Helicopter nonlinear control using adaptive feedback linearization

This thesis considers the problem of designing large envelope flight controllers for helicopters, in particular, accounting for the fact that it is virtually impossible to obtain an explicit analytical model for the equations of motion valid for the entire flight regime. The technique involves superimposing two control techniques in order to meet stability and performance objectives. The primary control is based on the inversion of an approximate model of the helicopter. The techniques of pseudoinverse-based full model inversion control, input-output linearization, and two time scale, singular perturbation control are compared for the purpose of inverting the nonsquare dynamics of the helicopter. The results indicate that the two time scale controller is most compatible with the natural behavior of the helicopter. In fact the two time scale controller, when synthesized based on linear aerodynamics from the hover flight condition, provides a stable response for essentially the entire flight envelope when applied to a comprehensive simulation model of the helicopter. The secondary control is an online neural network which adaptively corrects for the inversion error resulting from the approximate model inversion. It is shown that when the network structure is representative of the structure of the inversion error, then the closed loop performance is relatively insensitive to changes in the network parameters. This fact alleviates one of the classical problems in adaptive control which involves choosing an appropriate adaptation rate. It is shown that a relatively simple neural network can be augmented to an approximate model to provide good performance and tracking for the entire flight regime. The scope of the research and contributions include: (1) Development of a fixed structure, nonlinear, approximate model which is valid for a large flight regime without the use of table lookups; (2) Identification of the relationship between the zeros of the linear approximation of the system and the closed loop stability of the non-linear system, in particular, the relationship between the zeros of the linear approximation and the zero dynamics of the nonlinear system; (3) Analysis of the inversion error in order to determine the appropriate structure for an online neural network to account for model variations and disturbances throughout the flight envelope, (4) Investigation of the effect of varying the parameters of the network, and in particular, identification of the relationship between network structure and sensitivity of closed loop performance to parameter variations; (5) Evaluation of the robustness of the network by implementing the controller into a comprehensive simulation which contains significant unmodeled dynamics and uncertainty in the aerodynamic model.