Problem 1. Derive the state space model for each of the following circuit, using voltages on...
Consider the following RLC circuit, v1 and v2 are the two inputs and v0 is the output. (a) Obtain the state-space representation for the system if the state variables are defined as vc and iL. (b) Draw a signal flow graph based on the state-space model obtained in (a). (c) The output can be derived as V0(s) = G1(s)V1(s) + G2(s)V2(s). Use the state-space model obtained in (a) to find the transfer fnctions G1(s) and G2(s). 2 0
For each form show both state space equation and signal flow graph. Can you also include the Matlab code Problem 2. The system is given by its phase variable form state space equations 0 1 0 x(t) = | |x(t) + r(t) 0 -48-44 -12 0 y(t) 7 30lx(t) a) Find the transfer function of the system, and represent the system in cascade, parallel, controller-canonical, and observer-canonical forms. For each form show both state space equations and signal-flow graph. Do...
Problem 2. A signal flow graph for a system with input (k) and output y(k) is shown in Figure 1. 0.005 r(k) ei(k) z1v2(k) Vk) 0.03 0.1 0.05 e2(k) y(k) 0.07 e2(k) 11 0.7 0.2 V4(k) y(k) 0.9 0.4 Figure 1. Signal flow graph of a system. e) Find a state-space representation of the system in Figure 1 with state variables Find the transfer functionusing using Mason's gain rule and one other technique to verify the R(E) result g) Suppose...
3. For the non-ideal buck converter in Fig. 3, 1) Derive the state space model with state variable vector X as (it, vc), input variable vector U as (vi, io), output variable vector Y as vo. Derive the coefficient matrices in the model below. Note that duty cycle should be considered and included. dt ) di di dt 2)Select the line of a L, ie., a L-4-i, +A2Mz + Bı'y4B12%.and use perturbation-and- dt linearization approach to derive its small-signal representation....
please solve problems 1 and problems 2. PROBLEM 1: Derive state-space equations for the following circuit in the form of L1 where χ = :L2 L3 L1 and (a) y 7 V L3 R1 L1 L3 R3 Vt R2 Vc し2 (c) For Part (a), use the file CircuitStateSpace.slx (define the four matrices in Matlab) to verify your derivation using the following numerical values: R1-1; R3-1 R2-10; L1-1e-3 L3-1e-3 L2-10e-2 ; C1-10e-6 PROBLEM 2: (a) What are eigenvalues of the...
3. (Bonus) Determine a state variable model for the circuit in Figure 2. Note that If the voltage at the left and right hand side of a resistor R is v and vR, respectively, and the current is assumed to flow through the resistor from left to right, then the current passing through the resistor R is iR We know that the voltage drop across a capacitor is uc = the current passing through the capacitor branch is ic cat,...
In the state-space model form for an aircraft, the Dutch roll motion can be approximated using the following equations Assume the coefficients in the above state-space model have the following numerical values: N0.34 s-1 U1 154 fus = 5.236 ft/s2 Ya -7.8 ft/s2 N, =-0.616 s-2 y,-2.47 ft/s (a) Determine the Dutch roll eigenvalues (b) Dtermine the damping ratio and undamped natural frequency of the Dutch roll mode (c) Draw a pole-zero map of the system and provide pitctorial representation...
PROBLEM 1: The state-space representation of the inverter is the following (ignoring vs) 1 0(id The state-space representation of the current controller is the following: -1 01 0q C1 Vtd Combine the plant and the controller to obtain the state-space representation of the closed-loop sys tem X c1 C2 PROBLEM 1: The state-space representation of the inverter is the following (ignoring vs) 1 0(id The state-space representation of the current controller is the following: -1 01 0q C1 Vtd Combine...
please write clearly so I can read answer Derive the state-space model (state equation and output equation) in vector form for the following system. The system output is the angular velocity of the motor's shaft. Assume that the motor shaft is massless. 1.
this problem needs to be done using SciLab 9. A control system is given by the following state-space representation -8 101 [2 dt 1-6 00 y [1 0 0]x Please do the following: a. Find its transfer function representation. b. Calculate its zeros and poles c. Write a Scilab program to draw the step response and impulse response graphs in the same window with the step response graph in the upper half the window and the impuise response graph in...