Hi this is a simple project ,the details of the project are attached as a zip file,there are just 2 problems in this project Problem 1 A linear time invariant plant is given by (1) What are the open-loop poles? Is the open-loop system stable? (2) Is the system controllable? (3) Hamiltonian Approach (a) Find the unique positive definite solution to the ARE (Algebra Riccati Equation) by using the Hamiltonian Matrix approach. Please provide derivation and computational details such as eigenvalues, eigenvectors, etc. (b) Use the Matlab function ARE to verify your results. (c) Find the steady-state Kalman gain. (d) What is the closed-loop system? Find the closed-loop poles. Is the closed-loop system stable? (4) Pole Placement Approach: Find the optimal state-feedback gain by first computing the closed-loop pole positions, followed by pole placement design. (5) Suppose that the initial state is x x x 1 2 3 (0)= 4, (0)= 0, (0)= 5. Perform simulation and plot the optimal control, optimal state trajectory. What is the optimal performance in this case? Problem 2 It is desired to drive any initial state x(0) to zero in minimum time when u(t) ≤ 1 for all t. (1) For u = −1 and u = 1, solve the system equations to get x t 1( ) and x t 2( ). (2) Sketch phase plane trajectories for u = −1 and u . (3) Use Pontryagin’s minimum principle to derive the form of the optimal control law. (4) Find the switching curve and derive a minimum-time feedback control law. a. derive the optimal control u. b. Plot the optimal state trajectory on the phase plane. c. Plot the time trajectories of the optimal state and optimal control.
1)i want the project to be done in matlab as described in the zip file which is attached below. 2)i want detailed description of each and every step. 3)A totally completed project it is simple n easy. 4)need the project within the next 3 days
all details of project are attached as a file please see..y