Question

Problem 2: Consider again the two RLC circuits from HW1 Problem 6 C L IKs IKs L In HW1 Problem 6 you found the transfer function Vc(s)V(s) for each of the circuits, using Impedance Analysis. You essentially assumed zero initial conditions (for the capacitor's voltage S and for the inductor's current) 2.1. Develop a state-variable model for each of the circuits, where the state variables are (in both circuits) xi vc and x2 i That is, derive (for each circuit) a model consisting of two coupled first order equations: dx/dt as fimction ofxı, X and Vn, and dxy/dt as function of x, x: and Vn. 2.2. Create a Simulink simulation for each circuit, based on the state-variable models developed in (2.1). In each circuit use two integrators, one with an output of xi and another with an output of x. Assign arbitrary initial conditions to each integrator, and assume initially that vn = 0. Obtain plots of vc(t) and i(t) 2.3. Let v() be a step function of size 1V, and assume zero initial conditions. Compare the step response of each capacitor's voltage to the ones that you obtained in HW1 Problem 6. 2.4. Simulate the circuits with the initial conditions assumed in (2.2) together with the step input assumed in (2.3). Plot the capacitor's voltage and inductor's cuTent in each circuit.