Modeling Dynamic Systems: Definitions and Examples

This lecture introduces the modeling of dynamic systems, starting with definitions and examples in mechanical and electrical systems. It covers differential equations, transfer functions, and linearization. The instructor explains the concept of systems, inputs, outputs, and perturbations, illustrating with real-world examples. The lecture delves into the importance of past system behavior, leading to differential equations and the distinction between static and dynamic systems. It also explores the principles of linearity, superposition, and homogeneity. The application of transfer functions for easier system analysis is highlighted, with examples from mechanical and electrical systems. The lecture concludes with the linearization process around an operating point using the Taylor series and the derivation of linear models for dynamic systems.