# WUSTL ESE 543 - ESE 543 Homework 4 Chap 6,7,8 Brogan (2 pages)

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**View the full content.**## ESE 543 Homework 4 Chap 6,7,8 Brogan

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## ESE 543 Homework 4 Chap 6,7,8 Brogan

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- Pages:
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- School:
- Washington University in St. Louis
- Course:
- Ese 543 - Control Systems Design by State Space Methods

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Homework 3 8 2 1 10 1 6 30 from Brogan Solve for x if 1 1 3 x 5 2 5 4 1 x1 1 0 4 2 6 34 from Brogan Find all nontrivial solutions for x2 0 2 3 8 x3 3 6 35 from Brogan Determine whether nontrivial solutions exist for 1 2 2 4 x 1 0 0 0 x2 1 2 4 7 39 from Brogan Find the eigenvalues eigenvectors and Jordan form for 2 2 3 A 1 1 1 1 3 1 2 5 7 40 from Brogan Find the eigenvectors for A 0 3 1 2 and B 6 7 43 from Brogan Are A 1 2 1 5 0 0 2 0 similar matrices 2 1 2 0 7 8 25 from Brogan Find the inverse of A 1 1 0 using the Cayley Hamilton 2 1 2 theorem 1 1 2 8 8 26 from Brogan Find e At if A 0 1 9 Compute the singular values and singular vectors for A 1 2 0 4 10 Derive state space model for the following a For the 3 input 1 output controller K s AK BK CK DK r K1 s K2 s Az where K1 s q Kq s aq K z s az and K 2 s s s b For the 1 input 2 output 2 state plant model G s AG BG CG DG using the missile dynamics presented in class This is the model without the actuator Az G s q c using the state space models from a and b connect the controller and plant model together to form a closed loop state space model The solution should contain only the matrices from the controller AK BK CK DK and the plant AG BG CG DG

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