Static gain estimation for nonlinear dynamic systems from steady-state values hidden in historical data

Static gains are often required for control, diagnosis and optimization of nonlinear dynamic systems. This paper proposes a new approach to estimate static gains for nonlinear dynamic systems from steady-state values hidden in historical data. First, steady-state values of system inputs and outputs are extracted by automatically finding data segments in steady-state conditions. Second, static gains of nonlinear dynamic systems in different operating conditions are estimated via linear regression from these steady-state values. The proposed approach has two practical features: (i) estimated static gains can be verified in a convincing way, because the validness of extracted steady-state values is confirmed by visualizing data segments in steady-state conditions, and the accuracy of estimated static gains is verified by comparing the extracted steady-state values and their estimates; (ii) the proposed approach is simple to understand and implement in practice, since it only involves a linear equation between steady-state values and static gains, as well as a basic technique of linear regression. Numerical simulation and industrial application demonstrate the effectiveness of the proposed approach.