WUSTL ESE 543 - ESE 543 Homework 4 Chap 6,7,8 Brogan - D3061423

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WUSTL ESE 543 - ESE 543 Homework 4 Chap 6,7,8 Brogan

School name Washington University in St. Louis

Course Ese 543- Control Systems Design by State Space Methods

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Homework 3 1. 6.30 from Brogan. Solve for 821 10if 1 1 3 5254 1xx.. 2. 6.34 from Brogan. Find all nontrivial solutions for 1231040.238xxx3. 6.35 from Brogan. Determine whether nontrivial solutions exist for 1212240.00-1 -2xx4. 7.39 from Brogan. Find the eigenvalues, eigenvectors, and Jordan form for 22311 113 1A5. 7.40 from Brogan. Find the eigenvectors for 20.02A 6. 7.43 from Brogan. Are 1231 20 and 15 0 2AB. similar matrices? 7. 8.25 from Brogan. Find the inverse of 120110212A using the Cayley-Hamilton theorem. 8. 8.26 from Brogan. Find 121 if 01AteA 9. Compute the singular values and singular vectors for A = 1204. 10. Derive state space model for the following: a) For the 3-input 1-output controller Ks - ,,,KKK KABCDK1(s) K2(s)r+-+-Az qK1(s) K2(s)r+-+-Az q where 1zKsaKssz and 2qqKsaKss b) For the 1-input 2-output 2-state plant model Gs -  using the missile dynamics presented in class. (This is the model without the actuator). ,,,GGG GABCD G(s)AzqG(s)Azq 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 ,,,KKK KABCD and the plant ,,,GGG GABCD

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