Instructions: Unless there are extraordinary circumstances, late homework assignments will not be accepted. Some homewor

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Instructions Unless There Are Extraordinary Circumstances Late Homework Assignments Will Not Be Accepted Some Homewor 1 (131.44 KiB) Viewed 39 times

Instructions: Unless there are extraordinary circumstances, late homework assignments will not be accepted. Some homework problems should be worked by hand, and others will require the use of Matlab (as specified in each problem). If homework problems are to be done by hand, you are allowed (and encouraged) to use software to check your answers. For problems that require Matlab, you should submit the output as well as the code used to produce the output, including all necessary comments. Hand-written homework will be accepted provided it is legible. Use of computer software for typing answers is encouraged and homework needs to be submitted through the course account made on Gradescope. Printed assignments will not be accepted. Q1) (20 points) Consider the following state-space representation of the open-loop system: 1 = 0 0 1 1 0 -2 1 1 . + 19 u, y = [1 0 0 r. = . Let u=-Kr+Gr. Use Bass-Gura formula to find K such that the closed-loop system with state feedback has the following eigenvalues. Then check your result using both acker and place commands in MATLAB. 11,2 = -1; 13 = -2 Also find G so that the steady-state error for a unit step input is zero (you can use MATLAB for all the matrix multiplications). Q2) [20 points) 8 Consider a Luenberger observer, where A= and C= [0 2]. The desired 10. eigenvalues for the observer error dynamics matrix A - LC are 21,2 = -10 = 10j. Explain if it is possible to compute L to place these eigenvalues? If possible, compute L.