2. Consider the state equationx11 20x1dx2= 0 10x2dtx3001x3where x1, x2 and 23 are state variables. Please answer the following questions.(a) The state matrix(4)1 20A =0 1 0(5)0 0 1has three-fold eigenvalues with \₁==A2 A3 1. Find all independent eigenvectorscorresponding to this eigenvalue.(b) Find the modal matrix M associated with the state matrix A. Does M-1 AM lead toa Jordan form or not? Hint: The modal matrix M turns out to be a diagonal matrix.For a diagonal matrix, its inverse is given bya 000b0-11/a 00= 01/b000 с001/c1(6)(c) Find the state transition matrix (t).(d) Determine the stability of the system. Please justify your answer.

Step 1:(a) To find the independent eigenvectors corresponding to the eigenvalue λ=1, we need to…

Answered: 2. Consider the state equation x1 1 20…

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

See similar textbooks

Similar questions

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.
Use MATLAB to obtain a state model for the following equations; obtain the expressions for the matrices A, B, C, and D. In both cases, the input is f(t); the output: is y. a. 5d³yd²y +7. b. dy +3 dt³ dt² dt Y(s) 5 = F(s) s² +7s+4 - +6y=f(t)
HW # 2-3 : Consider the following inverted pendulum. a) Obtain the differential equation describing the system. e sin 0 b) Find the transfer function. m c) Obtain the state equation in terms of vector-matrix form. e cos 0 mg the center of gravity of the pendulum as (xG, YG). Then P XG = x + l sin 0 M YG I cos e %3D
Represent the translational mechanical system shown below in state space, where x3(t) is the output. State variables ニュ=X 3 = X2 Let -4 = X2 Es = X3 E6 = X3 x1(t) x2(t) x3(t) 1 N-sim 1 N-sim 1 Nim 1 Nim 1kg 1kg 1 kg J1 J2 J3 Fit)
Q3) Represent the rotational mechanical system shown below in state space representation (matrix form) where 10 6, (t) is the output. Use four state variables 10T 02 100 Kg-m 100 Kо-m 100N-m sec/rad 100 N-m/rad
equations: QB: Obtain the transfer function of system defined by the following state space Hi 0 4 8 [x₁ 0 8 5 X2 + -10-30-20x330/u [123] [x1 Y=[1 2 0] X₂ X3 snp-you tvave
Get representation in State Variables
MATLAB PROBLEM
Mechanics of machines QUESTION 4 Consider two degree of freedom of coupled pendulum with horizontal rod vibration system are shown in figure 4. MA KG. oooo MB BAW a Figure 4 k d L 4.1- Determine differential equations of motion in matrix form using The equation of equation with, and ß as generalized coordinates; 4.2- Develop state-space model.
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. Reduce the following differential equation to the state space equation form. a. y" (t) + 3y' (t) + 2y (t) = u(t) b. y" (t) = u(t) — b₁y' (t) — boy (t) c. 4y" (t) cos (t) y' (t) + sin (t) y (t) = u(t)
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.

SEE MORE QUESTIONS

Recommended textbooks for you

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Control Systems Engineering

Mechanical Engineering

ISBN:

9781118170519

Author:

Norman S. Nise

Publisher:

WILEY

Mechanics of Materials (MindTap Course List)

Mechanical Engineering

ISBN:

9781337093347

Author:

Barry J. Goodno, James M. Gere

Publisher:

Cengage Learning

Engineering Mechanics: Statics

Mechanical Engineering

ISBN:

9781118807330

Author:

James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher:

WILEY

SEE MORE TEXTBOOKS