A stochastic dynamic programming approach to selective catalytic reduction control

Abstract

Urea based selective catalytic reduction (SCR) control strategies regulate urea dosing in diesel powertrains with the goal of achieving NOx emissions targets while being robust to transient disturbances such as exhaust temperature. A model based approach is typically pursued, where an estimated quantity of NH3 stored on the SCR catalyst is controlled to a temperature dependent setpoint. The choice of setpoint, however, is typically defined heuristically which leads to suboptimal NOx and NH3 emission trade-offs. Alternatively, this paper approaches SCR control from a stochastic dynamic programming (SDP) perspective. The dosing control law is formulated by solving an infinite-horizon stochastic optimization problem using a probabilistic model of the future SCR disturbances. Simulations over standard drive cycles show the SDP based SCR control laws outperform a standard model based PI control approach, in terms of total NOx emissions for a given level of NH3 slip, by between 5% and 15%. The SDP controllers are shown to move closer to the global optimal result found via deterministic dynamic programming. Additionally, the SDP approach provides a framework to evaluate potential controller performance improvements made available by adding parameters to the control law. In this way, the incremental benefit of having an additional state in the state-feedback control law can be weighed against the increased memory cost of the extra dimension.