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Precision position and force control is a critical issue for automated microassembly systems to handle micro-objects delicately. This paper presents two new approaches to regulating both position and contact force of a piezoelectric multimorph microgripper dedicated to microassembly tasks. One of the advantages of the proposed approaches lies in that they are capable of controlling the position and contact force of a gripper arm simultaneously. The methodology is easy to implement since neither a state observer nor a hysteresis model of the system is required. The first approach is a position-based sliding mode impedance control which converts the target impedance into a desired position trajectory to be tracked, and the second one is established on the basis of a proportional-integral type of sliding function of the impedance measure error. Their tracking performances are guaranteed by two devised discrete-time sliding mode control algorithms, whose stabilities in the presence of model uncertainties and disturbances are proved in theory. The effectiveness of both schemes are validated by experimental investigations on a glass microbead gripping task. Results show that both approaches are capable of accomplishing promising interaction control accuracy.