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This paper proposes an enhanced model predictive discrete-time sliding mode control (MPDSMC) with proportional-integral (PI) sliding function and state observer for the motion tracking control of a nanopositioning system driven by piezoelectric actuators. One distinct advantage of the proposed controller lies in that its implementation only requires a simple second-order model of the system, whereas it does not need to know neither the hysteresis model nor the bounds on system uncertainties. The unmodeled hysteresis is eliminated by the one-step delayed disturbance estimation technique and the neglected residual modes are suppressed by employing a properly-designed state observer. Moreover, the reasons why the model predictive control methodology and PI action can eliminate the chattering effects and produce a low level of tracking error are discovered in state-space framework. Experimental results demonstrate that the performance of the proposed MPDSMC controller is superior to both conventional PID and DSMC methods in motion tracking tasks. A precise tracking is achieved by the nanopositioning stage along with the hysteretic nonlinearity mitigated to a negligible level, which validates the feasibility of the proposed controller in the domain of micro-/nanomanipulation.