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Consider a system described by the following equations: · 1 = I1 – 2x122 + u,...
. A linear, time invariant system is described as the following state equation and output equation,...
. A linear, time invariant system is described as the following state equation and output equation, dx1/dt= -x1(t)+x2(t)+u(t) dx2/dt=-x1(t)-x2(t)+x3(t) dx3/dt=-2x2(t)+x3(t)-2u(t) y(t)=x1(t)+2x2(t)+2x3(t) re-write the state space equation as following, determine matrices A, B, C and D:dx/dt=Ax+Bu y(t)=Cx+Du(t)
6. (15 points) The EoM of a system is given below. The inputs are u(t) and...
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)
Assignment 8 Remaining Time: 131:53:22 Question 1 Consider a system of differential equations describing the progress...
Assignment 8 Remaining Time: 131:53:22 Question 1 Consider a system of differential equations describing the progress of a disease in a population, given by F(x, y) for 1 point How Did I Do? a vector-valued function F. In our particular case, this is: d' = 3 – 3xy - 12 y' = 3xy – 34 where x(t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of...
(3) - F(2,4) to Consider a system of differential equations describing the progress of a disease...
(3) - F(2,4) to Consider a system of differential equations describing the progress of a disease in a population, given by for a vector-valued function F. In our particular case, this is: t' = 3 – 3zy - 12 y' – 3ay – 2y where I (t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of individuals is counted in units of 1,000 individuals. and =...
PROBLEM 1 (35 %) The mechanical system in the figure below consists of a disk of radius r, a block of mass m, a spr...
PROBLEM 1 (35 %) The mechanical system in the figure below consists of a disk of radius r, a block of mass m, a spring of stiffness (spring constant) k, and a damper with damping ratio b. The disk has moment of inertia Jabout its center of mass (pivot point O), and the block is subjected to an external force t) as shown in the figure. The spring is unstressed when x 0= 0. Assume small 0. (a) (10 points)...
Do problem 5.6 a. Obtain a complete SSR with input u and output h. Derive the...
Do problem 5.6
a. Obtain a complete SSR with input u and output h. Derive the system transfer function Go) Zs/u c. Derive the transfer function Y(s)/U(s) where the output is y Obtain a complete SSR for the given system, with input u = v and output 5.3 0.25t +2c-0.6w = 0 5.4 Given the nonlinear first-order system Derive the linear model by performing the linearization about the static equilibrium state a that res when the nominal input is "....
1. Consider the system described by the ODE's X1 = X2 i,--2x,-3x2 +11 Using the State Function of...
Write neatly please =)
1. Consider the system described by the ODE's X1 = X2 i,--2x,-3x2 +11 Using the State Function of Pontryagin to find the input u that minimizes u2 a. Determine the state function of Pontryagin H b. Find the optimal input and Ho c. Find the matrix A that will yield the governing equations Xy x2 12 If X1 (0) = 1,x2(0)=0 and x1(1)-x-(1)=0 determine the govern equations for λ! (0) and d. (0) in terms of...
1.2 [12 points] Determine the transfer functions for the following systems. (a) A system described by...
1.2 [12 points] Determine the transfer functions for the following systems. (a) A system described by the signal flow graph below: -1 Figure 2 (b) A second-order system with input u and output y described by the state variable model below: i- Ax + Bu y -2x, 01 where x- A-TT
Problem 6. Consider the system *1 = x1 + u iz = -x1 + x2 (a)...
Problem 6. Consider the system *1 = x1 + u iz = -x1 + x2 (a) Determine the stability of the open-loop system by checking the eigenvalues of the above system. (b) Define the output to be y = X1. Use the MATLAB command “Iqr” to find the constant optimal feedback control law gains by solving the infinite-horizon output regulator problem with Q=1 and R=0.1. (c) Determine the closed-loop stability by calculating the eigenvalues of the closed- loop system when...
The equations of motion for a mass-spring-damper system can be described by mE(t) + ci(t) +...
The equations of motion for a mass-spring-damper system can be described by mE(t) + ci(t) + k2(t) = F(t), where z(t) is the position of the mass, c is the damper coefficient, k is the spring constant, and F(t) is an external force applied to the mass as an input. If the system state vector is defined by 2(t) = lat) a(t)=F(t), y(t)=2(t), given below: x=Ax + Bu y=Cx + Du.
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)
Assignment 8 Remaining Time: 131:53:22 Question 1 Consider a system of differential equations describing the progress of a disease in a population, given by F(x, y) for 1 point How Did I Do? a vector-valued function F. In our particular case, this is: d' = 3 – 3xy - 12 y' = 3xy – 34 where x(t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of...
(3) - F(2,4) to Consider a system of differential equations describing the progress of a disease in a population, given by for a vector-valued function F. In our particular case, this is: t' = 3 – 3zy - 12 y' – 3ay – 2y where I (t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of individuals is counted in units of 1,000 individuals. and =...
PROBLEM 1 (35 %) The mechanical system in the figure below consists of a disk of radius r, a block of mass m, a spring of stiffness (spring constant) k, and a damper with damping ratio b. The disk has moment of inertia Jabout its center of mass (pivot point O), and the block is subjected to an external force t) as shown in the figure. The spring is unstressed when x 0= 0. Assume small 0. (a) (10 points)...
Do problem 5.6
a. Obtain a complete SSR with input u and output h. Derive the system transfer function Go) Zs/u c. Derive the transfer function Y(s)/U(s) where the output is y Obtain a complete SSR for the given system, with input u = v and output 5.3 0.25t +2c-0.6w = 0 5.4 Given the nonlinear first-order system Derive the linear model by performing the linearization about the static equilibrium state a that res when the nominal input is "....
Write neatly please =)
1. Consider the system described by the ODE's X1 = X2 i,--2x,-3x2 +11 Using the State Function of Pontryagin to find the input u that minimizes u2 a. Determine the state function of Pontryagin H b. Find the optimal input and Ho c. Find the matrix A that will yield the governing equations Xy x2 12 If X1 (0) = 1,x2(0)=0 and x1(1)-x-(1)=0 determine the govern equations for λ! (0) and d. (0) in terms of...
1.2 [12 points] Determine the transfer functions for the following systems. (a) A system described by the signal flow graph below: -1 Figure 2 (b) A second-order system with input u and output y described by the state variable model below: i- Ax + Bu y -2x, 01 where x- A-TT
Problem 6. Consider the system *1 = x1 + u iz = -x1 + x2 (a) Determine the stability of the open-loop system by checking the eigenvalues of the above system. (b) Define the output to be y = X1. Use the MATLAB command “Iqr” to find the constant optimal feedback control law gains by solving the infinite-horizon output regulator problem with Q=1 and R=0.1. (c) Determine the closed-loop stability by calculating the eigenvalues of the closed- loop system when...
The equations of motion for a mass-spring-damper system can be described by mE(t) + ci(t) + k2(t) = F(t), where z(t) is the position of the mass, c is the damper coefficient, k is the spring constant, and F(t) is an external force applied to the mass as an input. If the system state vector is defined by 2(t) = lat) a(t)=F(t), y(t)=2(t), given below: x=Ax + Bu y=Cx + Du.
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