Tham khảo tài liệu 'sliding mode control part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | High Order Sliding Mode Control for Suppression of Nonlinear Dynamics in Mechanical Systems with Friction 339 Although a rigorous robustness analysis is beyond the scope of this study numerical examples will show that the feedback controller is able of yielding robust control performance despite significant parameter departures from parameter nominal values. Stability must be preserved in the context of both structured uncertainties in the parameters as well as unstructured errors in modeling. A stability analysis for the proposed control configurations should parallel the steps reported in Aguilar-Lopez et al. 2010 and Aguilar-López Martínez-Guerra 2008 . 4. Applications In this section simulation results are presented for both position regulation and tracking of mechanical systems with friction 7 with the IHOSMC approach described above. The control performance is evaluated considering set point changes and typical disturbances of mechanical systems. We consider the following five examples i Mechanical system with Coulomb friction ii an inverted pendulum iii an AC induction motor and vi a levitation magnetic system. Mechanical system with Coulomb friction We consider a mechanical system described in Alvarez-Ramirez et al. 1995 with a Coulomb friction law. The dimensionless equation of motion is dX1 dt X2 18 X2 -F X1 X2 - KX1 Tl u dtm where m is the mass of the system Ti is an unknown external force which way be due to loads and or noise acting in the mechanism u is a manipulated forced used to control the system and the term F X1 X2 includes all friction effects and is determined by the following expression F X1 X2 pf X1 where p is the coefficient of friction and f X1 is the normal load which vary with displacement f x1 -Fk X1 0 -Fs f X1 ụsX1 0 f x1 Fk X1 0 19 Control objetive is the position tracking to the periodic reference yref X1 ref The parameters of the controller are set as Ỗ1Í 25 10 and ỏ2 i 1 . Model simulation parameters are taken .
