Fault tolerant control of a quadrotor using L-1 adaptive control

Purpose – The growing use of small unmanned rotorcraft in civilian applications means that safe operation is increasingly important. The purpose of this paper is to investigate the fault tolerant properties to faults in the actuators of an L1 adaptive controller for a quadrotor vehicle. Design/methodology/approach – L1 adaptive control provides fast adaptation along with decoupling between adaptation and robustness. This makes the approach a suitable candidate for fault tolerant control of quadrotor and other multirotor vehicles. In the paper, the design of an L1 adaptive controller is presented. The controller is compared to a fixed-gain LQR controller. Findings – The L1 adaptive controller is shown to have improved performance when subject to actuator faults, and a higher range of actuator fault tolerance. Research limitations/implications – The control scheme is tested in simulation of a simple model that ignores aerodynamic and gyroscopic effects. Hence for further work, testing with a more complete model is recommended followed by implementation on an actual platform and flight test. The effect of sensor noise should also be considered along with investigation into the influence of wind disturbances and tolerance to sensor failures. Furthermore, quadrotors cannot tolerate total failure of a rotor without loss of control of one of the degrees of freedom, this aspect requires further investigation. Practical implications – Applying the L1 adaptive controller to a hexrotor or octorotor would increase the reliability of such vehicles without recourse to methods that require fault detection schemes and control reallocation as well as providing tolerance to a total loss of a rotor. Social implications – In order for quadrotors and other similar unmanned air vehicles to undertake many proposed roles, a high level of safety is required. Hence the controllers should be fault tolerant. Originality/value – Fault tolerance to partial actuator/effector faults is demonstrated using an L1 adaptive controller

Relaxing Fundamental Assumptions in Iterative Learning Control

Iterative learning control (ILC) is perhaps best decribed as an open loop feedforward control technique where the feedforward signal is learned through repetition of a single task. As the name suggests, given a dynamic system operating on a finite time horizon with the same desired trajectory, ILC aims to iteratively construct the inverse image (or its approximation) of the desired trajectory to improve transient tracking. In the literature, ILC is often interpreted as feedback control in the iteration domain due to the fact that learning controllers use information from past trials to drive the tracking error towards zero. However, despite the significant body of literature and powerful features, ILC is yet to reach widespread adoption by the control community, due to several assumptions that restrict its generality when compared to feedback control. In this dissertation, we relax some of these assumptions, mainly the fundamental invariance assumption, and move from the idea of learning through repetition to two dimensional systems, specifically repetitive processes, that appear in the modeling of engineering applications such as additive manufacturing, and sketch out future research directions for increased practicality: We develop an L1 adaptive feedback control based ILC architecture for increased robustness, fast convergence, and high performance under time varying uncertainties and disturbances. Simulation studies of the behavior of this combined L1-ILC scheme under iteration varying uncertainties lead us to the robust stability analysis of iteration varying systems, where we show that these systems are guaranteed to be stable when the ILC update laws are designed to be robust, which can be done using existing methods from the literature. As a next step to the signal space approach adopted in the analysis of iteration varying systems, we shift the focus of our work to repetitive processes, and show that the exponential stability of a nonlinear repetitive system is equivalent to that of its linearization, and consequently uniform stability of the corresponding state space matrix.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133232/1/altin_1.pd

