Lecture 4: Response of First-Order Systems | Process Dynamics & Control (PDC) скачать в хорошем качестве

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.