Cyber-physical systems (CPSs) seamlessly integrate communication, computing, and control, thus exhibiting tight coupling of their cyber space with the physical world and human intervention. Forming the basis of future smart services, they play an important role in the era of Industry 4.0. However, CPSs also suffer from increasing cyber attacks due to their connections to the Internet. This article investigates resilient control for a class of CPSs subject to actuator attacks, which intentionally manipulate control commands from controllers to actuators. In our study, the supertwisting sliding-mode algorithm is adopted to construct a finite-time converging extended state observer (ESO) for estimating the state and uncertainty of the system in the presence of actuator attacks. Then, for the attacked system, a finite-time converging resilient controller is designed based on the proposed ESO. It integrates global fast terminal sliding-mode and prescribed performance control. Finally, an industrial CPS, permanent magnet synchronous motor control system, is investigated to demonstrate the effectiveness of the composite resilient control strategy presented in this article.