Nonlinear adaptive estimation with application to sinusoidal identification

Parameter estimation of a sinusoidal signal in real-time is encountered in applications in numerous areas of engineering. Parameters of interest are usually amplitude, frequency and phase wherein frequency tracking is the fundamental task in sinusoidal estimation. This thesis deals with the problem of identifying a signal that comprises n (n ≥ 1) harmonics from a measurement possibly affected by structured and unstructured disturbances. The structured perturbations are modeled as a time-polynomial so as to represent, for example, bias and drift phenomena typically present in applications, whereas the unstructured disturbances are characterized as bounded perturbation. Several approaches upon different theoretical tools are presented in this thesis, and classified into two main categories: asymptotic and non-asymptotic methodologies, depending on the qualitative characteristics of the convergence behavior over time. The first part of the thesis is devoted to the asymptotic estimators, which typically consist in a pre-filtering module for generating a number of auxiliary signals, independent of the structured perturbations. These auxiliary signals can be used either directly or indirectly to estimate—in an adaptive way—the frequency, the amplitude and the phase of the sinusoidal signals. More specifically, the direct approach is based on a simple gradient method, which ensures Input-to-State Stability of the estimation error with respect to the bounded-unstructured disturbances. The indirect method exploits a specific adaptive observer scheme equipped with a switching criterion allowing to properly address in a stable way the poor excitation scenarios. It is shown that the adaptive observer method can be applied for estimating multi-frequencies through an augmented but unified framework, which is a crucial advantage with respect to direct approaches. The estimators’ stability properties are also analyzed by Input-to-State-Stability (ISS) arguments. In the second part we present a non-asymptotic estimation methodology characterized by a distinctive feature that permits finite-time convergence of the estimates. Resorting to the Volterra integral operators with suitably designed kernels, the measured signal is processed, yielding a set of auxiliary signals, in which the influence of the unknown initial conditions is annihilated. A sliding mode-based adaptation law, fed by the aforementioned auxiliary signals, is proposed for deadbeat estimation of the frequency and amplitude, which are dealt with in a step-by-step manner. The worst case behavior of the proposed algorithm in the presence of bounded perturbation is studied by ISS tools. The practical characteristics of all estimation techniques are evaluated and compared with other existing techniques by extensive simulations and experimental trials.Open Acces

Generation of new exciting regressors for consistent on-line estimation of unknown constant parameters

The problem of estimating constant parameters from a standard vector linear regression equation in the absence of sufficient excitation in the regressor is addressed. The first step to solve the problem consists in transforming this equation into a set of scalar ones using the well-known dynamic regressor extension and mixing technique. Then a novel procedure to generate new scalar exciting regressors is proposed. The superior performance of a classical gradient estimator using this new regressor, instead of the original one, is illustrated with comprehensive simulations

Feedback Control Methods on Short-Period Orbits Of the Earth-Moon Equilateral Libration Points

Recent research by the authors suggests a unique approach to perform Lunar occultations for a diverse set of scientific applications. Under the circular restricted three-body problem assumptions, short-period orbits (SPOs) near the Earth-Moon equilateral Libration points have been suggested for optimal eclipse time and minimal fuel consumption requirements to stay in orbit. Nevertheless, under the presence of orbital perturbations, SPOs are no longer stable as gravitational effects from neighboring celestial bodies continuously perturb these orbits. In this sense, the current study compares a wide range of control methods, including Lyapunov-based adaptive control schemes and fuel-optimal control policies, to address the fuel consumption and tracking issues of the perturbed system. This inquiry attests that perturbations are effectively cancelled out to achieve the proposed scientific objectives with minimal station-keeping requirements

Fault reconstruction using a LPV sliding mode observer for a class of LPV systems

Journal ArticleCopyright © 2012 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Journal of The Franklin Institute. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of The Franklin Institute (2012), DOI: 10.1016/j.jfranklin.2011.06.026This paper proposes a new sliding mode observer for fault reconstruction, applicable for a class of linear parameter varying (LPV) systems. Observer schemes for actuator and sensor fault reconstruction are presented. For the actuator fault reconstruction scheme, a virtual system comprising the system matrix and a fixed input distribution matrix is used for the design of the observer. The fixed input distribution matrix is instrumental in simplifying the synthesis procedure to create the observer gains to ensure a stable closed-loop reduced order sliding motion. The 'output error injection signals' from the observer are used as the basis for reconstructing the fault signals. For the sensor fault observer design, augmenting the LPV system with a filtered version of the faulty measurements allows the sensor fault reconstruction problem to be posed as an actuator fault reconstruction scenario. Simulation tests based on a high-fidelity nonlinear model of a transport aircraft have been used to demonstrate the proposed actuator and sensor FDI schemes. The simulation results show their efficacy. © 2011 The Franklin Institute. Published by Elsevier Ltd. All rights reserved