Piezoelectric actuators (PEAs) are the key devices in micro/nano positioning system. However, the PEA performance is significantly degraded by the inherent non-linear behaviour. This behaviour is a consequence of the hysteresis properties contained within PEAs. Therefore, in micro/nano positioning applications, a robust control system has to be adopted for such actuators. This paper proposes a systematic control method that utilises a fast non-singular terminal sliding mode (FNTSM) based on online perturbation estimation technique for PEAs. Unlike other sliding mode methods, the FNTSM control method is characterised by chatter free. Besides, a zero error convergence can be guaranteed in finite time in the presence of disturbance and system uncertainties (i.e., hysteresis and gain changes). The design of the FNTSM control based on perturbation estimation (FNTSMPE) is presented. A model-free robust exact differentiator is used to estimate the states of the feedback system from merely measurable position signal. Theoretical analysis and the experimental results of FNTSMPE control reveal that high-precision and robust performance is achieved in comparison with ordinary FNTSM control.