2. The following system matrices are given --[i-1]+[].-c-[21]... (a) Design an integral control by the state augmentation. Compute the feedback gain matrix by hand using the pole placement method to place the closed-loop poles at PC12 = -V2+jV2 and pcz = -2. Give the state feedback gain matrices Ky. (b) Design a full-state observer by the pole placement method by hand to place the observer poles at 2012 = -272+ j2V2. Give the observer gain matrix L. (c) Simulate in MATLAB the integral control design with the full-state observer. Compute the unit step response y(t) of the closed-loop system for t = [0,8] sec using a time step At = 0.01 sec for discretization. Plot x (t) with (t), y(t) with (t), and u(t) versus t. 2. The following system matrices are given --[i-1]+[].-c-[21]... (a) Design an integral control by the state augmentation. Compute the feedback gain matrix by hand using the pole placement method to place the closed-loop poles at PC12 = -V2+jV2 and pcz = -2. Give the state feedback gain matrices Ky. (b) Design a full-state observer by the pole placement method by hand to place the observer poles at 2012 = -272+ j2V2. Give the observer gain matrix L. (c) Simulate in MATLAB the integral control design with the full-state observer. Compute the unit step response y(t) of the closed-loop system for t = [0,8] sec using a time step At = 0.01 sec for discretization. Plot x (t) with (t), y(t) with (t), and u(t) versus t