Robust Interval Criterion for a Steady Value

The work is a development of the interval criterion for determining the moment when the steady-state value of the transition signal occurs. These criteria are used in technologies related to testing complex objects under conditions of parametric uncertainty of its model. The transient signal is analyzed in on-line mode. Therefore, the accuracy of the decision about the time of the end of the tests determines the cost of conducting them. Such tests are characterized by significant dynamic errors that significantly exceed the allowed level. The reasons for this are the parametric uncertainty in the mathematical model of the object and the inability of the deterministic interval criterion to correctly issue a solution under these conditions. It was previously determined that the interval criterion is characterized by the presence of an asymptotic critical value of the criterion. Exceeding the object's real time constant over the critical value gives a false positive result. This situation is characterized by the fact that the desired moment is falsely determined significantly earlier than the optimal solution. You can avoid this situation if you set the criteria to the maximum constant of the object's time. However, this choice leads to significant time losses when analyzing the transition signal. The solution of the problem of guaranteed provision of a given level of dynamic error over the entire range of values of the object model parameter is possible using a robust algorithm. The basis for constructing a robust criterion is to control the duration of the observation interval. For this purpose, the current information about the analyzed signal is used. There are three ways to apply the current information. The first approach is based on the use of an extrapolated estimate of the established value. This allows you to determine the estimate of the current dynamic error and prevent a falsely positive decision of the criterion. The second approach is based on the analysis of the dynamics of the current increment of the transition signal at neighboring observation intervals. The third is based on the use of a reference model of the transition process in the measuring channel with a parameter equal to the critical value of the criterion. Based on the analysis of current information, the critical value of the criterion is redefined. With the new value, monitoring of the transition process continues until a positive decision is made about the moment when the steady value of the transition signal occurs.