The Control of Tilting using PD controller

To counteract centrifugal powers, train companies have decided to design tilting trains or railway lines with high radii curves. In the case of trains navigating corners, centrifugal force is a key function of velocity and radius, i.e. ‘v2/r'. If the train tilts, the resulting force is countered, meaning that the touch force remains constant. The carriages can have tilting mechanisms, for example, the bogies do not tilt but the coaches do, with the bogies serving as the fulcrum (Zhou, Zolotas, & Goodall 2010). The PD controller is designed to help in the train’s tilting process by controlling suspensions through optimization. The framework presents a simplified kind of control consisting of a single input and a single output. The controller factors in different characteristics of the tracks which include the curves and irregularities. The PD control utilizes the sensor information derived from the tilt angle and lateral acceleration. The feedback received is a product of the sensor information and dynamic interactions of the suspensions. The PD controls are designed in such a manner that they are able to showcase the diverse tilt performances due to the stochastic quality and deterministic response with regards to the accelerations in the curves (Hassan, Zolotas & Margetts 2017).

Placing of controls on the railway track irregularity helps in ensuring that the passengers are comfortable and enhances the speeds permitted for the tilting trains. A control system is crucial in controlling the different speeds that exists at particular locations. The permissible speed can be calculated by the controller and hence signals a reduction in speed and the tilt angle necessary to maneuver a corner. The linear control utilizes the concepts of frequency response, step response, impulse response and the transfer function. While designing the controller the following assumptions are taken into consideration in the command: First the overshoot, DS1 ought to be less than 5%, second DS2 or settling time should below 0.6 second with a criterion of 2%, Thirdly the steady-state error DS3, should be zero for a step input and the DS4, the steady-state error for a ramp ought to less than 0.15A with 𝑟(𝑡) = 𝐴𝑡, 𝑡 > 0.

Curve velocity, V = √Egr/G

Where:

E = Ea (track super elevation) + Ec (unbalanced super elevation)

g = acceleration due to gravity

r = radius of curve

G = track gauge

Train speed, Vn = Vt+s, where:

Vn = speed at over speed condition n (m/s)

Vt = target enhanced permissible speed (m/s)

sn = value of over speed for condition n (m/s) [sn = 0 when n = 1]

Work Cited

Chandra, S. (2008). Railway engineering. Oxford University Press, Inc.

Hassan, Zolotas & Margetts (2017) Optimized PID control for tilting trains, Systems Science & Control Engineering, 5:1, 25-41, DOI: 10.1080/21642583.2016.1275990 retrieved online from: https://doi.org/10.1080/21642583.2016.1275990

Ozana, S., & Docekal, T. (2016). PID controller design based on global optimization technique with additional constraints. Journal of Electrical Engineering, 67(3), 160–168.

Zhou, R., Zolotas, A., & Goodall, R. (2010). LQG control for the integrated tilt and active lateral secondary suspension in high speed railway vehicles. Control and automation (ICCA). Paper presented at the 8th IEEE international conference, Xiamen, China (pp. 16–21)

http://www.bbc.co.uk/news/magazine-35061511