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

An Adaptive Observer-based Robust Estimator of Multi-sinusoidal Signals

This paper presents an adaptive observer-based robust estimation methodology of the amplitudes, frequencies and phases of biased multi-sinusoidal signals in presence of bounded perturbations on the measurement. The parameters of the sinusoidal components are estimated on-line and the update laws are individually controlled by an excitation-based switching logic enabling the update of a parameter only when the measured signal is sufficiently informative. This way doing, the algorithm is able to tackle the problem of over-parametrization (i.e., when the internal model accounts for a number of sinusoids that is larger than the true spectral content) or temporarily fading sinusoidal components. The stability analysis proves the existence of a tuning parameter set for which the estimator\u2019s dynamics are input-to-state stable with respect to bounded measurement disturbances. The performance of the proposed estimation approach is evaluated and compared with other existing tools by extensive simulation trials and real-time experiments

Dorsal and pectoral fin control of a biorobotic autonomous underwater vehicle

This thesis involves an in-depth research on the maneuvering of bio-robotic autonomous undersea vehicles (BAUVs) using bio-mimetic swimming mechanisms. Motivation was derived from the amazing flexibility and agility the fish inherit with the help of their pectoral and dorsal fins; In the first part of the thesis, control of BAUVs using dorsal fins is considered. The force produced by the cambering of the dorsal fins is used for control. An indirect adaptive controller is designed for depth tracking along constant trajectories even when the system parameters are not known. Next, for following time-varying trajectories, an adaptive control system for yaw plane control of BAUVs is developed. It is capable of working efficiently even when large uncertainties in the system parameters are present and system nonlinearities are dominant; In the second part of the thesis, pectoral fin control of BAUVs is considered. The flapping of these oscillating fins provides the necessary force and moment for control. A discrete-time optimal controller for set point (constant path) control and inverse controller for tracking time varying trajectories in the yaw plane are derived. Further, an indirect adaptive control system that can accomplish depth trajectory tracking even when the model paramters are completely unknown is developed; The performance evaluation of the controllers is done by simulation using matlab/simulink

DISCRETE-TIME ADAPTIVE CONTROL ALGORITHMS FOR REJECTION OF SINUSOIDAL DISTURBANCES

We present new adaptive control algorithms that address the problem of rejecting sinusoids with known frequencies that act on an unknown asymptotically stable linear time-invariant system. To achieve asymptotic disturbance rejection, adaptive control algorithms of this dissertation rely on limited or no system model information. These algorithms are developed in discrete time, meaning that the control computations use sampled-data measurements. We demonstrate the effectiveness of algorithms via analysis, numerical simulations, and experimental testings. We also present extensions to these algorithms that address systems with decentralized control architecture and systems subject to disturbances with unknown frequencies

Globally stable tracking and estimation for single-phase electrical signals with DC-offset rejection

This work introduces a new algorithm, named Global Quadrature PLL (GQPLL) for tracking a sinusoidal signal and for estimating its frequency and amplitude. The proposed technique derives from the well-known PLL architecture based on Quadrature Signal Generation, that is widely used for tracking the fundamental of single-phase electrical signals. The proposed algorithm improves the existing quadrature-PLL solutions from two different perspectives. First, the cancellation of the DC-bias is embedded by construction. Moreover, a Lyapunov-based stability analysis guarantees the global convergence of the estimates for arbitrarily large adaptation gains, enabling fast adaptation transients. Simulations show that the proposed algorithm is able to deal with sudden variations of the fundamental frequency and of the DC-bias magnitude

The reduced order model problem in distributed parameter systems adaptive identification and control

The research concerning the reduced order model problem in distributed parameter systems is reported. The adaptive control strategy was chosen for investigation in the annular momentum control device. It is noted, that if there is no observation spill over, and no model errors, an indirect adaptive control strategy can be globally stable. Recent publications concerning adaptive control are included

Low-cost, high-resolution, fault-robust position and speed estimation for PMSM drives operating in safety-critical systems

In this paper it is shown how to obtain a low-cost, high-resolution and fault-robust position sensing system for permanent magnet synchronous motor drives operating in safety-critical systems, by combining high-frequency signal injection with binary Hall-effect sensors. It is shown that the position error signal obtained via high-frequency signal injection can be merged easily into the quantization-harmonic-decoupling vector tracking observer used to process the Hall-effect sensor signals. The resulting algorithm provides accurate, high-resolution estimates of speed and position throughout the entire speed range; compared to state-of-the-art drives using Hall-effect sensors alone, the low speed performance is greatly improved in healthy conditions and also following position sensor faults. It is envisaged that such a sensing system can be successfully used in applications requiring IEC 61508 SIL 3 or ISO 26262 ASIL D compliance, due to its extremely high mean time to failure and to the very fast recovery of the drive following Hall-effect sensor faults at low speeds. Extensive simulation and experimental results are provided on a 3.7 kW permanent magnet drive