1. The equations of motion of this system areÿ + 3y + 4y - 32 - 4Z = 0Ż +52 +6Z-5ý - 6y = f(t)* = A + Būy = Cx+DūPut these equations into state variable form and express the model as a matrix vectorequation if output of the system is y.Energy storage elementm1m2k₁k₂State variable*1=ýx₂ = Żx3 = yx4 =Zk₁myDk₂ C₂Hm₂

Answered: ÿ + 3y + 4y - 3Ż - 4Z = 0 Ż +52 +6Z -…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Q1. A mechanical system is shown in the following figure, where external force u₁ is the input and displacement y₂ is the output. The force acting on m₂ has a linear relationship with u₁ as u₂-Au₁. • List system equations and do Laplace transform to the system equations; • Draw block diagram of the control system. (Please construct the block diagram from system equations directly, do not derive or combine the equations. Do not need to reduce it) YI Y b₁ m₁ 11 112 + m₂ www
The following EOMs describe the behavior of a dynamic system ( à = -K₁a + din b = K₁a - K₂b K₂b - K3c = ċ Assume K₁, K2, K3 are constant, and din is the input. A. How many states does this system of equations have, and why? B. Write the state space form of the system as x = Ax + Bu. You will have to define your state vector and input vector. Clearly identify the matrices. C. Assume the desired output of the system is the vector y that consists of a and K₂b as individual elements. Write the output equation in the form of y = Cx + Du. Clearly identify the matrices.
4G I. 3:22 A moodle1.du.edu.om Consider the 3 degree of freedom robot manipulator as shown in the figure Link 3 Länk 2 Trint 1 The objective is to find the kinematics inverse of the robot Px=0.9 m, Py=0.6, L1=1.5m, L2=1.5m and qz= 2 rad The value of cos(q2) is equal to Choose... + The positive value of sin(q2) is equal to Choose... + The value of q2 in rad is Choose... + The value of qı in rad is Choose... + The value of q3 in rad is Choose... +
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.2
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.
11. Consider a system that can be modeled as shown. The input x in (t) is a prescribed motion at the right end of spring k 2. Find X(s) the system transfer function Xeq(s)* m k₂ ww Xin The values of the parameters are m= 30 kg, k ₁=700 N/m, k 2= 1300 N/m, and b=200 N- s/m. Write a MATLAB script file that: (a) calculates the natural frequency, damping ratio, and damped natural frequency for the system; and (b) uses the impulse command to find and plot the response of the system to a unit impulse input.
My Solutions > Lower Colorado River (Problem 11.12 in Chapra) The Lower Colorado River consists of a series of four reservoirs as shown in Fig. P11.12 in the textbook. Mass balances can be written for each reservoir, and the following set of simultaneous linear algebraic equations results: [ 13.422 0 00; -13.422 12.252 0 0; 0 -12.252 12.377 0; 00-12.377 11.797] * [C_1, c_2, c_3, c_4]' = [750.5, 300, 102, 30] where the right-hand-side vector consists of the loadings of chloride to each of the four lakes. The variables c_1, c_2, c_3, and c_4 are the resulting chloride concentrations for Lakes Powell, Mead, Mohave, and Havasu, respectively. Given this information, complete the following tasks: (a) Use the matrix inverse to solve for the concentrations in each of the four lakes. (b) How much must the loading to Lake Powell be reduced for the chloride concentration of Lake Havasu to be 75? (c) Using the matrix 2-norm (spectral norm), compute the condition number and how many suspect digits…
Given the vibrating system below: K4 Y(t) =Ysin30t where for = 30 and Y=20mm Find the following K1 K2 m C3 H C2 C1 C5 C4 1. Frequency Ratio 2. Displacement Transmissibility Ratio 3. Absolute displacement of the mass 4. Type of Damping 5. Equation of motion x(t). Assume Initial conditions for displacement and velocity 6. Graph 2 cycles of the vibrating system. You can use third party app for this. M = 10 kg K1=100 N/m K2= 80 N/m K3=75 N/m K4= 120 N/m C1 = 20Ns/m C2=40 Ns/m C3= 35Ns/m C4= 15 Ns/m C5= 10 Ns/m
Consider the following spring system. m. c2 = 10, c3 = , c4 = 2 C1 m2 = 2 Write the stiffness matrix K = Write the matrix MK Find the eigenvalues and eigenvectors of MK: • Smaller eigenvalue = with eigenvector • Larger eigenvalue = with eigenvector If this spring system oscillates without any external forces present, then the position of each mass satisfies the following general formula: u(t) = (a1 cos( t) + bị sin ( t) + (a2 cos( t) + bz sin( t) If the system begins oscillation with initial position u(0) = and initial velocity u'(0) = then the position of the masses at time t is given by u1(t) = uz(t) = Wir
2. Find the equation(s) of motion of the following system. How many DOF does this system have? The displacement of the mass is measured from the position where the spring is unstreched. Is this system linear or nonlinear? Define the state variables and express the equation(s) of motion in state form. Gravity should be included and the Coulomb friction coefficient of the rough ground is u. F,(0 x,(t) Friction, u
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…

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