Estimation of benchmark performance for nonlinear control systems

During the last two decades, performance assessment of control systems has been receiving wide attention. However, estimation of the benchmark performance of nonlinear control systems still remains open. In this work, we consider an estimation problem of the benchmark performance when control loops are intervened by the complex non-differentiable nonlinearity. The considered nonlinearity includes control valve stiction of the control systems, as well as switching action involved by protection valves widely used in the safety-related control systems. Based on the idea of Lebesgue sampling, the paper proposes a novel threshold autoregressive model for unbiased estimation of the benchmark performance. Basically, the proposed method is based on the partitioning of the closed-loop routine operating data when it reaches certain thresholds. Modeling each partitioned regime as an autoregressive model, the prediction error variance as the benchmark performance can be obtained by the principle of pooled variance. A numerical example well shows the effectiveness of the proposed method.