Understanding State-Space Modeling of a Series RLC Circuit Through MATLAB Simulation

This paper presents the state-space modeling and MATLAB simulation of a series RLC circuit. The inductor current and capacitor voltage are selected as the state variables because the inductor and capacitor are the energy-storage elements of the circuit. Using Kirchhoff’s Voltage Law and basic circuit equations, the state equations are derived and represented in the standard matrix form of state-space modeling. The corresponding transfer function is also derived for comparison. The developed model is implemented in MATLAB using a 1-V unit-step input. The capacitor voltage and inductor current responses are analyzed to understand the transient behavior of the circuit. The damping ratio, natural frequency, damped frequency, and eigenvalues are calculated to study the stability and oscillatory nature of the system. A phase-plane analysis is also performed by plotting capacitor voltage against inductor current, resulting in a clockwise inward spiral toward the steady-state point of 1 V and 0 A. Overall, the work demonstrates how state-space modeling connects the mathematical equations of an electrical circuit with MATLAB simulation and physical interpretation of the system's dynamic behavior.