Robust controller based on Smith predictor for an electric EGR valve control system

Abstract

We provide an experimental proof that the Smith Predictor outperforms the PID under hard robustness constraints. It is well-known that the Smith predictor delivers excellent performance for the nominal system but its robustness is much poorer than of a corresponding PID controller. For this reason, the Smith controller never became popular in typical industrial applications. In this paper we change dramatically this viewpoint; we show that the Smith predictor can be desensitized (robustified) to achieve robust performance and stability over a wide range of parameter variations and can visibly beat the PID controller in terms of performance vs. robustness trade-offs. The basic idea for the 447robustification is to detune the nominal design to allow for less than optimal nominal performance. In particular, we require smaller than optimal rise time. As a result, the Nyquist plot of the nominal system is modified in such a way that large delay variations can be tolerated with moderate only loss of performance in the nominal case. The theoretical considerations are supported by a successful application to an automotive problem: An Exhaust Gas Recirculation (EGR) control system. The EGR system is briefly presented. Robustness is one of the main issues in this system due to nonlinearities, time delays, and the effects of complex exhaust gases dynamics. It was found after extensive measurements, identification and simulation experiments that a good approximation of the system dynamics consists of a first order transfer function with a time delay where both transfer function coefficients and the time delay strongly depend on the operating conditions (load, r.p.m., and the reference signal: desired EGR rate). The Smith predictor, well tuned to the nominal case, was found to have an excellent performance for the nominal system while the robustness was rather poor. The trade-off between the performance and robustness was achieved by relaxing the specifications for the rise time. Simulation results for both nominal and robust designs are presented as well as comparable results for an optimally tuned robust PID controller.