1) Given Mathematical equation for Dc Motor below . 2 7K7K, V.-K_K_* ( Rr 7.K.? "mp M + Mathematical Model a) Simulate equation above using simulink if the reference signal is unit step with final value 0.8cm. By knowing the input is voltage and output is motor position x, avoid using state space method or transfer function. b) Implement Pid Controller for the system. Manual and automatic gain tuning must be done. Here is parameter for the Dc motor equation Item Symbol Value Unit M File unit Cart Mass M 0.94 kg M EMF constant KM 0.00767 Km Motor armature resistance R 2.6 12 Rm Motor efficiency n. 1 Nm Motor input voltage Motor pinion radius 6.35e-3 m rmp Planetary gearbox gear ratio K 3.71 Kg Planetary gearbox efficiency n 1 Ng Motor ratio K 0.00767 Kt Rotor moment inertia J. 3.9e-7 kg.m? Jm . 5.4 N.s/m Beq Viscous damping coefficient at the motor pinion 1) Given Mathematical equation for Dc Motor below . 2 7K7K, V.-K_K_* ( Rr 7.K.? "mp M + Mathematical Model a) Simulate equation above using simulink if the reference signal is unit step with final value 0.8cm. By knowing the input is voltage and output is motor position x, avoid using state space method or transfer function. b) Implement Pid Controller for the system. Manual and automatic gain tuning must be done. Here is parameter for the Dc motor equation Item Symbol Value Unit M File unit Cart Mass M 0.94 kg M EMF constant KM 0.00767 Km Motor armature resistance R 2.6 12 Rm Motor efficiency n. 1 Nm Motor input voltage Motor pinion radius 6.35e-3 m rmp Planetary gearbox gear ratio K 3.71 Kg Planetary gearbox efficiency n 1 Ng Motor ratio K 0.00767 Kt Rotor moment inertia J. 3.9e-7 kg.m? Jm . 5.4 N.s/m Beq Viscous damping coefficient at the motor pinion