# Identification and control of selective catalytic reduction systems

To protect the environment, NOx emission requirements for heavy-duty vehicles are being continuously tightened. One of the technologies used to meet the emission requirements is the selective catalytic reduction (SCR) system. This project is focused on identification and control of SCR systems in mobile applications, specifically in diesel engine driven heavy duty trucks. The project is a cooperation with Scania AB, supported by the Swedish Energy Agency, project nr 32299-1.

A diesel engine generates a certain amount of NOx based on the load and the speed. This NOx, together with the exhaust mass flow and the exhaust temperature, are passed into the SCR system. A block diagram of an SCR system is depicted in Fig. 1.

*Figure 1: Block diagram of a typical SCR aftertreatment system. One advantage of SCR aftertreatment systems is that they avoid the conflict between particle and NOx emissions of modern diesel engines. *

The objective of the work is to model the dynamics of the NOx emissions in the exhaust gas aftertreatment system on-line, and to control the process. This is to be achieved for the changing operating conditions exhibited in automotive applications. These changing conditions can be observed in Fig. 2., where the load and speed variations for the World Harmonized Transient Cycle (WHTC) are shown. The WHTC is to be used for Euro VI testing, it is a transient test with a length of 1800 s which specifies engine speed and load values for urban and highway driving.

*Figure 2: Engine load and speed for the WHTC. *

The first goal of the project is to identify a black-box model for the SCR system recursively. In prior publications the modeling of the SCR system has mostly been based on first principles models. This leads to high order nonlinear models, which are difficult to identify and use for controller design. A main idea of the project is therefore to use a low order non-linear model with continuous time parameters, thereby facilitating non-linear systematic controller design (techniques like feedback linearization are typically defined for ordinary differential equation (ODE) models).

Building on 10 and 11, new refined non-linear system identification methods were therefore first developed in 8 and 9. These methods are all based on a continuous time vector ODE, combining successive derivative states and one non-linear right hand side component. The nonlinearity is parameterized as a multi-variate polynomial in the states and inputs. A specific advantage is that the parameterization reduces the risk of over-parameterization - yet ODEs with general right hand sides can be locally modeled as proved in 10. One novelty of 8 and 9 is the fact that a more sophisticated numerical integration method is used, as compared to 10 and 11. Later the methods of 8 and 9 were analyzed theoretically in 4 and 5, where proofs of global convergence to a local minimum of the recursive prediction error (RPEM) criterion are given.

The practical identification results obtained using the new RPEM, and a block-oriented approach, are promising, see the papers 6 and 7. The model fit was up to 78% in the runs with WHTC applied, as illustrated in Fig. 4. The four signals used as inputs include NOx concentration at inlet [fraction], the injected urea [g/min], the temperature [K] and the exhaust flow [mol/s].

*Figure 3: Identification results using the RPEM. Left: Output from simulator, solid, and the output from the RPEM, dashed, in fraction for the identification data set with a model fit of 78.40 %. Right: Output from simulator, solid, and the output from the RPEM, dashed, for the validation data set with a model fit of 59.11%.*

Recently, the identification algorithms have been used in order to produce models for non-linear controller design. The papers 1 and 2 used the identified model for design of a feedback linearization controller with very good results. LQ control was used for control of the linearized loop. The controller performance was much better than for linear control, see Fig. 4. The paper 1 also presents results where the identification algorithm is integrated with the controller to do adaptive non-linear feedback linearizing control. Also here exccellent results were obtained. Further work performed in the project is discussed in the thesis 3.

*Figure 4: Controller performance. Left: the feedback linearisation controller, with a reference value, dashed line and the NOx priori to the catalyst together with the output NOx. Right: Controller performance using the equivalent linear controller.*

## References

1. S. Tayamon and T. Wigren, "Control of selective catalytic reduction systems using feedback linearization", Asian J. Contr., vol. 18, no. 3, pp. 802-816, 2016. DOI: 10.1002/asjc.1164.

2. S. Tayamon, T. Wigren and B. Carlsson "NOx control for SCR systems using feedback linearisation", ERNSI 2014, Ostend, Belgium, September 21-24, 2014.

3. S. Tayamon, "Nonlinear system identification and control applied to selective catalytic reduction systems", Ph.D Thesis, department of Information Technology, Uppsala Univ., Uppsala, Sweden, September, 2014.

4. S. Tayamon, T. Wigren and J. Schoukens, "Convergence analysis and experiments using an RPEM based on nonlinear ODEs and midpoint integration", Proc. IEEE CDC 2012, Maui, HI, pp. 2858-2865, December 10-13, 2012.

5. S. Tayamon and T. Wigren, "Convergence analysis of a recursive prediction error method", Proc. SYSID 2012, Brussels, Belgium, pp. 1496-1501, July 11-13, 2012.

6. S. Tayamon, D. Zambrano, T. Wigren and B. Carlsson, "Nonlinear black box identification of a selective catalytic reduction system", In Proceedings of 18:th IFAC world congress, Milan, Italy, August 27-September 2, 2011.

7. D. Zambrano, S. Tayamon, B. Carlsson and T. Wigren, "Identification of a discrete-time nonlinear Hammerstein-Wiener model for a selective catalytic reduction system", In Proceedings of ACC 2011, San Fransisco, U.S.A., June 27-29, 2011.

8. S. Tayamon and T. Wigren, "Recursive identification and scaling of non-linear systems using midpoint numerical integration", Technical Reports from the department of Information Technology 2010-025, Uppsala University, Uppsala, Sweden, October, 2010.

9. T. Wigren, L. Brus and S. Tayamon, "MATLAB software for recursive identification and scaling using a structured nonlinear black-box model - Revision 6", Technical Reports from the department of Information Technology 2010-022, Uppsala University, Uppsala, Sweden, September, 2010.

10. T. Wigren, "Recursive prediction error identification and scaling of nonlinear state space models using a restricted black box parameterization", Automatica, vol. 42, no. 1, pp. 159-168, 2006.

11. T. Wigren "Scaling of the sampling period in nonlinear system identification", in Proceedings of IEEE ACC 2005, Portland, Oregon, U.S.A., pp. 5058-5065, June 8-10, 2005.