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Generalized parameter estimation-based observers have proven very successful to deal with systems described in state-affine form. In this paper, we enlarge the domain of applicability of this method proposing an algebraic procedure to immerse} an $n$-dimensional general nonlinear system into and $n_z$-dimensional system in state affine form, with $n_z>n$. First, we recall the necessary and sufficient condition for the solution of the general problem, which requires the solution of a partial differential equation that, moreover, has to satisfy a restrictive injectivity condition. Given the complexity of this task we propose an alternative simple algebraic method to identify the required dynamic extension and coordinate transformation, a procedure that, as shown in the paper, is rather natural for physical systems. We illustrate the method with some academic benchmark examples from observer theory literature -- that, in spite of their apparent simplicity, are difficult to solve with the existing methods -- as well as several practically relevant physical examples.

In this paper we study the question of how to reconstruct the state of a power system using Phasor Measurement Units (PMUs). In our previous research we proved that this question has an affirmative answer imposing some rather strict structural assumptions: namely, neglecting the generator rotors saliency and assuming that the stator resistance of the synchronous generator is zero. It was shown in simulations that the performance of the proposed observer was sensitive to these assumptions, observing a transient quality degradation for realistic simulations not imposing these assumptions. Moreover, it was assumed in our previous work that the mechanical power and the field voltage are available for measurement, a scenario that it is not always realistic. In this paper we accomplish two ambitious objectives. First, we propose a new observer that does not impose the simplifying assumptions on the generator model. Secondly, we consider the more realistic scenario where only mechanical power is available for measurement. That is, we solve a problem of state reconstruction of a nonlinear system with partially known input measurements -- that is well-known to be a very challenging task. The design of the first observer relies on two recent developments proposed by the authors, a parameter estimation based approach to the problem of state estimation and the use of the Dynamic Regressor Extension and Mixing (DREM) technique to estimate these parameters. The use of DREM allows us to overcome the problem of lack of persistent excitation that stymies the application of standard parameter estimation designs. On the other hand, the observer for the partial input measurement scenario relies on the clever exploitation of the systems model. Simulation results illustrates the good performance of the proposed observers.

The paper considers the observer synthesis for nonlinear, time-varying plants with uncertain parameters under multiharmonic disturbance. It is assumed that the relative degree of the plant is known, the regressor linearly depends on the state vector and may have a nonlinear relationship with the output signal. The proposed solution consists of three steps. Initially, an unknown input state observer is synthesized. This observer, however, necessitates the measurement of output derivatives equal to the plant's relative degree. To relax this limitation, an alternative representation of the observer is introduced. Further, based on this observer, the unknown parameters and disturbances are reconstructed using an autoregression model and the dynamic regressor extension and mixing (DREM) approach. This approach allows the estimates to be obtained in a finite time. Finally, based on these estimates, an observer has been constructed that does not require measurements of the output derivatives. The effectiveness and efficiency of this solution are demonstrated through a computer simulation.

In this paper, we apply the recently developed generalized parameter estimation-based observer design technique for state-affine systems to the practically important case of linear time-varying descriptor systems with uncertain parameters. We give simulation results of benchmark examples that illustrate the performance of the proposed adaptive observer.

In this paper an adaptive state observer and parameter identification algorithm for a linear time-varying system are developed under condition that the state matrix of the system contains unknown time-varying parameters of a known form. The state vector is observed using only output and input measurements without identification of the unknown parameters. When the state vector estimate is obtained, the identification algorithm is applied to find unknown parameters of the system., Comment: 6 pages, 6 figures, submitted to IEEE Control Systems Letters

