Consider a DC motor with following parameters: J = 0.0113 Kg + m /s * b = 0.028 Nms L = 0.1 H R = 0.45 0hm K = 0.067 Nm/Amp K = 0.067 Vs/rad Consider the rotation speed is the output of the DC motor. P1. Please provide transfer function and state space model of a DC motor and plot block diagram. The input to the system is the applied voltage. The output of the system is the rotation speed of the motor. (10%) P2. In MATLAB, plot the step response of the provided DC motor, using both the transfer function and state space model. Please provide MATLAB code or a Simulink model. (10 %) P3. In MATLAB, please design a P, PI and PID controller of the provided DC motor. Please compare the results of different controller and different parameters used of the controller, i.e. compare rising time, settling time, steady state error, overshoot, etc. Please provide MATLAB code or a Simulink model. (40%) P4. Please design a state feedback controller of the provided DC motor. Please provide the design progress, and the step response of the designed controller. Please analysis the step response of the designed controller. (40%) DC motor controller design R e-k G b8