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Please find the solution with given four degree of freedom system:
![ni M2 m3 9xI (9X3 CA1 system Matri (9 x 9 size eqato) [B] Input matrix → [m] size SIZE](http://img.homeworklib.com/images/49a2f0e3-42da-44f0-85d1-3c408e109600.png?x-oss-process=image/resize,w_560)
![output watrix fox Y Ii 93 c1 output matvix 1x9 9 Cixi] si24 9 xl (10) 49ラSizeof the system matrix CA] 2 = 9x3 From equation (](http://img.homeworklib.com/images/3fc5d4f9-0892-4534-8d02-4ecf51065d80.png?x-oss-process=image/resize,w_560)
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Control System. please answere all the three questions. Please do not use wikipedia 13. If a state space descriptio...
The state space model of an interconnected three tank water storage system is given by the following equation -3 1 o 1[hi] dt The heights of water in the tanks are, respectively, hi, h2, hz. Each tan...
The state space model of an interconnected three tank water storage system is given by the following equation -3 1 o 1[hi] dt The heights of water in the tanks are, respectively, hi, h2, hz. Each tank has an independent input flow; the volume flow rates of input water into the three tanks are, respectively, qii,qi2, Oi3. Each tank also has a water discharge outlet and the volume flow rates of water coming out of the tanks are, respectively, qo1,...
The state space model of an interconnected three tank water storage system is given by the following equation: -3 1 0 1rh dt os lo 0 3] 10 1-3 The heights of water in the tanks are, respectively,...
The state space model of an interconnected three tank water storage system is given by the following equation: -3 1 0 1rh dt os lo 0 3] 10 1-3 The heights of water in the tanks are, respectively, h,h2,h3. Each tank has an independent input flow; the volume flow rates of input water into the three tanks are, respectively, qǐ1,W2,4a. Each tank also has a water discharge outlet and the volume flow rates of water coming out of the tanks...
8. Write down the state space equation for the system shown below US) + 2 y(s)...
8. Write down the state space equation for the system shown below US) + 2 y(s) $+3 2 s(s+1) 9. Derive the state space equation for the system shown where the coefficients of the system matrix are in diagonal form and the elements of the control matrix are unity. U(S) 1 X2 $+2 X 3+1 X = y $+3 $+4 S
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...
Given the two dynamic systems S2 a ER Si has state r1, control u, and output y. S2 has state (x2,...
Given the two dynamic systems S2 a ER Si has state r1, control u, and output y. S2 has state (x2, r3), control w and output z. (a) Draw a dynamic diagram of system S2 (b) Express the equations for S1 and S2 in matrix from and determine whether each system is controllable, observable. (c) These two systems are connected in series with w-y. The resulting system is called S3. Write down the matrix form of the equation for S3...
10.Represent the translational mechanical system shown in the Figure in state- space, where xX3(t) is the...
10.Represent the translational mechanical system shown in the Figure in state- space, where xX3(t) is the output IN- 11.Find the state equations and output equation for the phase-variable representation of the transfer function G(s) 2s+1/(s2+7s+ 9) 12. Convert the state and output equations shown to a transfer function. -1.5 2 u(t) X = X 4 0 Y [1.5 0.625]x 13. For each system shown, write the state equations and the output equation for the phase- variable representation 8s10 sh25 t26...
3. a) Find a sate space representation for a linear system represented by the following different...
3. a) Find a sate space representation for a linear system represented by the following differential equation, where v(t) denotes the input and y(0) is the output: 4y(t)- 2(t)-2y(t)3(t) b) Consider a linear system represented by the following differential equation, where st) denotes the input and yt) is the output: )+4() +4y(t)x(t) 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...
6. Consider a state-space system x = Ax+ Bu, y = Cx for which the control...
6. Consider a state-space system x = Ax+ Bu, y = Cx for which the control input is defined as u- -Kx + r, with r(t) a reference input. This results in a closed-loop system x (A-BK)x(t)+ Br(t) = with matrices 2 -2 K=[k1 K2 For this type of controller, ki, k2 ER do not need to be restricted to positive numbers - any real number is fine (a) What is the characteristic equation of the closed-loop system, in terms...
