Load Following (L-F) control of Nuclear Power Plant (NPP) under actuator faults and measurement noises remains challenging both in theory and in practice. To solve this challenge, a globally preassigned-time stable fault-tolerant control strategy of rapid L-F for a Pressurized Water Reactor based Small Modular Reactors (PWR-SMR) under control rod drive mechanism (CRDM) faults and sensor noises is first proposed. From a practical standpoint, considering some states of PWR-SMR cannot be measured directly and the sensor noises in practice, a finite-time tracking differentiator and a nonlinear ada...