Control Theory #09 Drawing Block Diagrams from DC Motor Equations

Instructor: Dr. Süleyman Burak ÇELİK

Many academic videos are categorized here: https://AcEdumy.com Welcome to Lesson 9 of the Control Theory course! In this lesson, we draw a complete block diagram for a DC motor system with coupled electrical and mechanical dynamics: ✅ DC motor equations: electrical + mechanical ✅ Back EMF and torque coupling relations ✅ State-space form with two state variables ✅ Two-loop block diagram construction ✅ Disturbance input (load torque TL) 📚 Topics covered: 00:00 - Introduction 00:21 - Problem Setup: DC Motor (u → ω) 00:37 - Electrical Equation (Ra, La, eb) 00:55 - Back EMF & Torque Coupling (cφ) 01:11 - Mechanical Equation (J, TL) 01:27 - Substituting Coupling Terms 01:41 - State Equation for Current (dia/dt) 01:55 - State Equation for Speed (dω/dt) 02:08 - Converting to Integrator Form 02:22 - Four-Step Method Check 02:39 - Building Current Summing Junction 02:54 - Input Path: u → 1/La 03:04 - Current Feedback Path: -Ra/La 03:18 - Speed Coupling: -cφ/La (Back EMF) 03:30 - Current Integrator (1/s → ia) 03:42 - Building Speed Summing Junction 03:56 - Torque Generation: cφ/J 04:08 - Disturbance Path: TL → -1/J 04:18 - Speed Integrator (1/s → ω) 04:28 - Output Definition (y = ω) 04:38 - Final Sign & Direction Check 04:50 - Complete DC Motor Block Diagram 05:03 - Practical Notes 05:14 - Summary & Closing Key Result: DC motor has TWO coupled loops — electrical loop (current ia) and mechanical loop (speed ω), linked by cφ in both directions! 🔔 Subscribe for more engineering tutorials! 📺 Previous: #08 - Drawing Block Diagrams from RLC Circuit 📺 Next: More Advanced Control Systems #ControlTheory #DCMotor #BlockDiagrams #ControlEngineering #Engineering #StateSpace #DifferentialEquations #ElectricalEngineering #MechanicalEngineering