Q1, pease help asap, please write clearly. Thanks in advance. 1. Given the transfer function of...
Q1, pease help asap, please write clearly. Thanks in
advance.
1. Given the transfer function of the control system. (60%) G(s) S) 5s+13 R(s) +6s+13 Y (1) Sketch the state diagram in the form of signal flow graph. (2) Find the state equations. (3) Find the output equation. (4) Find the fundamental matrix 2(t). (5) Find the state-transition matrix D(t) (6) Find the state vector x(t) if the input r(t) 2 and y(0)= (0) = 0 .
1. Given the...
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
The state space model of an interconnected three tank water storage system is given by the following equation -3 1 o 1[hi] dt The heights of water in the tanks are, respectively, hi, h2, hz. Each tank has an independent input flow; the volume flow rates of input water into the three tanks are, respectively, qii,qi2, Oi3. Each tank also has a water discharge outlet and the volume flow rates of water coming out of the tanks are, respectively, qo1,...
The state space model of an interconnected three tank water storage system is given by the following equation: -3 1 0 1rh dt os lo 0 3] 10 1-3 The heights of water in the tanks are, respectively, h,h2,h3. Each tank has an independent input flow; the volume flow rates of input water into the three tanks are, respectively, qǐ1,W2,4a. Each tank also has a water discharge outlet and the volume flow rates of water coming out of the tanks...
8. Write down the state space equation for the system shown below US) + 2 y(s) $+3 2 s(s+1) 9. Derive the state space equation for the system shown where the coefficients of the system matrix are in diagonal form and the elements of the control matrix are unity. U(S) 1 X2 $+2 X 3+1 X = y $+3 $+4 S
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...
Given the two dynamic systems S2 a ER Si has state r1, control u, and output y. S2 has state (x2, r3), control w and output z. (a) Draw a dynamic diagram of system S2 (b) Express the equations for S1 and S2 in matrix from and determine whether each system is controllable, observable. (c) These two systems are connected in series with w-y. The resulting system is called S3. Write down the matrix form of the equation for S3...
10.Represent the translational mechanical system shown in the Figure in state- space, where xX3(t) is the output IN- 11.Find the state equations and output equation for the phase-variable representation of the transfer function G(s) 2s+1/(s2+7s+ 9) 12. Convert the state and output equations shown to a transfer function. -1.5 2 u(t) X = X 4 0 Y [1.5 0.625]x 13. For each system shown, write the state equations and the output equation for the phase- variable representation 8s10 sh25 t26...
3. a) Find a sate space representation for a linear system represented by the following differential equation, where v(t) denotes the input and y(0) is the output: 4y(t)- 2(t)-2y(t)3(t) b) Consider a linear system represented by the following differential equation, where st) denotes the input and yt) is the output: )+4() +4y(t)x(t) 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...
6. Consider a state-space system x = Ax+ Bu, y = Cx for which the control input is defined as u- -Kx + r, with r(t) a reference input. This results in a closed-loop system x (A-BK)x(t)+ Br(t) = with matrices 2 -2 K=[k1 K2 For this type of controller, ki, k2 ER do not need to be restricted to positive numbers - any real number is fine (a) What is the characteristic equation of the closed-loop system, in terms...
Q1, pease help asap, please write clearly. Thanks in
advance.
1. Given the transfer function of the control system. (60%) G(s) S) 5s+13 R(s) +6s+13 Y (1) Sketch the state diagram in the form of signal flow graph. (2) Find the state equations. (3) Find the output equation. (4) Find the fundamental matrix 2(t). (5) Find the state-transition matrix D(t) (6) Find the state vector x(t) if the input r(t) 2 and y(0)= (0) = 0 .
1. Given the...
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
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