The main objective in optimizing train control is to eliminate the waist associated with classical design where train separation is determined through the use of “worst case” assumptions that are invariant to the system. In fact, the worst case approach has been in place since the beginning of train control systems. Worst case takes the most conservative approach to the determination of train stopping distance, which is the basis for design of virtually all train control. This leads to stopping distances that could be far more that actually required under the circumstances at the time the train is attempting to brake. Modern train control systems are designed to separate trains in order to provide safety of operation while increasing throughput. Calculations for the minimum distance that separates trains have traditionally been based on the sum of a series of worst case scenarios. The implication was that no train could ever exceed this distance in stopping. This distance is called Safe Braking Distance (SBD). SBD has always been calculated by static parameters that were assumed to be invariant. This is, however, not the case. Parameters such as adhesion, acceleration, weight, and reaction vary over time, location or velocity. Since the worst case is always used in the calculation, inefficiencies result in this methodology which causes degradation in capacity and throughput. This is also true when mixed traffic with different stopping characteristics are present at the same time. The classic theory in train control utilizes a SBD model to describe the characteristics of a stopping train. Since knowledge of these conditions is not known, poor conditions are assumed. A new concept in train control utilizes statistical analysis and estimation to provide knowledge of the conditions. Trains operating along the line utilize these techniques to understand inputs into their SBD calculation. This provides for a SBD calculation on board the train that is the shortest possible that maintains the required level of safety. The new SBD is a prime determinant in systems capacity. Therefore by optimizing SBD as describes, system capacity is also optimized. The system continuously adjusts to changing conditions.
Determination of vertex polynomials to analyse robust stability of control systems with interval parameters
