New On-line Algorithms for Modelling, Identification and Simulation of Dynamic Systems Using Modulating Functions and Non-asymptotic State Estimators: Case Study for a Chosen Physical Process

The paper presents an advanced application of computation methodology with complicated algorithms and calculation methods dedicated to optimal identification and simulation of dynamic processes. These models may have an unknown structure (the order of a differential equation) and unknown parameters. The presented methodology uses non-standard algorithms for identification of such continuous-time models that can represent linear and non-linear physical processes. Typical approaches, presented in the literature, most often utilize discrete-time models. However, for the case of continuous-time differential equation models, in which both, the parameters and the derivatives of the output variable are unknown, the solution is not easy. In the paper, for the solution of the identification task, the convolution transformation of the differential equation with a special Modulating Function will be used. Also, to be able to properly simulate the behaviour of the process based on the obtained model, the exact state integral observers with minimal norm will be used for the reconstruction of the exact value of the initial conditions (not their estimate). For multidimensional process case, with multiple control signals (many inputs), additional problems arise that make continuous identification and observation of the vector state (and hence simulation) impossible by the use of the standard methods. Application of the above-mentioned methods for solving this problem will be also presented. Both algorithms, for the parameter identification and the state observation, will be implemented on-line in two independent but cooperating windows that will simultaneously move along the time axis. The presented algorithms will be tested using data collected during the heat exchange process in an industrial glass melting installation.