Control Theory #05 - Plant Modeling: RLC Parallel Circuit

Instructor: Dr. Süleyman Burak ÇELİK

Welcome to Lesson 5 of the Control Theory course! In this lesson, we model an RLC parallel circuit - a second-order system: ✅ Review of RC circuit from Lesson 4 ✅ RLC parallel circuit setup ✅ Defining input (current) and output (voltage) ✅ Finding currents: i₁ through R, i₂ through C, i₃ through L ✅ Kirchhoff's Current Law application ✅ Eliminating integral terms via differentiation ✅ Final second-order differential equation 📚 Topics covered: 00:00 - Introduction 00:13 - Review: RC Circuit 00:34 - Circuit Setup 00:51 - Input/Output Definition (u=i, y=V) 01:14 - Kirchhoff's Current Law 01:37 - Finding i₁ (Resistor) 01:50 - Finding i₂ (Capacitor) 02:12 - Finding i₃ (Inductor) 02:49 - Combined Equation 03:19 - Removing Integral Term 03:51 - Substituting Control Variables 04:15 - Final Plant Model 04:53 - Summary Key Result: C·ÿ + (1/R)·ẏ + (1/L)·y = u̇ 🔔 Subscribe for more engineering tutorials! 📺 Previous: Plant Modeling - RC Circuit 📺 Next: Block Diagrams #ControlTheory #PlantModeling #RLCCircuit #SecondOrderSystem #DifferentialEquations #ControlSystems #Engineering #acedumy