Prerequisites
Linear Algebra
Contents:
This course can cover modeling of dynamic (time varying) systems, with applications in business, production-inventory and socio-economic systems. Course topics include:
- Brisk review of Introduction to Dynamical Systems and Linear Dynamical Systems (Motivation through examples in business/ industrial settings); Modeling linear dynamical systems using ODEs; Solution characterization, solution methods for first, second, higher order ODEs; Characterizing higher order ODEs as linear systems
- Motivating examples of dynamical systems with feedback
- Laplace transforms. Transfer functions: Block diagrams, poles, zeros, delays
- Stability, regulation, tracking and Controllability of dynamical systems.
- Proportional, Integral, Derivative (PID) control
- Root locus design method: Perspective, procedure finding root locus, design using lead, lag, notch compensation
- Frequency-Response Design method: Frequency-response design method, Bode/ Nyquist plots
- State space method: System description, block diagrams, state equations and analysis
- Discrete systems and non-linear systems
The second part can focus on capturing industrial and social systems using dynamics equations/ system dynamics methodology, including:
- Stock Management Structures and Industrial Dynamics
- Models for social systems and economics
- Simulation of linear and non-linear systems
- Simulation of Discrete-time and Continuous time systems
References
- Chi-Tsong Chen (1998) Linear System Theory and Design, 3rd edition, Oxford University Press
- Normal Nise, 2018,, Control Systems, Wiley India
- Morris W. Hirsch, Robert L. Devaney and Stephen Smale (2004) Differential Equations, Dynamical Systems, and an Introduction to Chaos, 2nd edition, Academic Press.
- John D. Sterman, 2000, Business Dynamics, McGraw Hill