Control Theory #11 - Impulse Response and Convolution

Instructor: Dr. Süleyman Burak ÇELİK

Many academic videos are categorized here: https://AcEdumy.com Welcome to Lesson 11 of the Control Theory course! In this lesson, we explore the impulse response and how convolution connects it to system output: ✅ Dirac impulse δ(t) — properties and Laplace transform ✅ Impulse response g(t) = S(δ(t)) ✅ Laplace pair: g(t) ↔ G(s) ✅ Convolution integral: y(t) = ∫g(t−τ)u(τ)dτ ✅ Laplace domain: Y(s) = G(s)·U(s) ✅ Three-step process: transform, multiply, inverse transform ✅ Examples: first-order lag and pure integrator 📚 Topics covered: 00:00 - Introduction 00:03 - What We Will Learn 00:21 - Dirac Impulse δ(t): Definition and Properties 00:42 - Impulse Response g(t) = S(δ(t)) 00:59 - Key Relationship: g(t) ↔ G(s) Laplace Pair 01:22 - Computing the Output: The Answer is Convolution 01:35 - Convolution Integral Formula 01:56 - Laplace Domain: Convolution → Multiplication 02:14 - Three-Step Process: Transform → Multiply → Inverse 02:39 - Example: First-Order Lag (K/(1+sT)) 03:03 - Example: Pure Integrator (1/s) 03:23 - Summary Key Result: The impulse response g(t) fully characterizes a system. Output for any input can be found by convolution in time or multiplication in the Laplace domain! 🔔 Subscribe for more engineering tutorials! 📺 Previous: #10 - Transfer Function Concept 📺 Next: #12 - Step Responses #ControlTheory #ImpulseResponse #Convolution #TransferFunction #LaplaceDomain #ControlEngineering #Engineering #DiracImpulse #SystemResponse #DifferentialEquations