Tracking Controller Design for MIMO Nonlinear Systems With Application to Automotive Cold Start Emission Reduction

Abstract

The main contribution of this paper is the development of a nonlinear multipleinput, multipleoutput (MIMO) tracking controller design using a discrete time sliding control approach. A Lyapunov stability analysis is used to prove the asymptotic stability of both the output errors as well as the parameter estimation errors. The application of the “New Invariance Principleâ€‌ is key to the proof of the parameter error convergence. The developed approach is applied to the cold start emissions problem. The software design process for automotive powertrains on vehicles is growing increasingly complex. Verification and validation provides a systematic procedure to follow for the implementation of control algorithms on physical systems. However, errors can arise that prove costly if not mitigated early on in the verification and validation process. Therefore, the detection and mitigation of potential uncertainties early on in the design process is vital. In this work, the determination of the system model uncertainty is the focus of an adaptation algorithm designed in parallel with a discrete time, MIMO sliding controller. The unknown parameter representing the model uncertainty is updated online in order to decrease tracking error and control effort. The MIMO formulation allows for implementation of both coupled and decoupled frameworks, thus providing a basis for the algorithm to be utilized on a variety of complex vehicle systems. The control algorithms are implemented on a cold start emissions engine model as a case study. A matlab simulink environment is used for simulation results, and an engine test cell is used for experimental validation. Simulation results demonstrate that the algorithm drives tracking error to zero in a fraction of the run time and that the algorithm may be applied with equal efficacy to coupled and decoupled systems. Experimental results demonstrate the ability of the adaptation algorithm to estimate uncertainty in the engine and decrease tracking error.