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 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...
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"...
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)...
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 point) In this problem you will solve the nonhomogeneous system -3 5]- -5 3 y t A. Write a fundamental matrix for the associated homogeneous system B. Compute the inverse C. Multiply by g and integrate tci (Do not include c1 and c2 in your answers). D. Give the solution to the systenm C + (Do not include ci and c2 in your answers).
(1 point) In this problem you will solve the nonhomogeneous system -3 5]- -5 3...
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...
(solution of LTV systems) Find the state transition matrices for o X(t) x(t) =10-1