Control Theory #12 - Step Responses

Instructor: Dr. Süleyman Burak ÇELİK

Many academic videos are categorized here: https://AcEdumy.com Welcome to Lesson 12 of the Control Theory course! In this lesson, we explore step responses — the most important test signal for analyzing control systems: ✅ Heaviside step function σ(t) — definition and Laplace transform ✅ Step response computation: Y(s) = G(s) · (1/s) ✅ Pure integrator response: y(t) = t·σ(t) — a ramp ✅ First-order lag ODE: T·dy/dt + y = K·u ✅ Step response: y(t) = K·(1 − e^(−t/T)) ✅ Time constant T: 63.2% at t = T, family of curves ✅ Stable (T greater than 0) vs Unstable (T smaller than 0) poles ✅ Time delay: y(t − Δ) ↔ e^(−sΔ)·Y(s) ✅ Standard transfer function blocks table 📚 Topics covered: 00:00 - Introduction 00:03 - What We Will Learn 00:24 - Heaviside Step Function σ(t) 00:44 - Step Response Computation 01:07 - Integrator Ramp Response 01:32 - First-Order Lag ODE 01:54 - First-Order Step Response 02:17 - Graph Family: Different Time Constants 02:43 - Stable vs Unstable (T smaller than 0) 03:09 - Time Delay 03:36 - Standard Transfer Function Blocks 04:11 - Summary Key Result: The step response reveals system dynamics! The time constant T determines speed, while pole location determines stability. Standard blocks (integrator, first-order lag, time delay) are the building blocks of all control systems! 🔔 Subscribe for more engineering tutorials! 📺 Previous: #11 - Impulse Response and Convolution 📺 Next: #13 - Closed-Loop Transfer Function #ControlTheory #StepResponse #Heaviside #FirstOrderSystem #TimeConstant #TransferFunction #TimeDelay #Stability #ControlEngineering #Engineering #LaplaceTransform #SystemAnalysis