In this paper, the constrained control problem of the prescribed performance control technique is discussed in discrete-time domain for single input-single output dynamical systems. The goal of this design is to maintain the tracking error trajectory in a predefined convergence zone described by a performance function in the presence of the uncertainties. In order to achieve this goal, the discrete-time quasi-sliding-mode control with a new sliding variable is proposed. Additionally, by using a modified convergence zone, the transient response of the system can be adjusted without producing the offset error in the steady state. The effectiveness of the proposed method is confirmed by experiments on a piezo-actuated positioning system.
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