Traditional Differential Algorithm Research Articles

An improved differential algorithm for the critical-angle refractometer

Due to the limit of the pixel size of the charge-coupled device (CCD) or complementary metal oxide semiconductor (CMOS) sensor, the traditional differential algorithm has a limited measuring accuracy by determining the critical angle in integral pixel. In this paper, we present a practical algorithm based on the centroid value of the reflective ratio around the critical angle pixel to address the traditional differential algorithm problem of determining the critical angle under sub-pixel in a critical angle refractometer (CAR). When the change of refractive index (RI) of a liquid sample is beyond the sensitivity of the traditional differential algorithm, the RI of the liquid can be obtained by using the centroid value of reflectivity around the critical angle pixel. The centroid value is associated with the RI change of the liquid in sub-pixel. Demonstrated by both theoretical analyses and experimental results using saline solutions with RI that changes in sub-pixel tested through the reflective CAR, the algorithm is found to be computationally effective and robust to expand the measuring accuracy of the Abbe-type refractometer in sub-pixel.

A Tactile Sensor Decoupling Process.

An improved hybrid homotopy method is proposed to decouple the multi-input model of tactile sensors. The time-embedded homotopy algorithm is proved to be very suitable for solving the problem. Three tracking factors that control the efficiency of the algorithm are studied: tracking operator, stepsize, and accuracy. Trust region methods are applied to track the zero paths instead of the traditional differential algorithm, and a periodic sampling method is proposed to improve the efficiency of the algorithm. Numerical experiments show that both the robustness and accuracy have received a huge boost after the hybrid algorithm is applied.

Precise control for vibration of rigid–flexible mechanical arm

In the present paper, based on the nonlinear dynamic equation of spacial flexible mechanical arm with dual-link bar, the method of linear quadratic control is used to eliminate the remain vibration of mechanical arm. In the process of computation, the traditional differential algorithm is replaced by the time integration method. Because of taking the more precise time-intervals in the given time-interval and avoiding a lot of computational difficulties, the method of this paper has the characteristics of high precision and unconditional stable. For a typical structure, the precise control law is obtained and the advantages of the algorithm in this paper are shown.