In this paper, an adaptive fault-tolerant control (FTC) scheme is proposed for a class of uncertain nonlinear systems with actuator failures, in which a backup actuator is available. Different from existing FTC methods applying dynamic redundant actuators, a situation of deferred actuator replacement is firstly taken into account, i.e., the backup one cannot connect to plant right after failure detection. To recover the tracking error into prescribed performance within a specified time, an error transformation is introduced to render Tangent Barrier Lyapunov Functions (TBLF) valid at the replacement instant, by which reconfigurable controller can be designed for the backup actuator. Simulation results on a flight control system are presented to illustrate the effectiveness of the FTC scheme.

In this paper, a novel adaptive fault-tolerant control (FTC) scheme for voice coil motor-driven fast steering mirror (FSM) systems is proposed. To improve the traditional four-point driving structure of voice coil motors, a six-point redundant driving architecture with hardware redundancy is firstly developed. By innovatively introducing the concept of drive groups, we establish a fault detection mechanism and a deactivation strategy for failed motors. Furthermore, a dual-mode adaptive FTC methodology that integrates compensation and switching techniques is proposed, ensuring both stability and transient performance of the FSM system throughout its operational lifecycle.

At ultra-low speeds, the quantization resolution of a position sensor typically exceeds the true angular displacement within one sampling period, so velocity information is almost entirely buried under quantization steps. This paper proposes a quantization-oriented adaptive high-order sliding mode differentiator (Q-AHOSMD). A saturation switching mechanism with the quantization resolution as prior knowledge suppresses high-frequency chattering over quantization plateaus; an event-driven differential velocity estimation scheme of the “update on jump, decay over plateau” type is constructed from quantization jump events; and an adaptive gain law is synthesized from velocity-mismatch feedback. Finite-time convergence of the error system and practical stability under quantization noise are proved, with explicit expressions for all ultimate bounds. Simulations show that, with a sampling period of 1 ms and a true velocity of 0.001°/s, the method achieves a root-mean-square (RMS) velocity estimation error of 0.00036°/s—about 94% lower than the backward difference method—with smooth output and no visible chattering. Requiring no dynamic model and tunable using only sensor specification parameters, the method provides an effective means of extending ultra-precision servo systems into the ultra-low-speed regime.