Choose an A matrix (with all non-zero elements) with n = 2 states and rank(A) =...

 

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Choose an A matrix (with all non-zero elements) with n = 2 states and rank(A) = 2. (a) [+1, 5 min] Find a B matrix such that the system is controllable. (b) [+1, 5 min] Find a suitable Q and R matrix if you are equally concerned about control cost and how quickly ₁ goes to 0, but you do not care what happens to x2. Explain your reasoning. (c) [+1, 5 min] Find the optimal state-feedback controller u(x) that minimizes (Use Matlab!) J = x¹Qx+u² /0 u Rudt (d) [+1, 15 min] Find a C matrix (with all non-zero elements) such that the system is unob- servable. Choose an A matrix (with all non-zero elements) with n = 2 states and rank(A) = 2. (a) [+1, 5 min] Find a B matrix such that the system is controllable. (b) [+1, 5 min] Find a suitable Q and R matrix if you are equally concerned about control cost and how quickly ₁ goes to 0, but you do not care what happens to x2. Explain your reasoning. (c) [+1, 5 min] Find the optimal state-feedback controller u(x) that minimizes (Use Matlab!) J = x¹Qx+u² /0 u Rudt (d) [+1, 15 min] Find a C matrix (with all non-zero elements) such that the system is unob- servable.

Answer rating: 100% (QA)

a B 1 0 0 1 The system is already controllable with the given B matrix b Q 1 0 0 ... View the full answer