Estimation Time Improvement of Heat Conduction Systems Using Balanced Truncation Method

Abstract

The model reduction process uses a balanced cut, obtains a reduced system that has fewer states than the initial system. This makes it difficult to compare the state of the reduced system with the initial system. Therefore, identification is needed to find the suitability of the state variables. In this paper, we discuss the process of identifying and estimating state variables in the reduced discrete-time linear system and implement these problems on heat conduction model. Model reduction using balanced truncation method is applied to discrete-time linear system of order s which is stable, controllable and observable in order to obtain the reduced system with order n that has a same characteristic. On the other hand, identification of the state variables from the reduced system is intended to simplify the comparison of the estimation result between the reduced system and the initial system. In this case, the Kalman filter algorithm is required for the estimation process. Furthemore as a case study, those problems are applied on heat conduction model. Model reduction using balanced truncation method is only applicable on heat conduction model which is stable, controllable and observable. Kalman filter algorithm can be implemented on the reduced system of heat conduction model, similarly identification of the state variables can be applied on the result of reduced system estimation. Based on the error values, the best estimation result is the estimation process of the initial system which obtained the smallest error, with a relative precentage change of at least 73, 2 %. In other case, based on the computational time, reduced system estimation is faster than the estimation process of the initial system.