Application of Model Reference Adaptive System in Natural Frequency Identification of an Active Beam Composite Structure

In many real-time systems we need to know the exact values of system parameters. Parameters identification for linear and stable systems can be done by taking special measurements. Problems can occur if the tested system is nonlinear and its parameters change due to certain variations or they depend on time. In such cases special procedures have to be applied. These procedures should operate quickly, and their computational time delay cannot affect on the entire control process. In this paper, determination of the frequency of cantilever beam with embedded piezoelectric actuator is studied. A short overview of Model Based Methods is described. A nonlinear equation of motion of the beam is rewritten as an equation with step wise changes of its natural frequency. Proposed mathematical identification methods use some input and output variables for identifying lack of information about certain parameters in a mathematical model. We take into account Decoupling Observers and Model Reference Adaptive System (MRAS). Due to the structure of the mathematical description, MRAS system found out to be more adequate option. Algorithms based on Model Identification Techniques (MIT), as well as an algorithm satisfying Lyapunov stability condition, were tested. The latter was robust on certain residual effects. Therefore, we chose it for the final test. Obtained results confirmed this choice. Presented figures show characteristics of natural frequency that have been identified. Therefore, the implemented adjusting algorithm satisfying Lyapunov stability found out to be suitable for an application in DSP. However, reducing the processing time is still a problem for future studies.