Скачать или смотреть 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