Detailed State-Space Model Derivation of Double Mass-Spring-Damper System with Python Simulations

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In this dynamical systems, control engineering, and control theory tutorial, we develop a state-space model of a double mass-spring-damper system. We also explain how to simulate the derived state-space model in Python. We use two approaches for discretizing the model of the mass-spring-damper system. The first approach is based on the Backward Euler method and the second approach is based on the Python Control Systems Library. The main motivation for creating this video tutorial comes from the fact that mass-spring-damper systems are prototypical and generic systems that can represent physical models of a large number of dynamical systems, such as car suspension systems, harmonic oscillators, robotic arms, etc.