Dynamic Inversion Based Higher Order Model Reference Adaptive Control of Scalar Systems with Time Varying Parameters

Dynamic Inversion is a promising control scheme, especially for systems with large parametric variations and high nonlinearities. In aerospace control, it is usually used to control aircraft with large flight envelope and highly nonlinear aerodynamics. Traditionally, this was catered for by using Gain Scheduling, which is a time consuming process. One major disadvantage of Dynamic Inversion is that it requires precise knowledge of system dynamics and parameters. To overcome this, some adaptation scheme could be used to estimate the parameters and uncertainties online. Model Reference Adaptive Control (MRAC) is a widely used adaptive control method in such scenarios. Conventionally, MRAC operates under the assumption that the reference or desired dynamics mirror those of the system. Yet, Dynamic Inversion transcends this constraint, often necessitating desired dynamics of higher order than that of the system itself. In this paper, we derive MRAC control laws accommodating higher order desired dynamics, for scalar systems with constant parameters. Subsequently, we extend this framework to systems featuring time-varying parameters, leveraging the concept of congelation of variables. We then apply these proposed control laws to tackle a pertinent pitch control problem, followed by simulation results and discussion.