Thesis researches the creation of methods for synthesis and identification of mathematical models of minimum order for decreasing time when used in tasks of analysis and optimisation of processes in multidimensional dynamic objects.
For the first time the research proves that the process in minimum phase dynamic objects with negative feedback which are described by the linear differential equation of the high orders, may be equivalently described within the scope of minimum phase ones by the differential equations of minimum order, which equals the sum of maximum order of the derivative in the right part and a three num.
For the minimum phase linear multidimensional dynamic objects, that operate in the mode of the real time signal transmission and which do not have the derivatives in the right part of the differential mathematical model, there had been for the first time developed the method for identification of the processes by the mathematical models not higher than that of the third order, equivalent as for the cutoff frequency. The algorithm of the method is based on the system of the equations, one part of which shall be synthesised with the consideration of the boundary conditions, set by the minimum frequency and cutoff frequency, and the other part shall be synthesised using the standard procedure of the least squares method with the use of Bode magnitude plots. The suggested method of synthesis and identification of the equivalent models had been transformed into the multidimensional continuous linear minimum phase dynamic objects, described by the differential equations with the derivatives in the right part.
For the closed minimum phase linear multidimensional dynamic objects, the mathematical models of the open loop of which do not have the derivatives in the right part of the differential mathematical model, there had been for the first time developed the method of synthesis and identification of processes by the mathematical models not higher than those of the third order, but equivalent as for the critical frequency. The suggested method of synthesis and identification of the equivalent models is transformed into the closed multidimensional continuous linear minimum phase dynamic objects, the open loops of which are described by the differential equations with the derivatives in the right part.
There had been suggested the method of synthesis and identification of the equivalent mathematical models of minimum phase dynamic systems of the high order with the algorithm, plunged into the frequency domain, in the class of non-minimum phase, that is, in the kind of differential models not higher than those of the second order with an argument, which is late by a certain time during the signal transmission from the input to the output of the system.
It had been proved that the optimal mathematical model of the stationary time series, which is the model of the process on the statistically distributed discrete dynamic object is the model of autoregression-moving average of the third order on the autoregressive component as well as on the component of the moving average. Entering information on the object’s spectrum critical frequency as well as direction and redirection of the moving average trend on the model were the conditions, chosen as the optimal criteria to prove this argument.
There had been generalised the synthesis method of mathematical models of nonlinear dynamic systems with nonlinear characteristics in the form of polynomials and the models of inertial part in the form of magnitude and phase responses, which is based on the algorithm of converting multiple Volterra integral equations, set in the time domain, into the single integral equations, for the solution of which there used the magnitude and phase responses of the inertial part of these systems, on the tasks of reduction of nonlinear dynamic systems with random order of their nonlinear characteristics and the second order of the transfer functions of their inertia components. On the example of nonlinear dynamic systems with the third order of nonlinear characteristics and the second order of the inertia part of these systems there had been specified the algorithm of parametric identification of their equivalent models.
Practical value of the results obtained is that, first of all, they complement to the theory of synthesis and identification of the mathematical models of dynamic systems with the conditions of using the equivalent mathematical models with the minimum allowed order instead of mathematical models of multidimensional dynamic objects, that is, objects of the high orders in the tasks of their analysis and optimisation, they also complement this theory with the methods for identification of the equivalent models, for which there had been created specific realisation algorithms and calculation correlations for the evaluation of the adequacy