In this paper, we address the problem of online parameter estimation of a Proton Exchange Membrane Fuel Cell (PEMFC) polarization curve, that is the static relation between the voltage and the current of the PEMFC. The task of designing this estimator -- even off-line -- is complicated by the fact that the uncertain parameters enter the curve in a highly nonlinear fashion, namely in the form of nonseparable nonlinearities. We consider several scenarios for the model of the polarization curve, starting from the standard full model and including several popular simplifications to this complicated mathematical function. In all cases, we derive separable regression equations -- either linearly or nonlinearly parameterized -- which are instrumental for the implementation of the parameter estimators. We concentrate our attention on on-line estimation schemes for which, under suitable excitation conditions, global parameter convergence is ensured. Due to these global convergence properties, the estimators are robust to unavoidable additive noise and structural uncertainty. Moreover, their on-line nature endows the schemes with the ability to track (slow) parameter variations, that occur during the operation of the PEMFC. These two features -- unavailable in time-consuming off-line data-fitting procedures -- make the proposed estimators helpful for on-line time-saving characterization of a given PEMFC, and the implementation of fault-detection procedures and model-based adaptive control strategies. Simulation and experimental results that validate the theoretical claims are presented., Comment: 16 pages, 18 figures, requires IEEEtran.cls 2015/08/26 version V1.8b

The article investigates an algorithm for identifying an unknown constant parameter for a scalar regression model using a nonlinear operator that allows us to obtain a new regression equation (with an expanded number of unknown parameters) for which the influence of interference in measurement or disturbance will be minimal., Comment: in Russian language

The paper proposes an adaptive observer of the state vector of a nonlinear time varying system based on measurements of the output variable. The problem is solved under the assumption that the control matrix (vector) and the nonlinear component of the equation of state of the system contain unknown constant parameters. When developing an adaptive observer, the GPEBO (generalized parameter estimation based observer) method was used, also known as a generalized observer based on parameter estimation, which was proposed in [1]. During the synthesis of the observer, a preliminary parametrization of the original nonlinear system is carried out. Then the resulting system is reduced to a linear regression model. At the next stage, unknown constant regression parameters are estimated using the least squares method with the forgetting factor [2, 3]. The article suggests the development of the result proposed by the authors in [4]. In [4], a linear non-stationary system containing unknown parameters in a control matrix (vector) was considered. This result is an extension of the result obtained in [4] for the case when the equation of state of the system contains a partially unknown nonlinearity., Comment: in Russian language

The article is devoted to the problem of synthesis of observers of state variables for linear stationary objects operating under conditions of noise or disturbances in the measurement channel. The paper considers a fully observable linear stationary system with known parameters. It is assumed that the state variables are not measured, and the measured output variable contains a small amplitude (in general, modulo less than one) additive noise or disturbance. It is also assumed that there is no a priori information about the disturbance or noise in the measurement channel (for example, frequency spectrum, covariance, etc.). It is well known that a large number of methods of observer synthesis have been obtained for this type of objects, including the Kalman filter, which has proven itself in practice. Under the condition of complete observability and the presence of some a priori information about the process (which is typical for the case when a disturbance in the measurement channel can be represented as white noise), approaches based on Kalman filtering demonstrate the highest quality of convergence of estimates of state variables to true values. Without taking into account the numerous results obtained using the application of the Kalman filter, an alternative idea of constructing an observer of state variables is considered in this paper. The alternative of the new approach is primarily due to the fact that there is no need to use the usual approaches based on the Luenberger observer. The paper proposes an approach based on the evaluation of unknown parameters (in this case, an unknown vector of initial conditions of the variables of the object state) of a linear regression model., Comment: in Russian language

In this paper we provide the first solution to the challenging problem of designing a globally exponentially convergent estimator for the parameters of the standard model of a continuous stirred tank reactor. Because of the presence of non-separable exponential nonlinearities in the system dynamics that appear in Arrhenius law, none of the existing parameter estimators is able to deal with them in an efficient way and, in spite of many attempts, the problem was open for many years. To establish our result we propose a novel procedure to obtain a suitable nonlinearly parameterized regression equation and introduce a radically new estimation algorithm - derived applying the Immersion and Invariance methodology - that is applicable to these regression equations. A further contribution of the paper is that parameter convergence is guaranteed with weak excitation requirements.

