Once the aerodynamic coefﬁcients have been obtained for the ﬂexible aircraft using the ‘eta’ values (i.e. the S&C aerodata database is in hand) along with the mass and inertia properties, the S&C analysis can begin with SDSA.
SDSA covers the following functionalities:
- Stability analysis:
- eigenvalues analysis of linearised model in open and closed loop case
- time history identification (nonlinear model)
- Six Degree of Freedom ﬂight simulation:
- test flights, including trim response
- Flight Control System based on Linear Quadratic Regulator (LQR) theory, including
- Human Pilot model
- Stability Augmentation System
- Actuator model o LQR based FCS
- Performance prediction
- Miscellaneous (data review, results review, cross plots, etc.)
This figure illustrates the structure and functionality of this module:
SDSA uses the same Six DoF mathematical nonlinear model of the aircraft motion for all functions. For the eigenvalue analysis, the model is linearized by computing the Jacobian matrix of the state derivatives around the equilibrium (trim) point numerically. The ﬂight simulation module can be used to perform test ﬂights and record ﬂight parameters in real-time. The recorded data can be used for identiﬁcation of the typical modes of motions and their parameters (period, damping coefﬁcient, phase shift). The stability analysis results are presented as “ﬁgures of merits” based on JAR/FAR, ICAO, and MIL regulations. The SDSA embedded ﬂight control system is based on a LQR approach.
The FCS module allows computing control matrices for the whole envelope, saving them for future use during simulation or stability analysis. Therefore, it allows for the computation of stability characteristics for the “closed loop” case and ﬂight simulation with FCS. The performance option is designed to compute basic performance parameters: ﬂight envelope (Vmin and Vmax versus altitude of ﬂight), selected manoeuvres (e.g. regular turn), range and endurance characteristics.
For all mentioned functionalities the starting point is the computation of the trimmed state with sufﬁcient initial conditions. The SDSA interacts with the user through a system of GUIs, for initial conditions, weather conditions, including gusts (wind shear) and turbulence, etc. The test ﬂight settings include initial state, disturbances, and single / double step controls.
SDSA is a standalone application integrated into CEASIOM. As a module of CEASIOM, it receives all the necessary data (aerodynamics, mass, inertia, available thrust), when available, without special prompting.
Example of an eigenvalues analysis: