Lecture 5: Sinusoidal Response of First-Order Systems | Process Dynamics & Control скачать в хорошем качестве

Lecture 5: Sinusoidal Response of First-Order Systems | Process Dynamics & Control

Welcome to Lecture 5 of Process Dynamics and Control (PDC) for Chemical Engineering. In this lecture, we analyze the sinusoidal response of first-order systems, which is a key concept for understanding frequency response, amplitude ratio, and phase lag in dynamic systems. This lecture also includes important GATE-level numerical problems based on first-order system responses. Using mathematical derivations and physical interpretation, we study how a first-order process behaves when subjected to a sinusoidal input, and how system parameters affect the output response. 📌 Topics covered in this lecture: • Review of first-order system transfer function • Sinusoidal input signal: – Amplitude – Frequency – Angular frequency • Laplace transform of sinusoidal input • Derivation of sinusoidal response of a first-order system • Separation of: – Transient response – Steady-state response • Physical interpretation of transient decay term • Steady-state sinusoidal output expression • Amplitude ratio (gain) of first-order system • Phase lag and its physical meaning • Effect of frequency on amplitude ratio and phase angle • Comparison of input and output sinusoidal signals 📈 Key results discussed: • Output amplitude reduction with increasing frequency • Phase lag as a function of system time constant 🧮 Numerical Problems (GATE-oriented): • Ramp input response of a first-order system • Deviation between input and output variables • Maximum deviation and time lag • Practical interpretation of time constant • Solved problems similar to GATE Chapter 4 questions • Step-by-step analytical solutions and plots 🎯 Who should watch this video? • B.Tech / B.E Chemical Engineering students • GATE Chemical Engineering aspirants • Students preparing for dynamic system analysis • Learners aiming to understand frequency response basics 📚 Course Information: This lecture is part of the complete Process Dynamics & Control course. All lectures are arranged sequentially in the same playlist. 📌 Prerequisites: • Laplace Transforms (Lecture 3) • First-order system response (Lecture 4) • Basic differential equations