7.5? Assume that the linearized and time-scaled equation of motion for the ball; bearing levitation device is it e x = a" + w. Here w is a constant bias due to the power amplier. Introduce integral error control, and select three control gains K : [ K1 Kg Kg' } so that the closed~loop poles-are at nl and 1 :[: j and the steady-state error to w and to a (step) position command will . _ . '1 be zero. Let y = J: and the reference input r : ymf he a constant. Draw a block diagram of your design showing the locations of the feedback gains Kg. Assume that both 3': and x can be measured. Plot the response of the closed- loop system to a step command input and the response to a step charge in the bias input. Verify that the system is Type I. Use Matlab (Simulink) software to simulate the system responses