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Problem 1: State Transition Matrix, Homogeneous Solution * Find Ф(t-t")-cA(1-1) fr evach of the f...
Problem 1: State Transition Matrix, Homogeneous Solution * Find Ф(t-t")-CA(1-1) fr each of the fo...
Problem 1: State Transition Matrix, Homogeneous Solution * Find Ф(t-t")-CA(1-1) fr each of the following LTI system by diagonalizing A, (if it is diagonalizable) using the Laplace tranform Compute the solution for ◆ Plotz,(t) and r2(t) vs. time Plot (t) v0) We were unable to transcribe this image
Problem 1: State Transition Matrix, Homogeneous Solution * Find Ф(t-t")-CA(1-1) fr each of the following LTI system by diagonalizing A, (if it is diagonalizable) using the Laplace tranform Compute the solution for...
20 points] Q1. The Stately State Transition Matrix, Ф 16 2 3 13 Consider a state transition matrix, Ф, for a SISO LTI system A1. A- 5 11 10 8 9 76 12 Please determine and justify: (a) Ф(t) for this s...
20 points] Q1. The Stately State Transition Matrix, Ф 16 2 3 13 Consider a state transition matrix, Ф, for a SISO LTI system A1. A- 5 11 10 8 9 76 12 Please determine and justify: (a) Ф(t) for this system A 4 14 15 1 ] (b) Ф(s) for this system A (c) System A's characteristic polynomial (d) Ф(z) for this system A via Tustin's method (ie, trapazoid-rule) (e) A difference equation assuming: (1) a step input at...
3. Consider the state equation dt -2 -31 x2(t) dt Determine the state-transition matrix ф(t) and ...
Consider the state equation
3. Consider the state equation dt -2 -31 x2(t) dt Determine the state-transition matrix ф(t) and the state vector x(t) for t 2 0 when the input is u(t) 1 for t 20.
3. Consider the state equation dt -2 -31 x2(t) dt Determine the state-transition matrix ф(t) and the state vector x(t) for t 2 0 when the input is u(t) 1 for t 20.
Problem 5 5. Find the state transition matrix, the zero-input response, the zero-state response, and the...
Problem 5
5. Find the state transition matrix, the zero-input response, the zero-state response, and the complete response for the following continuous-time system -2 0 3 -5 1]x(t) x(t) = dt x(t)u() x(0) = 2/3 y(t) =[0 u(t) = et for t20
can somebody please help me with this problem ! Problem 2 (25 Points). Let asys state...
can somebody please help me with this problem !
Problem 2 (25 Points). Let asys state and output equation matrices: ete followin -3 0 A2 For this system, answer the following imperatives. (a) Find the eigenvalue matrix Λ and comment on the stability of the system (justify your comment). Use the convention that 1 2 and order Л accordingly. (b) Find the eigenvectors and the modal matrix M. (c) Find the state transition matrix Φ(t). Hint: first find the "diagonalized"...
2. For the simple pendulum shown in Figure 2, the nonlinear equations of motion are given by θ(t)...
do (b) and (c) only.
2. For the simple pendulum shown in Figure 2, the nonlinear equations of motion are given by θ(t) + 믈 sin θ(t) + m 0(t)-0 Pivot point L, length Massless rod , mass Figure 2. A simple pendulum 3. Consider again the pendulum of Figure 2 of problem 2 when g = 9.8 m/s, 1 = 4.9m, k =0.3, and (a) Determine whether the system is stable by finding the characteristic equation obtained from setting...
find the following: a)state transition matrix? b)output as function of time? c)design a state feedback controller to...
find the following:
a)state transition matrix?
b)output as function of time?
c)design a state feedback controller to place closed loop at (-3)
and (-5)
Question (: (10 hO Considering the following system, 01x + 0 t<0 tt t20 Where x(0)-L1] , u(t)-(% ,u(t) a) Find the state transition matrix. (3 marks) b) Find the output as a function of time. (3 marks) c) Design a state feedback controller to place the closed loop poles at (-3) and (-5). (4 marks)...
0.1.For the following Laplace transform, F(s) a) Determine the steady state solution fs using the Final value theorem. b) Find the corresponding time function f(t) using partial fractions. a Use b...
0.1.For the following Laplace transform, F(s) a) Determine the steady state solution fs using the Final value theorem. b) Find the corresponding time function f(t) using partial fractions. a Use block diagram reduction to obtain the transfer function YIR of the following feedback system. Fuc R(s) Manifold Air b Ga(a) G1) Pressure Sparks pai FIQUREdle soed cortenal aetem
0.1.For the following Laplace transform, F(s) a) Determine the steady state solution fs using the Final value theorem. b) Find the corresponding...
Problem 4 Given: St t(t) # -t e g(t) a) Compute fg () using convolution integral method. b) Compute g*f () with Laplace transform. o) What are the differences between the results of questions (a)...
Problem 4 Given: St t(t) # -t e g(t) a) Compute fg () using convolution integral method. b) Compute g*f () with Laplace transform. o) What are the differences between the results of questions (a) and (0) above? d) Find the Laplace transform of the following function: (t 0 to +oo) e dt e) Find the equivalent solution of (d) using MATLAB method) (find 2 methods)
Problem 4 Given: St t(t) # -t e g(t) a) Compute fg () using...
