Unit 1

Fundamental concepts in mathematical modeling: Abstraction-linearity and superposition-balance and conservation laws and the system boundary approach.
Lumped element modeling: Mechanical systems- Translational, rotational. Hydraulic systems. Thermal systems.RLC electrical systems. Modeling analogies.

Unit 2

Modeling of first order and second order systems: Governing equations for free and forced responses – transient response specifications – experimental determination of time constant and damping coefficient. Laplace Transforms. State space formulation.
Frequency response of Linear Time Invariant (LTI) systems: Frequency response of first order and second order systems – Transfer function – mathematical features – Bode plots-Relating time domain, frequency domain and state space.
Introduction to modeling and analysis of nonlinear engineering systems.

Unit 3

Introduction to linear system identification – time and frequency domain identification – discrete time input output models for LTI systems – linear least square parameter estimation.

Course Objectives

• Provide a generalized framework on modelling of engineering system through lumped parameter elements
• Introduce and apply different mathematical tools to analyse models of engineering systems
• Familiarize the use of software tools for solving engineering problems.

Course Outcomes

• CO1: Develop mathematical models for engineering systems in different domains and derive analogies
• CO2: Analyze first and second order linear and nonlinear systems in time and frequency domain
• CO3: Perform system identification for linear time invariant systems
• CO4: Simulate mathematical models of engineering systems using simulation software.

CO – PO Mapping

Textbook(s)

• Cha P.D, Rosenberg J.J and Dym C.L, Fundamentals of Modeling and Anlayzing Engineering Systems, Cambridge University 2000
• Keesman, Karel J. System identification: an introduction. Springer Science & Business Media, 2011.

Reference(s)

• Katsuhiko Ogata, System Dynamics, 4th Edition, Pearson Prentice Hall, 2004.
• Karnopp D C, Margolis D L and Rosenberg R C,Modeling and Analysis of Mechatronic Systems, Wiley Interscience, 3^rd Ed, 1999.
• Doebelin E O, System Dynamics: Modeling, Analysis, Simulation and Design, Marcel Dekker 1998.

Evaluation Pattern