To model an RLC circuit with multiple resistors (R), inductors (L), capacitors (C), and mutual inductances using state space representation, you can use MATLAB's `power_statespace` function. Below is a simple example that demonstrates how to define mutual inductances in a state space model.
Example RLC Circuit with Mutual Inductance
Consider a simple circuit with:
- Two inductors L1 and L2
- One resistor R
- One capacitor C
- Mutual inductance M between L1 and L2
Step-by-Step Guide
1. Define the Circuit Components
- Inductors L1 and L2
- Resistor R
- Capacitor C
- Mutual inductance M
2. Write the State Space Equations
- Define the state variables: currents through the inductors
and
, and voltage across the capacitor
. - Write the differential equations based on Kirchhoff's laws and the mutual inductance.
3. Convert to State Space Representation
- Formulate the state space matrices A, B , C , and D .
Here's an example MATLAB code that demonstrates this process:
disp('State Space Model:');
[y, t, x] = lsim(sys, u, t);
title('Current through L1 (i_L1)');
title('Current through L2 (i_L2)');
title('Voltage across C (v_C)');
Explanation:
1. Component Values
- Define the values for L1, L2 , M , R , and C .
2. State Variables:
-
: Current through inductor L1 -
: Current through inductor L2 -
: Voltage across capacitor C
3. State Space Matrices:
- Matrix A : Contains the coefficients of the state variables and mutual inductance.
- Matrix B : Represents the input to the system (voltage source applied to L1.
- Matrix C : Outputs all state variables.
- Matrix D : Represents direct feedthrough (none in this case).
4. Simulation:
- Use `lsim` to simulate the system response to a step input and plot the results