Identification of Physical Helicopter Models Using Subspace Identification

Abstract

Subspace identification is a powerful tool due to its well-understood techniques based on linear algebra (orthogonal projections and intersections of subspaces) and numerical methods like singular value decomposition. However, the state space model matrices, which are obtained from conventional subspace identification algorithms, are not necessarily associated with the physical states. This can be an important deficiency when physical parameter estimation is essential. This holds for the area of helicopter flight dynamics, where physical parameter estimation is mainly conducted for mathematical model improvement, aerodynamic parameter validation, and flight controller tuning. The main objective of this study is to obtain helicopter physical parameters from subspace identification results. To achieve this objective, the subspace identification algorithm is implemented for a multirole combat helicopter using both FLIGHTLAB simulation and real flight-test data. After obtaining state space matrices via subspace identification, constrained nonlinear optimization methodologies are utilized for extracting the physical parameters. The state space matrices are transformed into equivalent physical forms via the "sequential quadratic programming" nonlinear optimization algorithm. The required objective function is generated by summing the square of similarity transformation equations. The constraints are selected with physical insight. Many runs are conducted for randomly selected initial conditions. It can be concluded that all of the significant parameters can be obtained with a high level of accuracy for the data obtained from the linear model. This strongly supports the idea behind this study. Results for the data obtained from the nonlinear model are also evaluated to be satisfactory in the light of statistical error analysis. Results for the real flight-test data are also evaluated to be good for the helicopter modes that are properly excited in the flight tests.