PDC Lecture 3: Laplace Transforms for Process Control | Chemical Engineering скачать в хорошем качестве

PDC Lecture 3: Laplace Transforms for Process Control | Chemical Engineering

Welcome to Lecture 3 of Process Dynamics and Control (PDC) for Chemical Engineering. In this lecture, we introduce Laplace Transforms, which are one of the most important mathematical tools used in Process Dynamics and Control. Laplace Transforms help us convert time-domain differential equations into algebraic equations, making dynamic system analysis much simpler. 📌 Topics covered in this lecture: • What is Laplace Transform and why it is needed in Process Control • Difference between steady-state and dynamic analysis • Definition of Laplace Transform • Laplace Transform of basic functions: – Step function – Unit step function – Ramp function – Exponential function – Sine and cosine functions • Laplace Transform of derivatives • Solving first-order differential equations using Laplace Transform • Examples relevant to Process Dynamics and Control • Introduction to Inverse Laplace Transform • Partial fraction method • Final value theorem and initial value theorem • Physical interpretation of Laplace Transforms in process systems This lecture builds the mathematical foundation required to derive transfer functions and analyze dynamic behavior of chemical processes. 🎯 Who should watch this video? • B.Tech / B.E Chemical Engineering students • GATE Chemical Engineering aspirants • Students new to Process Dynamics and Control 📚 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 and ordinary differential equations. 💬 Please post your doubts in the comments. GATE-level numerical problems will be discussed in upcoming lectures.