Lane keeping control of the single track vehicle model with linear tire characteristics is analyzed in the presence of time delay. In order to compensate time delay, the predictor control approach called finite spectrum assignment is applied. This controller uses an internal model of the plant to predict current system states in spite of the time delay. The predictions are based on a simplified version of the vehicle model, neglecting tire dynamics. The predictive control approach is compared with traditional feedback control using analytically derived stability maps and numerical simulations. Robustness to parameter mismatches and numerical issues related to the implementation of the control law are also analyzed.

No abstract

A simple mechanical model of the skateboard-skater system is analysed, in which the effect of human control is considered by means of a linear proportional-derivative (PD) controller with delay. The equations of motion of this non-holonomic system are neutral delay-differential equations. A linear stability analysis of the rectilinear motion is carried out analytically. It is shown how to vary the control gains with respect to the speed of the skateboard to stabilize the uniform motion. The critical reflex delay of the skater is determined as the function of the speed. Based on this analysis, we present an explanation for the linear instability of the skateboard-skater system at high speed. Moreover, the advantages of standing ahead of the centre of the board are demonstrated from the viewpoint of reflex delay and control gain sensitivity.

A simple mechanical model for the lateral and yaw motion of a vehicle is presented while taking into account rolling constraints. The governing equations are derived by utilizing the Appellian framework. Analytical and numerical bifurcation analysis is performed while utilizing a PD controller. The results provide insight into the local and global stability of forward and reverse motion of automated passenger vehicles and harvesters.

A simple mechanical model of the skateboard-skater system is analyzed, in which a linear PD controller with delay is included to mimic the effect of human control. The equations of motion of the non-holonomic system are derived with the help of the Gibbs-Appell method. The linear stability analysis of rectilinear motion is carried out analytically using the D-subdivision method. It is shown how the control gains have to be varied with respect to the speed of the skateboard in order to stabilize the uniform motion. The critical reflex delay of the skater is determined as a function of the speed and the fore-aft location of the skater on the board. Based on these, an explanation is given for the well-known instability of the skateboard-skater system at high speed. INTRODUCTIONSkateboard was invented only in 1950's and already enjoys worldwide popularity. The challenge of understanding the motion of the skateboard is due to the kinematic constraints and the complexity of the skater-skateboard system. If the skateboard is tilted around its longitudinal axis then the wheel-pairs also turn around their steering axes because of the wheel mounting geometry. This phenomenon makes the mechanical model non-holonomic and the equation of motion can be derived by means of the Gibbs-Appell method [1]. The effect of speed on the stability of the skateboard was investigated a not long after the invention of skateboards [2] but publications (see, for exam-