Given the system represented in state space as follows: dx=[ -1 -7 6; -8 4 8;...
Given the system represented in state space as follows:
dx=[ -1 -7 6; -8 4 8; 4 7 -8]x+[-5 ;-7; 7]
y=[-9 -9 -8 ]*x
convert the system to one where the new state vector , z, is
z=[-4 9 -3; 0 -4 7; -1 -4 -9]*x
find and compare both of system’s eigenvalues
how can we code this problem with MATLAB?
Homework Answers
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Given the system represented in state space as follows:
dx=[ -1 -7 6; -8 4 8;...
Problem 1 A system is represented in state space as 8 -4 1 -4 5 7...
Problem 1 A system is represented in state space as 8 -4 1 -4 5 7 -9 0 0 a) Find the transfer function b) Find the poles
3. a) Find a state space representation for a linear system represented by the following differen...
3. a) Find a state space representation for a linear system represented by the following differential equation, where v(t) denotes the input and y(1) is the output: b) Consider a linear system represented by the following differential equation, where x() denotes the input and y(t) is the output: )+4()+4y()x(t) i) Write down its transfer function and frequency response function i) What is the form of the steady state response of the above system due to a periodic input that has...
Problem 4: (65 points) Let a system be given by the state space representation 8 8...
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
Q3. The state-space representation of a dynamical system is given as follows: (2) (y = 2...
Q3. The state-space representation of a dynamical system is given as follows: (2) (y = 2 x 1. By finding the eigenvalues, eigenvectors of the A matrix, compute el via the diagonal transformation. 2. Assume that the control input is u(t) = 0, compute x(1) and y(t). 3. Assume that the input is u(t) = 1 + 2e-21, compute x(t) and y(t). 4. Given your answers to the previous question, compute x(t) when 1 00
A state space linear system is shown below. Use Matlab to solve the following problems. Requirement...
A state space linear system is shown below. Use Matlab to solve the following problems. Requirement for project report: (1) Results; (2) Matlab code. dx1/dt=-x1(t)+u(t) dx2/dt=x1(t)-2x2(t)-x3(t)+3u(t) dx3/dt=-3x3(t) y(t)=-x1(t)+2x2(t)+x3(t)+u(t) (1) Assume the system has input u(t)=e-3t if t>t0 and zero initial state x(0)=[0;0;0]. Using the transition matrix obtained, compute the system’s output (analytical solution), and plot the output as a function of time (t within 0 to 10). (2) Using the function lsim to simulate the system’s output (analytical solution), and...
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3. (25 points) For parts a & b, determine the state space representation and write the matlab code to solve the transfer function a. The circuit below where the input is v, and the output is Va 500 mF V, LX 0 b. A system is represented by the differential equation below where the output is y() and the input is z(). 440180 + 5y0) 2) d' y(t) dr d y(t) dt ontpm ria bles 2L
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Please only solve part C Assume the following state space representation of a discrete-time servomotor system. (As a review for the Final Exam, you might check this state space representation with th...
Please only solve part C
Assume the following state space representation of a discrete-time servomotor system. (As a review for the Final Exam, you might check this state space representation with the difference equation in Problem 1 on Homework 2. This parenthetical comment is not a required part for Homework 8.) 2. 0.048371 u(n) 1.9048x(n) lo.04679 [1,0]x(n) y(n) Compute the open-loop eigenvalues of the system. That is, find the eigenvalues of Ф. Check controllability of the system. Or, answer the...
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A system (a plant) is represented as a state-space model in the form: dt (1) Deduce and draw a simulation diagram for the system. Implement it afterwards in Simulink. For a unit stepin- put, simulate and plot the trajectories in the state space, and the output y(t) of the system, for a set of four different initial conditions: x(0)-[0 ofT,x(0-[1 o, x(0-0 IT,x(0-[0 I]T
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set of linear equations are given as follows 10 x +20 y +9z 414 +7 x -14y +12z 363 -3x +12 y +11 z-475 If the above system of linear equations is represented by the matrix system where the unknown vector vI-x y z) A- coefficient of the linear systems, and b-right-hand side vector 1) Write the matrix A 2) Using a for-loop, write a Matiab-code to compute matros-matrix product Le., C A'A 3) Select the correct value of C'b...
Problem 1 A system is represented in state space as 8 -4 1 -4 5 7 -9 0 0 a) Find the transfer function b) Find the poles
3. a) Find a state space representation for a linear system represented by the following differential equation, where v(t) denotes the input and y(1) is the output: b) Consider a linear system represented by the following differential equation, where x() denotes the input and y(t) is the output: )+4()+4y()x(t) i) Write down its transfer function and frequency response function i) What is the form of the steady state response of the above system due to a periodic input that has...
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
Q3. The state-space representation of a dynamical system is given as follows: (2) (y = 2 x 1. By finding the eigenvalues, eigenvectors of the A matrix, compute el via the diagonal transformation. 2. Assume that the control input is u(t) = 0, compute x(1) and y(t). 3. Assume that the input is u(t) = 1 + 2e-21, compute x(t) and y(t). 4. Given your answers to the previous question, compute x(t) when 1 00
3. (25 points) For parts a & b, determine the state space representation and write the matlab code to solve the transfer function a. The circuit below where the input is v, and the output is Va 500 mF V, LX 0 b. A system is represented by the differential equation below where the output is y() and the input is z(). 440180 + 5y0) 2) d' y(t) dr d y(t) dt ontpm ria bles 2L
3. (25 points) For...
Please only solve part C
Assume the following state space representation of a discrete-time servomotor system. (As a review for the Final Exam, you might check this state space representation with the difference equation in Problem 1 on Homework 2. This parenthetical comment is not a required part for Homework 8.) 2. 0.048371 u(n) 1.9048x(n) lo.04679 [1,0]x(n) y(n) Compute the open-loop eigenvalues of the system. That is, find the eigenvalues of Ф. Check controllability of the system. Or, answer the...
A system (a plant) is represented as a state-space model in the form: dt (1) Deduce and draw a simulation diagram for the system. Implement it afterwards in Simulink. For a unit stepin- put, simulate and plot the trajectories in the state space, and the output y(t) of the system, for a set of four different initial conditions: x(0)-[0 ofT,x(0-[1 o, x(0-0 IT,x(0-[0 I]T
A system (a plant) is represented as a state-space model in the form: dt (1) Deduce...
2- Solve for y(t) for the following system 1 01 -3 represented in state space, where u(t) is the unit step. Use the Laplace transform approach to solve the state eqiation. 1 u(t) 0 -6 1|x + 0 -5 [0 1 1 ]x; x(0) = 0 %3D
set of linear equations are given as follows 10 x +20 y +9z 414 +7 x -14y +12z 363 -3x +12 y +11 z-475 If the above system of linear equations is represented by the matrix system where the unknown vector vI-x y z) A- coefficient of the linear systems, and b-right-hand side vector 1) Write the matrix A 2) Using a for-loop, write a Matiab-code to compute matros-matrix product Le., C A'A 3) Select the correct value of C'b...
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