Chemical Engineering, IIT Bombay
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Sharad Bhartiya
Identification
Modelling
Optimisation
Process Control
Systems Biology
Personal Information
Full Name: Sharad Bhartiya
Room No: 311, Chemical Engineering
+91 (22) 2576 7225 (O)
+91 (22) 2576 8225 (R)
+91 (22) 2572 6895 (Fax)
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Detailed Information / Research Group Web-Page
Background
B.E. R.E.C., Durgapur, 1991
M.Tech.., IIT Madras, 1993
Ph.D., Oklahoma State University, 2000
Awards & Fellowships
Amar Dye Chem Award, 2004
R&D
Publications
A list of publications is available in this link.
R&D Areas/Projects
Modelling and control of switched systems
Many applications in chemical engineering often exhibit a switching character due to the presence of discrete modes in the course of their operation. First principles models of such systems constructed using process simulators are far too complex for use in online applications, especially in model based control. For such systems, numerous control-relevant modeling approaches have been reported in literature such as Mixed Logic Dynamical (MLD) models and Piece Wise Affine (PWA) models among others. These models describe the evolution of states in each discrete mode using linear equations. Fewer control-relevant models have been reported that address the nonlinear behavior of switched systems. Our method involves a trajectory based linearization and employs a model bank with a set of local linear models for each discrete operational mode. The model bank is generated by linearizing the first principles model across a carefully designed trajectory based on accuracy of multi-step ahead predictions. The numerous models thus obtained are clustered using the gap metric as the distance measure and representative models are selected. The selected linear models are aggregated using Bayesian or Fuzzy approaches to obtain the global model for the nonlinear switched system. An experimental case study of a benchmark problem consisting of three tanks are used to validate the proposed modeling strategy. Currently, we are extending this strategy for control of a simulated moving bed chromatographic process.
A Dual Terminal set MPC formulation for control of linear switched systems
Switching characteristics of hybrid systems bring discontinuity and nonlinearity in their course of operation and pose major challenges in developing stabilizing Model Predictive Control (MPC) for them. For Piecewise Affine (PWA) Systems, the MPC problem requires on-line solution of Mixed Integer Programs (MIPs) for obtaining the input profile. Since, complexity of the optimization problem that needs to be solved in MPC increases combinatorially with respect to the integer variables, on-line computing of MPC control law for large scale problems and/or problems with large horizons turns out to be expensive.This work attempts to synthsize a stabilizing MPC formulation, under the popular framework of terminal cost - terminal constrained set MPC, which enables tuning the complexity of the control algorithm while ensuring stability. The proposed approach introduces a novel idea of a pre-terminal set, that eliminates the need for binary decision variables to model mode transitions after the trajectory enters in pre-terminal set, thereby reducing the on-line complexity although at the expense of optimality. Currently, these ideas are being extended to robust tube-based MPC.
Explicit Model Predictive Control
Multiparametric (mp) programming pre-computes optimal solutions offline which are functions of parameters whose values become apparent online. This makes it particularly well-suited for applications that need rapid solution of online optimization problems such as in model predictive control (MPC). In this work, we have developed a novel approach to multiparametric programming problems based on an enumeration of active sets and use it to obtain parametric solution for a convex quadratic program (QP). To avoid the combinatorial explosion of the enumeration procedure, an active set pruning criterion is presented that makes the enumeration implicit. The method guarantees arriving at the smallest number of regions with no regions of the parameter space left unexplored. The method has been successfully used for implementation of MPC on an experimental magnetic levitation setup with a sampling time of a few milliseconds. Currently we are working on obtaining lower complexity approximations of the control law-parameter maps.
Systems Biology (Collaborator: Prof. K.V. Venkatesh, IIT Bombay)
Living systems must adapt quickly and stably to uncertain environments. A common theme in cellular regulation is presence of multiple feedback loops in the network. An example of such a feedback structure is regulation of tryptophan concentration in Escherichia coli. A pertinent question is whether such multiple feedback loops is a case of regulatory overkill, or do these different feedback regulators have distinct functions? (Freeman, Nature, 295, 313-319, 2000). Another moot question is how can robustness to uncertainties be achieved structurally through biological interactions. We are currently establishing correlations between the feedback structure and robustness using feedback theory. We are also focussing on how feedback designs in nature cope with intrinsic noise.
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