An adaptive model-free control with nonsingular terminal sliding-mode (AMC-NTSM) is proposed for high precision motion control of robot manipulators. The proposed AMC-NTSM employs onesample delayed measurements to cancel nonlinearities and uncertainties of manipulators and to subsequently obtain sufficiently simple models for easy control design. In order to maintain high gain controls even when the joint angles are close to the reference target values and accordingly achieve high precision and fast response control, a nonlinear sliding variable is also adopted instead of a linear one, asymptotically stabilizing controls by guaranteeing even a finite-time convergence. In addition, sliding variables are reflected on control inputs to support fast convergence while achieving uniform ultimate boundedness of tracking errors. The control gains of the proposed AMC-NTSM are adaptively adjusted over time according to the magnitude of the sliding variable. Such adaptive control gains become high for fast convergence or low for settling down to steady motion with better convergence precision, when necessary. The switching gains of the proposed AMC-NTSM are also adaptive to acceleration such that inherent time delay estimation (TDE) errors can be suppressed effectively regardless of their magnitudes. The simulation and experiment show that the proposed AMC-NTSM has good tracking performance. INDEX TERMS Adaptive control, time-delay control, time-delay estimation, nonsingular terminal slidingmode, robot manipulator.

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In this paper, we present the implementation method of a Simulink block for dynamic matrix control (DMC) that can be used in a rapid control prototyping (RCP) environment and consider the speed control of a DC motor using the developed DMC block. Firstly, we introduce a lab-built RCP system briefly. Secondly, we present a method to implement the DMC block using C-language, which enables DMC algorithm to be represented in a library block that can be used in Simulink environment. Finally, we use the developed DMC block for the speed control of a DC motor, through which we show that the DMC-based control system can be easily implemented and it can be applied to real-time control of systems with relatively fast sample rates.