State dependent ramp metering control of motorway bottlenecks using non-linear pole assignment

Ramp Metering (RM) utilises traffic lights at the on-ramp entrances to limit access to the main carriageway of the motorway, in order to maintain flow close to capacity. In comparison to linear design, adaptive or predictive control systems can offer improved performance, albeit with the disadvantage of increased complexity, which can be prohibitive in the context of RM. By contrast, the present article develops a state dependent parameter (SDP) approach to traffic modelling and an associated non-linear pole assignment RM algorithm that is relatively straightforward to implement. Although the SDP model describes occupancy, its parameters are functionally dependent on other variables in the system, such as average velocity. In this manner, SDP models capture the time varying and non-linear dynamics of motorway flows but can, nonetheless, be estimated off-line. The paper illustrates the approach using telemetered measurements from near Southampton in the UK. Algebraic solutions to the control problem are similarly derived off-line and evaluated on-line using a macroscopic simulation model.