3. Consider the state equation dt -2 -31 x2(t) dt Determine the state-transition matrix ф(t) and ...
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...
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
Problem 1: State Transition Matrix, Homogeneous Solution * Find Ф(t-t")-cA(1-1) fr evach of the following LTI system by diagonalizing A, (if it is diagonalizable using the Laplace transform . Compute the solution for Plot a(t) and 2(t) Plot (t) v0) time We were unable to transcribe this image
Problem 1: State Transition Matrix, Homogeneous Solution * Find Ф(t-t")-cA(1-1) fr evach of the following LTI system by diagonalizing A, (if it is diagonalizable using the Laplace transform . Compute the solution...
(b) Consider the matrix differential equation for the vector x(t) d dt - B2+ where B= (69) 4 10 5 -1 (i) Find a particular solution to the matrix differential equation. (ii) Evaluate exp(Bt). (iii) Find the general solution to the matrix differential equation. Express the general solution in terms of the components of the vector (0).
(b) Consider the matrix differential equation for the vector x(t) d dt - B2+ where B= (69) 4 10 5 -1 (i) Find a particular solution to the matrix differential equation. (ii) Evaluate exp(Bt). (iii) Find the general solution to the matrix differential equation. Express the general solution in terms of the components of the vector (0).
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...
x(t)-A()x(t) + B(t)u(t) 2. Consider the following system y(t)-C(t)x(t) where A(t)- 0 1) Derive the state transition matrix Φ(t, τ). 2) Derive the impulse response function g(t, z).
x(t)-A()x(t) + B(t)u(t) 2. Consider the following system y(t)-C(t)x(t) where A(t)- 0 1) Derive the state transition matrix Φ(t, τ). 2) Derive the impulse response function g(t, z).
2. Consider the system described by the ODE's 2x1-3x2 +4u Using the State Function of Pontryagin to find the input u that minimizes dt a. Determine the state function of Pontryagin H. b. Find the optimal input and H c. Find the matrix A that will yield the governing equations x1 ai If xi (0) : 0.x2(0) = O and xi (1) = İ. x 2(1) =0 determine the govem equations for λǐ(0) and λ2(0) in terms of the elements...
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...
3. For the system given by 1 0 (a) Determine Ф(s) and Ф(t). (b) Determine x(t) if u(t) is a step function and x(010]