Скачать или смотреть Lecture 4: Response of First-Order Systems | Process Dynamics & Control (PDC)

Welcome to Lecture 4 of Process Dynamics and Control (PDC) for Chemical Engineering.

In this lecture, we study the dynamic response of first-order systems, which form the foundation of Process Dynamics and Control. Using a physical example (mercury thermometer), we derive the first-order mathematical model, obtain the transfer function, and analyze the time response of the system for different standard inputs.

This lecture is extremely important for GATE Chemical Engineering, as first-order systems frequently appear in both theory and numerical problems.
📌 Topics covered in this lecture:

• Concept of input–output response in dynamic systems
• Physical interpretation of system order
• Modeling of a first-order system using energy balance
• Lumped parameter model and key assumptions
• Derivation of first-order differential equation
• Transfer function of a first-order system
• General procedure for development of transfer functions
• Deviation variable formulation
• Application of Laplace Transform to dynamic equations
• Standard form of first-order transfer function
• Transient response of first-order systems

📈 Time-domain responses discussed:

• Step response
• Impulse response
• Ramp response

⏱ Time Constant (τ):

• Physical meaning of time constant
• Interpretation of 63.2% response
• Effect of time constant on system speed

🎯 Key learning outcomes:

By the end of this lecture, students will be able to:
• Identify first-order systems in real processes
• Derive transfer functions from physical models
• Understand transient behavior of chemical processes
• Analyze system response for standard inputs

👨‍🎓 Who should watch this video?

• B.Tech / B.E Chemical Engineering students
• GATE Chemical Engineering aspirants
• Students learning Process Dynamics and Control for the first time

📚 Course Information:

This lecture is part of the complete Process Dynamics & Control course.
All lectures are arranged sequentially in the same playlist.

📌 Prerequisites:

• Basic calculus
• Ordinary differential equations
• Laplace Transforms (covered in Lecture 3)

💬 Discussion & Next Steps:

Please watch the entire lecture carefully and post your doubts in the comments.
GATE-level numerical problems and higher-order system analysis will be discussed in upcoming lectures.