a) The Closed-loop Transfer function. b) Characteristic equation. c) Type and Order of the system.
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- R$ RL V (t) V(t) L Figure 7: A tuning circuit for radio 5. Figure 7 shows a tuning circuit used in radio. Derive the state equation using the linear graph approach. Also let the output variable be the voltage vo(t). Derive the output equation.2- Using Matlab, what are the step response curves of the closed-loop system, as shown in fig.1. the feedback represents the second-order dynamic system. (fill in the following table) For=0.4 Wn 1 3 6 9 10 R(S) 0.1 0.3 0.6 0.9 1 For w 5 rad/sec 3 Settling time Peak response 2 Wn s(s+23wn) Settling time Peak response C(s) Discuss the follow Which parameters or w occur on the rise time of the response? Which parameter increases the speed of response? Which parameters can be decreases the response amplitude? Which parameter decreases the steady error state? fig.2a) Suspension system of a car. Finding the transfer function F₁(s) = Y(s)/R(t) and F₂ (s) = Q(s)/R(t), consider the initial conditions equal to zero. car chassis www K₂ M₂ 1 Tire M₁ K₁ B₁ y(t)= output q(t) r(t)= input Where [r, q, y] are positions, [k1, k2] are spring constants. [B₁] coefficient of viscous friction, [M₁, M₂] masses. b) Find the answer in time q(t) of the previous system. With the following Ns values: M₁ = 1 kg, M₂ = 0 kg, k₁ = 4 N/m, k₂ = 0 N/m, B₁. = 1 Ns/m, considered m a unit step input, that is, U(s) = 1/s
- Match the transfer function with correct Bode phase plots. G(s) = 5 $+7 G(s)=s+5 G(s) = s+10 S S G(s) = S+ 10 QUESTION 10 90 deg 00 0 deg -90 deg 180 deg B. D 90 deg @ 0 deg -90 deg 180 deg 90 deg @ 0 deg -90 deg 180 deg 90 deg @ 0 deg -90 deg 180 deg7- Name the functions used, for multiplication of two polynomials p1, and p2 in MATLAB. a) convolution (p1, p2) b) multiply(p1, p2) c) conv(p1, p2) d) mult (p1, p2) 8- The Transfer Function of an L.T.I. system is entered as: a) trans_func(num, den) b) transferfunction (num, den) c) tf (num, den ) d) TF(num, den ) 9. What is the nature of the arrangement of the coefficients to store the expression y = 3s5+ s² + 6 in MATLAB? a) y=[3,0,0,1,0,6] b) y=[3,1,6] c) y=[3;0;0;1;0;6] d) y=[6,0,1,0,0,3] 10. To enter the transfer functions G(s): 2 to Matlah command useRequired information Use the following transfer functions to find the steady-state response yss() to the given input function f(t). NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. T(-) Y(s) F(s) s(e) 10 b. = 9 sin 2t s²(s+1) ' The steady-state response for the given function is yss() = | sin(2t + 2.0344).
- Consider the following Initial Value Problem (IVP) dy /at = -t * sin (y); y(t = 0) =1 Solve for y(t=0.5) using a) Forward Euler method with At = 0.25. (Solve by hand) Develop a Matlab script that solves for y (t = 5) using Forward Euler method. Use the time step levels given below and plot t vs y in the same plot. Include the plot with the right format (axis labels, legends, ...) in your solution sheet and include your Matlab script in the solution as well. i) At = 0.25 ii) At = 0.125 b) Backward Euler method with At = 0.25 (Solve by hand)10- To enter the transfer functions G(s)= a) G= th(2, [3,2]) b) c) d) G(s) TH (2, [2, 3]) G= tf (2, [3,2]) G(s)= TF(2, [2, 3]) 2 3s+2 c) A marginally stable response d) A marginally unstable response to Matlab command use: 3s+1 11- To enter the transfer function g(s)= $2+35+2 ,can be use a) num=[3, 1]; den= [1, 3, 2]; g-tf (den, num) num=[3, 1]; den=[1, 3, 2]; g=tf (num, den) b) c) num=[3; 1]; den=[1, 3, 2]; g=tf (den, num) d) num=(3, 1); den=(1, 3; 2); g-tf (num, den) 12- What is the output of the code (>>p=[0 1]; q=[ 1 -1 0]; step(p,q) ) a) An unstable response b) A stable response (s+1)(1) Consider the system represented by the block diagram. The closed loop transfer function T(s)-Y(s)/R(s) is (a) T(s)-50/(s+55 s+50). (b) T(s)=10/(s+50 s+55) (c) T(s)=10/(s+55 s+10). (d) None of the above. R(s)- 10 + s+5 5 Y(s)
- Given the trasnfer function G(s) numerator and denominator coefficients for Matlab code should be: O s³+2s+1 2s4+2s²+1' the num= [1 0 2 1] and den=[2 020 1] O num=[1 2 1] and den=[2 0 2 1 1] O num=[1 2 1] and den=[2 2 1] O num=[1 0 2 1] and den=[2 2 0 1]In this problem, you will have to first create a Python function called twobody_dynamics_first_order_EoMS. Given a time t and a state vector X, this function will return the derivatives of the state vector. Mathematically, this means you are computing X using some dynamics equation X = f(t, X). Once you have this function in Python, you can solve the differential equations it contains by using solve_ivp. The command will be similar to, but not necessarily exactly, what is shown below: solve_ivp(simple_pendulum_first_order_EoMS, t_span, initial_conditions, args=constants, rtol 1e-8, atol 1e-8) which integrates the differential equations of motion to give us solutions to the states (i.e., position and velocity of a satellite). In the above, t_span contains the initial time to and final time tƒ and it will compute the solution at every instant of time (you will define this later in Problem 1.3 below). The integration is done with initial state vector Xo which defines the initial position…1) a) Derive the mathematical model for the system shown below. b) Find a state variable model (matrix form) for the system. b) Determine state matrix, input matrix, and output matrix, when f (t) is defined as the input and X2 is defined as output for the system. (Here, both of the X1 and x2 , are time-dependent functions) » f(t) X1 X2 3,000 N 1,000 N 4,000 30 kg 20 kg 200 유 N.s