7.50 Suppose a DC drive motor with motor current u is connected to the wheels of a cart in order to control the movement of an inverted pendulum mounted on the cart. The linearized and normalized equations of motion corresponding to this system can be put in the form =0+v+u, v=0-v-u where angle of the pendulum, v = velocity of the cart. (a) We wish to control by feedback to u of the form u = -K10 - K20 - K3v. Find the feedback gains so that the resulting closed-loop poles are located at-1,-1±j√√3. (b) Assume that and v are measured. Construct an estimator for and 6 of the form * = A* + Ly - C*). where x =[] and y = 9. Treat both v and u as known. Select L so that the estimator poles are at -2, and -2.