Partial driving automation systems execute sustained lateral and longitudinal control, while humans are required to supervise the automated driving features. Similar with drivers using manual driving settings, those using automated driving systems may also experience drowsiness. However, existing systems that aim to detect driver drowsiness tend to be unreliable. This study applies a dual-control scheme in the partial driving automation context in which the driver must keep their hands on the vehicle's steering wheel. This scheme executes a partial steering control when a vehicle lane departure is anticipated (because of inappropriate torque input) and then activates a deceleration control if the driver does not properly perform the required action. To determine whether the driver is supervising the partial driving automation, the scheme attempts to create an opportunity for driver-automation interactions. Thus, the controller's objectives are twofold: safety control and driver state identification. This study investigated the effectiveness of the scheme for identifying driver drowsiness and preventing lane departures using only vehicle information. Twenty drivers participated in a fixed-base driving simulator experiment in a sleep-inducing environment. While we observed cases in which the system could effectively bring the vehicle to a controlled stop, the timeliness and accuracy of the driver state identification remained as issues owing to indirect links between the drivers' drowsiness level and controller activation. We conclude that although the dual-control scheme is a useful mechanism to avoid lane departures, the driver state identification needs to be improved to ensure timely and effective detection of driver drowsiness.