System identification algorithm for negative imaginary systems

In this paper, we present a modified subspace system identification algorithm that ensures the negative imaginary property in the identified model. This is achieved by imposing constraints that guarantee negative imaginariness and stability of the identified model. The importance of having negative imaginary model comes from the fact that the negative imaginary property occurs in many important applications. For instance, flexible structure systems with collocated force actuators and position sensors are negative imaginary systems. Obtaining a mathematical model for this class of systems using system identification methods often results in inaccurate models that poorly reflect the negative imaginary property. This paper aims to overcome this problem. As an application of these results, an example of modelling a flexible system with a piezoelectric actuator and position sensor is presented.