Time-delay margin computation of Model Reference Adaptive Control using the Razumikhin theorem

Heise, Christian D.; Holzapfel, Florian

doi:10.1109/cdc.2014.7039435

Cited by 4 publications

(1 citation statement)

References 18 publications

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“…Pade approximation [185] and Razumikhin Method [186,187] has been used to approximate the TDM. For the case of the Pade approximation, the lower bounds of the final result it deemed to be too conservative.…”

Section: Time Delay Marginmentioning

confidence: 99%

L1 adaptive control augmentation for a hypersonic glider

Banerjee¹

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ii ABSTRACTThe aim of this research is to investigate control strategies to carry out a pull out of a ballistic trajectory (initially the same as the sub-orbital ballistic HyShot and HIFiRE trajectories) and a pulsed roll angle bank manoeuvre for a hypersonic glider. This study investigates the performance of two different control methodologies in the presence of aerodynamic, gravimetric and actuator uncertainties: pole placement control (PPC) (as the baseline) and adaptive control (to augment the PPC).Through simulations, it is shown that the PPC carries out the pull up manoeuvre (by tracking the flight path angle, ) on a scaled Generic Hypersonic Aerodynamics Model Example (GHAME model). Once the pull-up manoeuvre is carried out the lateral/directional PPCs perform satisfactorily in tracking the commanded roll angle, and maintaining a sideslip angle, , of zero degrees. The PPCs presented are all SingleInput Single Output (SISO) controllers. Pole-zero plots are utilised to highlight the stability properties of the PPC. All the controllers are stable. The differences in the performance and robustness for the various uncertainty cases are highlighted through the tracking error norm and the time delay margin (TDM). The performance of the PPC significantly worsens in the presence of uncertainties. This deterioration is quantified using tracking error norms, error dynamics acceleration and a control surface metric.adaptive control is employed as a control strategy to augment the PPC as it allows the decoupling of the control and the estimation loop. The control augmentation design is employed for both the longitudinal and the lateral/directional channels in the presence of matched and unmatched uncertainties. A piecewise constant adaptive law (to estimate the uncertainties) is adopted for all the channels. An additional challenge present in this research is that the flight path angle dynamics of the system display non-minimum phase behaviour. The control theory requires the inversion of the system dynamics, which renders the control law, which cancels the unmatched uncertainties, unstable. An inverse ABSTRACT iii DC gain method is presented and tested. Using this modification, the inversion of the system dynamics is avoided. The main step forward that has been taken in this thesis is the extension of the application of theory and its application to a non-minimum phase state feedback Linear Time Varying (LTV) systems. This modified law prevents a reformulation of the control problem, for example computing an alternative representation of the state estimator in the augmented controller in order to have all the uncertainties come in through the matched channel of the system or having a virtual inertial measurement unit (IMU) in order to make the measured values minimum phase. The augmented controller is able to cancel the uncertainties and is able to restore the performance of the controller and bring the system closer to the desired system performance. The improvement provided by the augmented controller is d...

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Section: Time Delay Marginmentioning

confidence: 99%