Reducing the Order of Complex Models Using the Robust Control Toolbox

Abstract

The city of Berezniki, Perm region is located on an underworked mine area. For several years, the city has been experiencing active subsidence of the soil, which provoke the destruction of buil-dings. Therefore, for several years now, the city's buildings and structures have been monitored, which makes it possible to analyze the degree of subsidence. Models of a sufficiently high order are used for an accurate analysis of the situation and forecasting. The article is about a possibility of modeling the deformation of buildings associated with soil subsidence, as a result of mine workings in the city of Berezniki. The purpose of the study is to consider the capabilities of the ‘Robust Control Toolbox’ for reducing the order of complexity of models. An example of an eight-story building included in the collection of reference examples for reducing models of linear dynamic systems is used. Materials and methods. Typical steps for solving the problem of model reduction are presented, commands and tools used to solve this problem are described. The parameters of the model in the state space are determined, which has 48 states, which are displacements or rates of change. The singular values of Hankel are used to select states that can be neglected. The model is reduced using an adaptive error boundary. Reduction using the multiplicative error bound is considered. Comparison of the results of reduction of the model by all described methods is carried out, the choice of the best method of reduction of the model is substantiated. Results. An analysis of the approximation error was performed for all the methods. The maximum relative error has been calculated. An example of calculating the order of the model for a given error value of 5% is given. The order of the result model is 34 states with the error less is then 1%, which is less than the original model. As a result, the AFCs of the original and reduced models, as well as the transient processes of the models, were constructed. The plots in the frequency domain of the models practically coincide, which indicates an adequate description of the system. Conclusions. As a result, it was shown that it is possible to reduce the size of the model by 14 orders of magnitude, goal achieved.