By Yaobin Chen and Lingxi Li (Auth.)
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111) Based on this result and on Eq. 4, Macc is calculated as follows. From Eq. 115) xÃ ¼ ½ qÃw qÃ1 lÃ T À Á À Á À Á _ x þG x ; F ¼ M x €x þ V x; and 3 ! 119) Here, Mfþ is a pseudo-inverse matrix of Mf, and the values in this simulation are Mfþ ¼ 0:5 0 À0:5 0 ! 1. 3 are realized in MATLAB. 1 Set-Point Velocity Control Simulation on Flat Ground A common-used stabilization technique is the Linear Quadratic Regulator (LQR). The plant Â ÃT state is chosen as a five-dimensional vector given by x ¼ q1 l q_ w q_ 1 l_ .
Xu, Variable structure systems: Toward the 21st Century, Springer, Berlin, 2002. H. Man et al. -Y. -J. Lin, Robust nonsingular terminal sliding model control for nonlinear magnetic bearing system, IEEE Transaction on Control Systems Technology 19 (3) (2011) 636e643.  H. F. Li, Terminal sliding mode control for spacecraft formation flying, IEEE Transaction on Aerospace and Electronic Systems 45 (3) (2009) 835e846. S. Guo, C. Li, Terminal sliding mode control for coordinated motion of a space rigid manipulator with external disturbance, Applied Mathematics and Mechanics 29 (5) (2008) 583e590.
Park, T. Tsuji, Terminal sliding mode control of second-order nonlinear uncertain systems, International Journal of Robust and Nonlinear Control 9 (1999) 769e780.  S. Kidane, R. Rajamani, L. J. Starr, M. Donath, Development and experimental evaluation of a tilt stability control system for narrow commuter vehicles, IEEE Transactions on Control System Technology 18 (6) (2010) 1266e1279.  A. Shimada, N. Hatakeyama, High speed movement control making use of zero dynamics on inverted pendulum, Journal of SICE 42 (9) (2006) 1035e1041.
Advances in Intelligent Vehicles by Yaobin Chen and Lingxi Li (Auth.)