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Rational basis functions are introduced into iterative learning control to enhance the flexibility towards nonrepeating tasks. At present, the application of rational basis functions either suffers from nonconvex optimization problem or requires the predefinition of poles, which restricts the achievable performance. In this article, a new data-driven rational feedforward tuning approach is developed, in which convex optimization is realized without predefining the poles. Specifically, the optimal parameter which eliminates the reference-induced error is directly solved using the least square method. No parametric model is involved in the parameter tuning process and the optimal parameter is estimated using the measured data. In the noisy condition, it is proved that the estimated optimal parameter is unbiased and the estimation accuracy in terms of variance is analysed. The performance of the proposed approach is tested on an ultraprecision wafer stage. The experimental results confirm that high performance is achieved using the proposed approach. [ABSTRACT FROM AUTHOR]

To achieve treadmill speed adaption to the user's walking speed and reduce treadmill acceleration ripples during walking for enhancing a non-intrusive walking sense, this paper presents a novel strategy to analytically design the acceleration of treadmill by introducing a virtual force and a virtual force moment balance kinetic model. To explicitly handle the treadmill velocity to adapt the user's walking speed as well as treadmill acceleration ripples, the designed acceleration of treadmill and its derivative are specially selected as the input variables of treadmill controller. Since the user's relative position and absolute walking speed are all taken into account, the resulting velocity and acceleration ripples of treadmill can be properly updated to improve the sense of reality during the user walking by only tuning the defined design parameters and control parameters. The experiments are conducted and the effective of the proposed strategy is verified by results. [ABSTRACT FROM AUTHOR]