Reference no: EM132253318

Assignment -

For this assignment, you will need the template code RLC.m (attached).

A series resistor-inductor-capacitor circuit (see Fig. 1) can be described as a linear system, in which, for constant voltage, the current across the components follows the equation

d²/dt² I(t) + R/L d/dt I(t) + (1/LC) I(t) = 1/L dV/dt (1)

where I is the current, R the resistance, L the inductance, C the capacitance and dV/dt the rate of change of the voltage at the power source.

1. Write (1) in state space formulation, as a continuous time linear time invariant system. You may assume that the rate of change of the voltage is the control input (i.e., u = dV/dt) and the system state is the current and its first time derivative (i.e., x = (I, dI/dt)^T).

2. Derive the equations for the system in discrete time, such that you can compute x_t+1 as a function of x_t and u_t. Using RLC.m as a template, implement a simulation of the system, such that you can compute the current for 0 ≤ t ≤ 20 s from initial state x₀ = (0, 0)^T at a sampling rate of δt = 2 ms. Assume that L = 20H, C = 0.1 F, R = 4Ω and dV/dt = 10 V/s throughout the 20 s.

3. Modify the values of resistor, capacitor, and inductor in RLC.m. Run the modified program and comment on the results (settling time and overshoot) justifying your arguments based on the above chosen values.

Note - This one requires matlab and liner control system knowledge.

Attachment:- Assignment Files.rar