Control Theory #13 - Second-Order Step Response

Instructor: Dr. Süleyman Burak ÇELİK

Many academic videos are categorized here: https://AcEdumy.com Welcome to Lesson 13 of the Control Theory course! In this lesson, we explore second-order step responses — where the damping ratio D determines the system behavior: ✅ Second-order lag ODE: T²ÿ + 2DTẏ + y = Ku ✅ Transfer function: G(s) = K / (1 + 2DTs + T²s²) ✅ Poles: s₁,₂ = (1/T)(−D ± √(D²−1)) ✅ D greater than 1: Overdamped — two real poles, no oscillation ✅ D = 1: Critically damped — fastest without overshoot ✅ D smaller than 1: Underdamped — complex poles, oscillatory ✅ D smaller than 0: Unstable — diverging oscillation ✅ Graph family: D = −0.1, 0.1, 0.4, 0.7, 1.0, 1.5 ✅ Pole locations in the s-plane 📚 Topics covered: 00:00 - Introduction 00:03 - What We Will Learn 00:30 - Second-Order ODE & Transfer Function 01:05 - Poles of the Second-Order System 01:42 - Case 1: D greater than 1 (Overdamped) 02:13 - Case 2: D = 1 (Critically Damped) 02:49 - Case 3: D smaller than 1 (Underdamped) 03:17 - Graph Family: Different D Values 04:04 - Pole Locations in the s-Plane 04:43 - Summary Key Result: The damping ratio D is the single most important parameter for second-order systems. It determines whether the response is overdamped, critically damped, or underdamped — and the pole locations in the s-plane tell the full story! 🔔 Subscribe for more engineering tutorials! 📺 Previous: #12 - Step Responses (First-Order) 📺 Next: #14 - Block Diagram Simplification #ControlTheory #SecondOrder #DampingRatio #StepResponse #Overdamped #CriticallyDamped #Underdamped #Poles #SPlane #ControlEngineering #Engineering #TransferFunction