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Question 11 The Newton's second law is presented as mat mały = u(t) a) Find the...
ï = 2u – 48 - 8x (a) Use Laplace transform to solve for the transfer function (b) (show steps). (b) Bring into state space form. X = AX + BU Y = CX + DU Y = {0} and X = X;} and U = {4}} (c) Find the transfer function from state space form (show le steps). e there a transfer functons, and what is the X2)
Problem 1: Given the transfer function from input u(t) to output y(t), Y (s) U(s) = s 2 − 4s + 3 (s 2 + 6s + 8)(s 2 + 25) (a) Develop a state space model for this transfer function, in the standard form x˙ = Ax + Bu y = Cx + Du (b) Suppose that zero input is applied, such that u = 0. Perform a modal analysis of the state response for this open-loop system. Your...
6. (15 points) The EoM of a system is given below. The inputs are u(t) and u2(t the outputs are x1, , x2. Write the state space representation of the system.X AX+BU and Y = CX + DU) 2x1 + 4x1-2x2 + 8x1-2X2 = 24(t) + 6u2(t) 3X2ー6x1 + 3x2-3x1 + 9X2-u2(t)
Can someone please explain how to solve the problem below? 6. State Space Systems: a. (5 pts) Determine the state space system in controllable canonical form that implements the transfer function Y(s)_ 252 +5 U(s) s+4s+7s +12 b. (10 pts) For the state space system given below, design a controller u =-Kx+v such that the eigenvalues of the closed loop system are -10, – 20. To 17 , y = Cx C = [25] x = Ax+Bu with A= ln...
This is for Controls Systems class. Please solve everything, and show all work and correct answers and matlab codes for positive rating. A - C, E - F do by hand. D, G-I do in Matlab as instructions direct. (Show codes and plots for matlab solutions too!), show the code and plots obtained for positive rating. Provided below is the Handout 7 equations that are needed for this problem for use. 1. The state space model of a system is...
Problem 1 Given the transfer function from input u(t) to output y(t), s2-4s +3 Y(s) U(s) (s2 + 6s + 8)(82 + 25) (a) Develop a state space model for this transfer function, in the standard form y=Cx + Du (b) Suppose that zero input is applied, such that u 0. Perform a modal analysis of the state response for this open-loop system. Your analysis should include the nature of the time response for each mode, as well as how...
Feedback u(t) u1(t) y1(t) System 1 y(t) System 2 y2(t) u2(t) Please find the final equivalent state space representation. Note: the state space representation of Systi is: Sii = AjX; + B;Ui Yi = Cixi (i.e. D;=0)
Problem 4: (65 points) Let a system be given by the state space representation 8 8 10 * = X+ u(t), y = [1 -1]x – u(t) 1 1 -1 0 Y(S) d) (7) Find the transfer function US) e) (5) Is the system BIBO stable? 3 f) (9) Let the initial state x(0) -3 u(t) = 0) for all t > 0. = Find the zero input response (i.e., with the input
For a mass-spring oscillator, Newton's second law implies that the position y(t) of the mass is governed by the second-order differential equation my'' (t) + by' (t) + ky(t) = 0. (a) Find the equation of motion for the vibrating spring with damping if m= 10 kg, b = 100 kg/sec, k = 260 kg/sec?. y(0) = 0.3 m, and y'(0) = -0.4 m/sec. (b) After how many seconds will the mass in part (a) first cross the equilibrium point?...
June 18, 2019 2. A system is characterized by the following differential equation: (18 pts) y) + 2¢(t) +4y(t) = ü(t) +6u(t). A. Determine the transfer function, Y(s)/U(s). B. Derive a state-space representation (using matrices) for the system WITHOUT using Equations (2-34), (2-35) and (2-36) in the required textbook since all these equations have not been presented in class. C. Draw the simulation diagram that corresponds to the state-space representation in Part B June 18, 2019 2. A system is...