely but can aid the sign process. As an example, thermal noise in systems utilizing micro-cantilevers can be the limiting factor in the achievable performance. However, using thermal noise, nominal model and bounds on modeling errrors can be obtained in a straightforward manner. Such phenomena will be studied and exploited for modeling.
Ongoing research has indicated that complex behavior is possible in the cantilever-sample dynamics. Control design can play an important role in stabilizing desirable behavior that exist amidst the complex dynamics. Increased speeds of operation and better resolutions are the important benefits of such a design, which will be pursued under this project. Also, with increasing miniaturization the quantum-mechanical effects in the micro-cantilever start to become relevant and a need to control such effects becomes important.
Uncertainty in any model for a cantilever based device is unavoidable. One of the reasons for such uncertainty is that the cantilever dynamics is determined by the material being probed by the cantilever. Moreover, some disturbances present in such devices are characterized in a stochastic framework while others are described in a deterministic, time-domain setting. Thus controllers which can handle performance specifications with respect to such disturbances in the presence of uncertainty can be particularly valuable. The study of better techniques, software development and implementation of such controllers in a device which employs a micro-cantilever is proposed.
A course which educates the student in modeling, validation and implementation issues of design will be developed. This course will comprise of an appropriate combination of theory and experiment. Aspects relevant to micro-cantilever based devices will also be incorporated. Lectures to be given by entrepreneurs will highlight the financial issues to be considered for the success of a project. In another course, recent methodologies of controller design which rely on convexity theory will be presented. This course will unify most of the convex analysis techniques that are being utilized in the design of contollers. Efficient computational tools to design such controllers will be given. ***
