Underwater vehicles are widely employed as platforms for marine monitoring and operations, with rudders playing a crucial role in controlling their movements. Traditional underwater vehicles utilize servos to steer rudders, which results in high production and maintenance costs. To reduce the manufacturing costs of small underwater vehicles, this paper proposes a design featuring a three-position cross rudder driven by a binary-controlled electromagnet. Additionally, a novel virtual rudder angle controller is developed, which utilizes PWM frequency conversion to perform rudder control, ensuring motion performance comparable to that of conventional underwater vehicles. By establishing kinematic and dynamic models of a typical underwater vehicle (REMUS100), a corresponding virtual rudder angle control strategy is introduced. Based on the binary-controlled three-position cross rudder and virtual rudder angle controller, the effectiveness of the motion control method is verified by numerical simulation. The results confirm that the proposed virtual rudder angle controller successfully executes turning and spatial path-tracking tasks. The binary-controlled three-position cross rudder, together with the virtual rudder angle controller, offers a cost-effective solution for the practical application of small unmanned underwater vehicles, particularly for disposable underwater vehicles that do not require recovery.