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2. (6 points). Consider a state space system: C1 =22 22 = - 2.c 1 -...
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
UestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Fin...
uestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Find a state equation and state transition matrices (A,B, C and D) of the system for a step input 6u(t). ii) Find the state transition matrix eAt) ii) Find the output response of system y(t) to a step input 6u(t) using state transition matrix, iv) Obtain the output response y(t) of the system with two other methods for step input óu(t). Question IV. A system is described...
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...
(4 points) Find a basis for the vector space {A € R2X2 | tr(A) = 0}...
(4 points) Find a basis for the vector space {A € R2X2 | tr(A) = 0} of 2 x 2 matrices with trace 0. = B={ HI (7 points) Determine which of the following transformations are linear transformatio 1. The transformation T defined by T(21, 22, 23) = (C1, 42,3). ? 2. The transformation T defined by T(21, 12) = (21,81 · 22). ? yes no 3.The transformation T defined by T(21,22) = (4x1 – 2x2,3x2). ? 4. The transformation...
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...
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
1. Write the state-space equations for the system shown below ri (t) +2 (t) u (t) Figure 1: Syste...
1. Write the state-space equations for the system shown below ri (t) +2 (t) u (t) Figure 1: System of Problem#1 2. Evaluate the state transition matrix eA for the matrix below and find the homogenous solution given x (0) 1 1 ] A=10-21 3. Find the power lution in powers of x. Show the details of your work. s (b) y" +4y=0 4. Determine if either the Frobenus or regular power series could be the method of your choice...
1. A state space linear system is shown below. dx1(t)/dt=x1(t)+x2(t)-x3(t)+u1(t) dx2(t)/dt=--x3(t)-u1(t) dx3(t)/dt=-x3(t)-u2(t) y(t)=-x1(t)+x3(t) (1) Re-write the...
1. A state space linear system is shown below. dx1(t)/dt=x1(t)+x2(t)-x3(t)+u1(t) dx2(t)/dt=--x3(t)-u1(t) dx3(t)/dt=-x3(t)-u2(t) y(t)=-x1(t)+x3(t) (1) Re-write the state space equation as following, determine matrices A, B, C and D dx(t)/at=Ax+Bu y(t)=Cx+Du (2) Determine the matrix Q that is Q=[B A*B (A^2)*B (A^3)*B L (A^(n-1)*B] (3) Determine if the rank of Q is n (n=3) and determine if the system is controllable
( Specify the canonical form types of the following State Equations 22 22 +1 u (t)...
( Specify the canonical form types of the following State Equations 22 22 +1 u (t) [ 0 1 0 0 | 0 0 1 0 0 0 0 1 l-ao-az -az -az. a With the output: 1960-cu -- - y(t) = Cx(t) = [bo bi b2b3]
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
uestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Find a state equation and state transition matrices (A,B, C and D) of the system for a step input 6u(t). ii) Find the state transition matrix eAt) ii) Find the output response of system y(t) to a step input 6u(t) using state transition matrix, iv) Obtain the output response y(t) of the system with two other methods for step input óu(t). Question IV. A system is described...
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...
(4 points) Find a basis for the vector space {A € R2X2 | tr(A) = 0} of 2 x 2 matrices with trace 0. = B={ HI (7 points) Determine which of the following transformations are linear transformatio 1. The transformation T defined by T(21, 22, 23) = (C1, 42,3). ? 2. The transformation T defined by T(21, 12) = (21,81 · 22). ? yes no 3.The transformation T defined by T(21,22) = (4x1 – 2x2,3x2). ? 4. The transformation...
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...
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
1. Write the state-space equations for the system shown below ri (t) +2 (t) u (t) Figure 1: System of Problem#1 2. Evaluate the state transition matrix eA for the matrix below and find the homogenous solution given x (0) 1 1 ] A=10-21 3. Find the power lution in powers of x. Show the details of your work. s (b) y" +4y=0 4. Determine if either the Frobenus or regular power series could be the method of your choice...
( Specify the canonical form types of the following State Equations 22 22 +1 u (t) [ 0 1 0 0 | 0 0 1 0 0 0 0 1 l-ao-az -az -az. a With the output: 1960-cu -- - y(t) = Cx(t) = [bo bi b2b3]
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