Determination of Stable Time-delay Regions in Incremental Control Systems
I.Z. El-Hajj (TU Delft - Aerospace Engineering)
Qi Ping Chu – Mentor (TU Delft - Control & Simulation)
Erik Jan van Kampen – Mentor (TU Delft - Control & Simulation)
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Abstract
Incremental control techniques such as Incremental Nonlinear Dynamic Inversion (INDI) and Incremental Backstepping (IBS) have gained recent popularity, especially in the aerospace community, due to their versatility and effectiveness which entails robustness to imprecise knowledge about the controlled system as well as robustness to external disturbances. Despite a control authority that has been proven, in several applications, to exceed that of classical control techniques, there is yet much to be studied about these control techniques. Theoretical gaps include the effectiveness of these techniques in handling time-delays as well as their robustness to sampling rates. Addressing this theoretical gap has been the focus of the research that is presented in this thesis. To meet this research aim, the control system has been analyzed through the lens of the Time-Delay System (TDS) framework. In particular, the analytic curve frequency sweeping approach as well as a set of suitable matrix inequalities that are based on the discretized Lyapunov functional method have been applied to perform this analysis in the frequency domain and
the time domain, respectively. Moreover, the time-domain results have been extended to the case of neutral time-delay systems, the derivation of which is also presented in this thesis. Furthermore, a new robust stability analysis technique is presented which is based on combining the analytic curve frequency sweeping approach with the edge theorem. This approach is made applicable to systems with different uncertainty structures through determining generator quasipolynomials that form a convex hull that overbounds the family of quasipolynomials considered. The effectiveness of these methods has been shown through their application to an INDI-controlled damped pendulum and to the INDI-controlled short period dynamics of a fixed-wing aircraft, and it is shown that the results from the frequency-domain analyses and the time-domain analyses corroborate.