Dr Paramita Guha

2006-2012
Current Position: Scientist, CSIO, Chandigarh.

Most of the physical systems are governed by partial differential equations (PDEs). It is very difficult to obtain the analytical solutions even for simple geometries. One possible solution to this problem is to convert them into ordinary differential equations (ODEs). The finite element method (FEM) plays a very important role here. The PDE models can be discretized and a corresponding ODE model can be generated. In many problems, instead of a simple computation of the solution for specific material properties, boundary conditions etc., solutions have to be determined for a range of values for such parameters. Hence, repeated computations become necessary and unavoidable, increasing the computational efforts and time considerably. Moreover, in the process of discretization, the size of the model increases to few thousands to millions, which is unsuitable for further uses. Here model reductions play critical role which convert sized ODE model to another smaller sized ODE with almost same dynamic properties.This thesis involves study of model reduction methods for some typical computation-intensive problems in distributed parameter systems.The overall aim of this work is to improve the model reduction schemes for distributed parameter systems where characteristics are governed by ODEs. Several controllers have also been designed on those reduced models, such that these models can perform desired tasks. It has also been shown in this thesis that the outputs of the original and reduced models both with controllers match almost perfectly. The error between the outputs are also analyzed and estimated.In this thesis, the computational problems studied include, electromagnetic and coupled problems, heat conduction problems, induction heating problems and microelectromechanicalsystems (MEMS). Following the introductory chapter 1, a survey of the literature regarding vfew major issues and trends in computational distributed parameter systems and model reduc-tion techniques are presented in chapter 2. In chapter 3, the electromagnetic and coupled field circuit systems are studied. It involves modeling and model reductions for linear as well as nonlinear field-circuit coupled systems. Reduced order modeling and design of nonlinear con-trollers for heat conduction problems are reported in chapter 4. The error between the outputs of the original and reduced models are analyzed and estimated for several distributed systems and given in chapter 5. In chapter 6, an HJB based controller is designed for an induction heating system to steer the temperature profile from an initial value to a desired one. Modeling and control of MEMS devices require special attention, since its operations involve coupling of thermal, electrical, mechanical, fluidic phenomena. A new model reduction technique is pro-posed and a controller based on this reduced model is designed for a MEMS device to perform a desired task. These are reported in chapter 7 and 8. Finally a brief summary of the thesis and the scope of the future work are presented in the concluding chapter 9.The study illustrates the possibility of improving model reduction schemes by exploiting the structures of the finite element models. The theoretical basis of the approach is illustrated along with the resulting computational schemes. The schemes are illustrated and implemented for many practical systems with some simplifications, however, can easily be applied without those modifications.The required computational efforts are assessed in terms of the sizes, types and number of system equations required to be solved. The general advantages of the pro-posed computational schemes are discussed in detail, along with the possibilities of further generalizations and extensions. Finally, directions of further work are identified and discussed.

Publications

Journals

• P. Guha, M. Nabi, "Reduced Order Finite Element Modeling of a Nonlinear System: An Application to Induction Heating System", Accepted in International Journal of Engineering Systems Modelling and Simulation, (Inderscience)


• P. Guha, M. Nabi, ""Reduced Order Modeling of a Microgripper using SVD-Second-Order Krylov Method", International Journal for Computational Methods in Engineering Science & Mechanics, Taylor & Francis, 16, 65-70, 2015.


• P. Guha, M. Nabi, "Estimation of Errors for a POD based Reduced Order System: Application to Induction Heating", International Journal of Computational Methods in Engineering Science and Mechanics, Taylor & Francis, 13 (5), 334-341, 2012.


• P. Guha, M. Nabi, "Model Reduction and Controller Design of a Nonlinear Heat Conduction Problem using Finite Element Method", International Journal of Automation & Computing, Springer, 9 (5), 474-479, 2012.


• P. Guha, M. Nabi, “Optimal Control of a Nonlinear Induction Heating System using a Proper Orthogonal Decomposition based Reduced Order Model”, Journal of Process Control, Elsevier, 22 (9), 1681–1687, 2012.

Conferences

• P. Guha & M. Nabi, "Tracking and Control of Gripping Force of a Reduced Order Microgripper System", 10th Asian Control Conference, Malaysia, May, 2015


• P. Guha, M. Bazaz & M. Nabi, "Model Based Reduction for field circuit Coupled Systems" , International Conference on Computer Applications In Electrical Engg. Recent Advances, Roorkee, India, Oct 2013.


• P. Guha & M. Nabi, “Reduced Order Modeling and Robust Controller Design for a Heat Conduction Problem”, International Conference on Image Information Processing (ICIIP), Simla, India, Nov, 2011.


• P. Guha, S. A. Nahvi & M. Nabi, "Optimal Control of Temperature Profile for a Distributed Parameter Heat Conduction Problem with Generic Nontrivial geometry using Krylov Projection based Model Order Reduction", 3rd International Conference on Control and Optimization with Industrial Applications, Ankara, Turkey, Aug 2011.


• P. Guha & M. Nabi, "Reduced order finite element based modeling and simulation for thermal processing of 3D work-piece with nonlinear materials and generic geometries",2nd International Conference on Automation & Information Technology in Iron & Steel Making Processes, Ranchi, India, Dec 2009.


• P. Guha & M. Nabi, "Comparative study of Krylov and POD based model reduction methods for nonlinear electrothermal induction heating system", 2nd International Conference on Automation & Information Technology in Iron & Steel Making Processes , Ranchi, India, Dec 2009.


• P. Guha & M. Nabi, “A Control law for a nonlinear heat conduction problem on nontrivial domains using FEM”, 17th Mediterranean Conference on Control & Automation (MED’09), Thessaloniki, Greece, June, 2009.


• M. Nabi, M. Bazaz, P. Guha, “Krylov-Subspace Based Model Order Reduction for Field-Circuit Coupled Systems”, 19th European Conference on Circuit theory and design 2009 (ECCTD ’09), Antalya, Turkey, 23rd -27th August, 2009, pp. 480-484.