# Realisation of a Novel Functionally Redundant Actuation System for a Railway Track-Switch
## 4 Controller Design, Implementation and Model Validation
### Controllers Design  
The synchronisation of the motion of the three actuator bearers and their six motors is essential for the correct operation of the switch. Hence, all actuator bearers use the same control algorithm and control gains. Examining the control loops for each bearer, we see that both motors within the single actuator bearer, are controlled by three cascaded loops: inner-loop motor current controller, centre-loop motor velocity controller and outer-loop position controller (see Figure 8). Both the inner current controller and the motor velocity controller are proportional-integral (PI) controllers. The outer loop position controller is a proportional (P) controller which was found to offer zero steady-state error performance due to the natural inclusion of integral action via the velocity loop. The control performance and stability requirements for the system shown in Table 2. The maximum current is considered in the design process, but in practice is limited  
Figure 6: (a) Finite Element (FE) model of switch rails, (b) Multibody Simulation (MBS) model of the switch panel in Simpack. Figure 7: Co-simulation of the switch system. automatically by the motor drivers. The phase and gain margin requirements of 6 dB and 60\({}^{\circ}\) are essential to ensure robust relative stability of the system in the presence of uncertainties. The settling time requirement is set to be less than 7 s to comply with the UK railway switching time norms. The maximum allowable overshoot is specified is as 2\({}^{\circ}\) to ensure that the cams do not over-rotate during transit. This is a very large margin of error which ensures that the cam will not touch other mechanical components by over-rotating. For each active bearer, the two cam control systems are supplied with the desired cam angle as their setpoint (see Figure 8). The feedback signal from the cam encoders is used in controlling the motion of both motors such that the switch rails reach their expected position, Reverse or Normal, as commended by the set-point angle (0\({}^{\circ}\) or 180\({}^{\circ}\), respectively). The Nichols plots generated as part of the controller design process are shown in Figure 9; it is clear that the control stability margin requirements are met. The current controller Nichols plot (see Figure 9a) shows an infinite gain margin and phase margin of 90.2\({}^{\circ}\) which are well above the requirement. The middle loop is then analysed in the same manner to generate gains for the velocity controller. The Nichols plot in Figure 9b, shows the gain and phase margins to be 57 dB and 90.6\({}^{\circ}\), respectively. Once again these margins are large compared to the control requirements, but the time responses are sufficiently fast that it is not necessary to use higher gains. The outer position loop controller is designed last and the corresponding Nichols plot is shown in Figure 9c. The gain and phase margins are 61.5 dB and 88.6\({}^{\circ}\), respectively, which again more than satisfy the \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Required Value** \\ \hline Gain Margin & \textgreater{}6 dB \\ Phase Margin & \textgreater{}60\({}^{\circ}\) \\ Maximum overshoot & \textless{}2\({}^{\circ}\) \\ Maximum Current & \textless{}20 A \\ Settling Time & \textless{}7 s \\ Steady-state error & 0\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Control requirements for designing the controller for the switch system. Figure 8: Designed single bearer level controller for the track switch. control requirement shown in Table 2. The high margins ensure the stability of the system even in the potential event of high gain and phase modelling errors/uncertainties; which give confidence that the closed-loop systems on the real switch will be stable and behave according to requirements.