Simulating Linear State-Space Model of the Inverted Pendulum Step-by-Step in Simulink & MATLAB

Описание: Welcome to this tutorial! 👋
In this video, we’ll learn how to simulate a linear state-space model using MATLAB Simulink, with a complete example based on the inverted pendulum system.

We’ll start from the nonlinear model, apply small-angle approximations, and then linearize the system around the chosen operating point (α = 0, ω = 0, x₂ = 0, v₂ = 0). You’ll see how to:

Derive and calculate the operating point (uₒₚ) from the steady-state equations

Construct the A and B matrices (A_c, B_c) for the linearized model in MATLAB

Implement the state-space equations in a MATLAB Function Block

Use Simulink Integrator and Scope blocks to simulate and visualize the system response

Analyze system stability by checking eigenvalues of A_c

By the end of this tutorial, you’ll understand how to:
✅ Build and simulate linear models in Simulink
✅ Use deviation variables (Δx, Δu) in linearized systems
✅ Interpret simulation results and identify system instability

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This example lays the foundation for upcoming videos, where we’ll design and apply LQ optimal control to stabilize the inverted pendulum.

📘 Topics Covered:

Nonlinear → Linear Model Transition

Operating Point Calculation

State-Space Representation

Simulink Setup for Linear Models

System Stability Analysis

🧠 Software Used:

MATLAB R2020 / Simulink

Inverted Pendulum Linear Model

📺 Next Video:
👉 LQ Optimal Control of the Linearized Inverted Pendulum in Simulink

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