China
Africa
Explore chapters and articles related to this topic
Variables, functions and mappings
Published in Alan Jeffrey, Mathematics, 2004
For a different example of a parametric representation, we now consider the lemniscate introduced in Example 1.15, a special case of which was shown in Fig. 1.22(b) using the polar representation r2 = 9cos(2θ). The geometrical definition of a lemniscate is the locus of points the product of whose distances from two fixed points called the foci is a constant. Let us derive the algebraic equation of a lemniscate, show how its representation in polar coordinates arises, and then how a parameterization simplifies the task of drawing the curve.
Meta-heuristic algorithms for the control tuning of omnidirectional mobile robots
Published in Engineering Optimization, 2020
Omar Serrano-Pérez, Miguel G. Villarreal-Cervantes, Juan C. González-Robles, Alejandro Rodríguez-Molina
It is clear that the control tuning approach presented in Section 2 is based on a specific trajectory. Nevertheless, the best (‘optimal’) gains obtained with this approach can track other elemental paths that can be used for characterization in trajectory planning (Wang and Tsai 2004; Lacevic, Velagic, and Hebibovic 2005): the circle, the Lemniscate curve, and the straight line. The above is confirmed with the suitable performance of the proposal shown in Figure 6, where different paths in are tracked by the OMR using the control gains obtained with DE Best 1 Bin. Then, the offline control tuning approach not only carries out a specific trajectory but also other trajectories with suitable control performance.
Simulations of dust dynamics around a cone hood in updraft conditions
Published in Journal of Occupational and Environmental Hygiene, 2018
K.I. Logachev, A.M. Ziganshin, O.A. Averkova
We built an experimental setup to validate our findings in a laboratory setting. Our setup was capable of measuring axial and radial velocities upstream of the exhaust hood absent updraft (Figure 2). The setup comprised a fan[1] (Systemair EX-18 4c), a 0.125 m diameter round plastic air duct joined through a 0.112 m round diameter header piece with the lemniscate of Bernoulli shape and having a static pressure chamber[4] with a piece of filter fabric[5] installed to dampen air pulsation. The translucent pipe[7] had a radius of 0.56 m.
ESO based sliding mode control for the welding robot with backstepping
Published in International Journal of Control, 2021
Pengcheng Wang, Dengfeng Zhang, Baochun Lu
In order to verify the performance of the controller, the simulation experiment uses matlab/robotic toolbox as the simulation platform, the simulation experiment uses the Bernoulli lemniscate as the target curve, the 5-DOF connecting rod robot as the experimental carrier, the terminal actuator position and posture coordinates are . The desired curve is as followed and the unite is (dm):