# Modeling and Numerical Computation of the Longitudinal Non-Linear Dynamics of High-Speed Elevators
## 4 Study of the Nature and Law of Elevator Dynamics
### Impact of Control Strategies on Elevator Operation  
During high-speed elevator operation, frequent acceleration and deceleration occur, significantly impacting passengers' ride experience. Experimental findings indicate that passengers' sensation of sinking and floating in the elevator correlates directly with the acceleration and rate of acceleration change. Excessive acceleration can lead to significant discomfort for passengers. Moreover, recognizing the impact of frequent acceleration and deceleration on elevator operation efficiency and costs, studying the elevator's ideal speed curve, and selecting suitable motion laws are essential for enhancing the operation quality.  
Currently, four common operating profiles are utilized for high-speed elevators: triangle, trapezoid, parabolic, and parabolic-linear composite shapes. Figure 10 illustrates the speed curves corresponding to these control strategies.  
The basic parameters of the aforementioned high-speed elevator were input and the elevator control strategies were sequentially defined. Using a time step of 0.001 s, calculations were conducted to derive the acceleration response maps for the four conventional operational laws. The outcomes are illustrated in Figure 11.  
Figure 10: _Cont._  
Figure 9: Comparison of elevator frequencies at different operating heights.  
Figure 11: _Cont._  
Figure 10: Speed profiles of four control strategies. (**a**) Triangular control strategy speed profile; (**b**) trapezoidal control strategy speed profile; (**c**) parabolic control strategy velocity profile; (**d**) parabolic-linear control strategy velocity profile.  
Figure 11a illustrates the response of the triangular control strategy, showing significant fluctuations throughout the process. In Figure 11b, the response obtained from the trapezoidal control strategy demonstrates three distinct phases corresponding to acceleration, constant speed, and deceleration. Notably, fluctuations are prominent across these phases, particularly evident during the constant speed interval. The triangular and trapezoidal control strategies exhibit abrupt speed changes at the beginning and end of acceleration and deceleration, leading to discomfort for passengers due to sudden transitions in speed during the intermediate phases from acceleration to constant speed and constant speed to deceleration. Hence, they are unsuitable as operation laws for high-speed elevators.  
Figure 11c,d depict the response diagrams of the line control strategy and the parabolic-linear control strategy, respectively. The response of both control strategies is roughly divided into three segments, corresponding to acceleration, constant speed, and deceleration. Notably, during the acceleration phase, the response of the parabolic-linear control strategy exhibits greater and more prolonged fluctuations compared to the parabolic control strategy due to an additional segment of uniform acceleration. This additional stage allows the elevator to reach a given speed faster. Conversely, in the constant speed phase, the response of the parabolic-linear control strategy demonstrates smaller fluctuations compared to the parabolic strategy. Similar to the acceleration phase, in the deceleration phase, the parabolic-linear control strategy's response is better suited for high-speed elevators.