Question 7: Solve the entire problem using Laplace Transforms. Recall the DE for our two-vessel water clock ах - Ax, wh...
Question 7: Solve the entire problem using Laplace Transforms. Recall the DE for our two-vessel water clock ах - Ax, where A dt k(0)= DE IC: -1] Let X(s) denote the Laplace transform of x(t). Then x(s) = (sl-A)-1 (0) There is no forcing term, so this is just the zero-input or homogeneous solution. Solve for X(s) and record your answer in the answer template. The first component has been given for you Question 7: The solution in the transform...
Problem 1: State Transition Matrix, Homogeneous Solution * Find Ф(t-t")-CA(1-1) fr each of the following LTI system by diagonalizing A, (if it is diagonalizable) using the Laplace tranform Compute the solution for ◆ Plotz,(t) and r2(t) vs. time Plot (t) v0) We were unable to transcribe this image
Problem 1: State Transition Matrix, Homogeneous Solution * Find Ф(t-t")-CA(1-1) fr each of the following LTI system by diagonalizing A, (if it is diagonalizable) using the Laplace tranform Compute the solution for...
20 points] Q1. The Stately State Transition Matrix, Ф 16 2 3 13 Consider a state transition matrix, Ф, for a SISO LTI system A1. A- 5 11 10 8 9 76 12 Please determine and justify: (a) Ф(t) for this system A 4 14 15 1 ] (b) Ф(s) for this system A (c) System A's characteristic polynomial (d) Ф(z) for this system A via Tustin's method (ie, trapazoid-rule) (e) A difference equation assuming: (1) a step input at...
Consider the state equation
3. Consider the state equation dt -2 -31 x2(t) dt Determine the state-transition matrix ф(t) and the state vector x(t) for t 2 0 when the input is u(t) 1 for t 20.
3. Consider the state equation dt -2 -31 x2(t) dt Determine the state-transition matrix ф(t) and the state vector x(t) for t 2 0 when the input is u(t) 1 for t 20.
Problem 5
5. Find the state transition matrix, the zero-input response, the zero-state response, and the complete response for the following continuous-time system -2 0 3 -5 1]x(t) x(t) = dt x(t)u() x(0) = 2/3 y(t) =[0 u(t) = et for t20
can somebody please help me with this problem !
Problem 2 (25 Points). Let asys state and output equation matrices: ete followin -3 0 A2 For this system, answer the following imperatives. (a) Find the eigenvalue matrix Λ and comment on the stability of the system (justify your comment). Use the convention that 1 2 and order Л accordingly. (b) Find the eigenvectors and the modal matrix M. (c) Find the state transition matrix Φ(t). Hint: first find the "diagonalized"...
do (b) and (c) only.
2. For the simple pendulum shown in Figure 2, the nonlinear equations of motion are given by θ(t) + 믈 sin θ(t) + m 0(t)-0 Pivot point L, length Massless rod , mass Figure 2. A simple pendulum 3. Consider again the pendulum of Figure 2 of problem 2 when g = 9.8 m/s, 1 = 4.9m, k =0.3, and (a) Determine whether the system is stable by finding the characteristic equation obtained from setting...
find the following:
a)state transition matrix?
b)output as function of time?
c)design a state feedback controller to place closed loop at (-3)
and (-5)
Question (: (10 hO Considering the following system, 01x + 0 t<0 tt t20 Where x(0)-L1] , u(t)-(% ,u(t) a) Find the state transition matrix. (3 marks) b) Find the output as a function of time. (3 marks) c) Design a state feedback controller to place the closed loop poles at (-3) and (-5). (4 marks)...
0.1.For the following Laplace transform, F(s) a) Determine the steady state solution fs using the Final value theorem. b) Find the corresponding time function f(t) using partial fractions. a Use block diagram reduction to obtain the transfer function YIR of the following feedback system. Fuc R(s) Manifold Air b Ga(a) G1) Pressure Sparks pai FIQUREdle soed cortenal aetem
0.1.For the following Laplace transform, F(s) a) Determine the steady state solution fs using the Final value theorem. b) Find the corresponding...
Problem 4 Given: St t(t) # -t e g(t) a) Compute fg () using convolution integral method. b) Compute g*f () with Laplace transform. o) What are the differences between the results of questions (a) and (0) above? d) Find the Laplace transform of the following function: (t 0 to +oo) e dt e) Find the equivalent solution of (d) using MATLAB method) (find 2 methods)
Problem 4 Given: St t(t) # -t e g(t) a) Compute fg () using...
Question 7: Solve the entire problem using Laplace Transforms. Recall the DE for our two-vessel water clock ах - Ax, where A dt k(0)= DE IC: -1] Let X(s) denote the Laplace transform of x(t). Then x(s) = (sl-A)-1 (0) There is no forcing term, so this is just the zero-input or homogeneous solution. Solve for X(s) and record your answer in the answer template. The first component has been given for you Question 7: The solution in the transform...
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