Bio
Prof. Nita H. Shah is a distinguished academician and researcher in the field of Mathematics, currently serving as a Professor and Head of the Department of Mathematics at Gujarat University, Ahmedabad, India. With a robust academic foundation comprising B.Sc., M.Sc., M.Phil., and Ph.D. in Mathematics, she specializes in Operations Research and Dynamics of Infectious Diseases. Prof. Shah has an extensive publication record, with over 415 international and 50 national papers to her credit, and has guided 33 scholars. Her research contributions span inventory systems, supply chain coordination, and control strategies for infectious diseases, reflecting a deep commitment to advancing mathematical modeling and its applications. She holds an ORCID iD of 0000-0002-6453-2044 and is recognized as a Fellow of the institution, underscoring her leadership and expertise in the scientific community.
Educational Journey
Gujarat University
B. Sc., M. Sc., M. Phil., Ph. D. in Mathematics, Professor & HoD • Operations Research & Dynamics of Infectious Diseases
Experience
Gujarat University
0 - 0Gujarat Cancer & Research Institute
0 - 0Research
Pole Placement Approach for Controlling Double Inverted Pendulum
In this paper, we present in-depth analysis of the classical double inverted pendulum (DIP) system using the DIP modeling and the pole placement approach to control it. The double inverted pendulum system has the characteristics of multiple variables, non-linear, absolute instability; it can reflect many key issues in the progress of control, such as stabilization, non-linear and robust problems etc. DIP model is a simplified model of the anterior-posterior motion of a standing human. DIP has four equilibrium points (Down-Down, Down-Up, Up-Down, Up-Up). The objective of this paper is to keep the double pendulum in an Up-Up unstable equilibrium point. Modeling is based on the Euler-Lagrange equations, and the resulted non-linear model is linearized around Up-Up position. The built of mathematical model of double inverted pendulum plays a guiding role on the stability of the system. The eigen-values of the system which are the poles of the system have enormous influenced on stability and system response. Pole placement is the control method which places the poles at the desired position to control the system by calculating gain matrix of the system. In this paper, the performance of the pole placement method is analyzed by MATLAB to control the double inverted pendulum.
Optimal Pricing, Shipments and Ordering Policies for Single-Supplier Single-Buyer Inventory System with Price Sensitive Stock-Dependent Demand and Order-Linked Trade Credit
The integrated inventory policy of single-supplier single-buyer is studied under orderdependent trade credit terms. The demand is assumed to be price-sensitive stock-dependent. Under order-dependent trade credit scenario, the buyer is eligible for settlement of account at a allowable delay period if the order quantity is larger than that of pre-specified order by the supplier. The objective is to maximize joint profit of the supply chain with respect retail price of the unit and order time and number is given to compute optimal decision policy. The numerical example is given to illustrate the mathematical concept. Sensitivity analysis is carried out to deduce managerial insights.
