Misalignment is a serious fault in high-speed rotating machinery available in modern industries. This fault may occur due to an offset between the bearing and shaft axes or an offset between the connected shafts. This can cause undesirable reaction forces associated with moments at both the coupling and bearings, generating additional vibrational motions that lead to system failure and eventually hindering an industry’s overall performance. Therefore, to utilize the machines efficiently, reduce economic losses, and ensure risk-free operation by workers, it is necessary to examine the effects of misalignment and unbalance faults on the rotor system and identify them with suitable methods. Keeping this view in mind, the present paper examines the dynamic behavior of a coupled rigid rotor system with active magnetic bearing supports at the ends of both rotors. The coupled rotor consists of two rigid shafts, four offset discs, and one coupling connecting the shafts. In this complex system, it is assumed that the rotating axes of the two rotors are misaligned from the active magnetic bearings. Including the rotor unbalance fault, coupling misalignment, AMBs misalignment faults, and the inertia force, the generalised equations of motion of the coupled rotor system are derived in the transverse vertical and horizontal directions using Lagrange’s equation. Further, the time domain rotor displacement and controlling current responses are generated by developing a SIMULINK model. It would be very interesting to investigate and study the unbalance and misalignment fault effects at various spin speeds of the rotor and also at ramp-up speeds in a high-speed coupled rotating machinery.