Fig. 1 Equivalent circuit for a separately excited DC motor Fig.1 shows an equivalent circuit for a separately excited DC motor. For this circuit, design a simple model of an automatic motor control. Follow the following algorithm: 1.1 Formulate the mechanical and electrical equations. 1.2 Formulate the first order differential equations. 1.3 Formulate the state space analysis. 1.4 Simulate your automatic motor control in Matlab/Simulink for the following conditions: 1.4.1 Underdamped 1.4.2 Overdamped 1.4.3 Critically damped