Problem of an adaptive state observer design for nonlinear system with unknown time-varying parameters and under condition of delayed measurements is considered. State observation problem was raised by many researchers (see for example Sanx et al. (2019)). In this paper the results proposed in Bobtsov et al. (2021b), Bobtsov et al. (2021a), Bobtsov et al. (2022a), Bobtsov et al. (2022b) are developed. The problem is solved under assumption that the state matrix can be represented as sum of known and unknown parts. The output vector is measured with a known constant delay. An adaptive observer which reconstructs unknown state and unknown time-varying parameter is proposed., Comment: Submitted to IFAC World Congress 2023

In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical applications, and none of the existing parameter estimators is able to deal with them in an efficient way. The proposed estimation procedure is illustrated with two modern applications: fuel cells and human musculoskeletal dynamics. The procedure does not assume that the parameters live in known compact sets, that the nonlinearities satisfy some Lipschitzian properties, nor rely on injection of high-gain or the use of complex, computationally demanding methodologies. Instead, we propose to design a classical on-line estimator whose dynamics is described by an ordinary differential equation given in a compact precise form. A further contribution of the paper is the proof that parameter convergence is guaranteed with the extremely weak interval excitation requirement.

This paper deals with the problem of on-line identification of the parameters of a realistic dynamical model of a photovoltaic array connected to a power system through a power converter. It has been shown in the literature that, when interacting with switching devices, this model is able to better account for the PV array operation, as compared to the classical five parameter static model of the array. While there are many results of identification of the parameters of the latter model, to the best of our knowledge, no one has provided a solution for the aforementioned more complex dynamic model since it concerns the parameter estimation of a nonlinear, underexcited system with unmeasurable state variables. Achieving such objective is the main contribution of the paper. We propose a new parameterisation of the dynamic model, which, combined with the powerful identification technique of dynamic regressor extension and mixing, ensures a fast and accurate online estimation of the unknown parameters. Realistic numerical examples via computer simulations are presented to assess the performance of the proposed approach -- even being able to track the parameter variations when the system changes operating point.

Problem of adaptive state observer synthesis for linear time-varying (LTV) system with unknown time-varying parameter and delayed output measurements is considered. State observation problem has attracted the attention of many researchers $[4]$. In this paper the results proposed in the $[2]$, $[9]$, $[10]$ are developed. It is supposed that the state matrix can be represented as sum of known and unknown parts. Output vector is measured with known constant delay. An adaptive identification algorithm which reconstructs unknown state and unknown time varying parameter is proposed., Comment: 6 pages, 10 figures

The article deals with the problem of synthesis of an adaptive observer of state variables of a linear time-varying SISO dynamic system. It is assumed that the control signal and the output variable are measurable. It is assumed that the state matrix of the plant contains known variables and unknown constant parameters, and the control matrix (vector) is unknown. The synthesis of the observer is based on the GPEBO method (generalized parameter based observer) proposed in $[1]$. Synthesis of adaptive provides for preliminary parametrization of the initial system and its transformation to a linear regression model with further identification of unknown parameters. To identify unknown constant parameters a classical estimation algorithm was used (the least squares method with a forgetting factor). This approach has proven itself well in cases where the known regressor is frequency poor (that is, the spectral composition of the regressor contains less than $r/2$ harmonics, where r is the number of unknown parameters) or does not satisfy the so-called undamped excitation condition. To illustrate the efficiency of the proposed method an example is presented in the article. A time-varying second-order object with four unknown parameters was considered. Parameterization of the initial dynamic model was performed and a linear static regression containing six unknowns parameters was obtained (including the vector of unknown initial conditions of system state variables). An adaptive observer was synthesized and the results of computer modeling illustrating the achievement of a given goal were presented. The main difference from the results published earlier in $[2]$ is the new assumption that the linear a time-varing system contains not only unknown parameters in the state matrix, but also the matrix (vector) for control contains unknown constant coefficients., Comment: 16 pages, in Russian language, 9 figures

We consider a Th\'evenin equivalent circuit capturing the dynamics of a power grid as seen from the point of common coupling with a power electronic converter, and provide a solution to the problem of online identification of the corresponding circuit parameters. For this purpose, we first derive a linear regression model in the conventional abc coordinates and next design a bounded observer-based composite identifier that requires local measurements and knowledge of the grid frequency only. An extension that guarantees exponential convergence of the estimates, under the additional assumption of knowledge of the grid X/R ratio, is further provided. The performance of the proposed identifier, which subsumes a conventional gradient descent algorithm, is illustrated via detailed computer simulations.

In this paper we are interested in the problem of adaptive synchronization of a voltage source converter with a possibly weak grid with unknown angle and frequency, but knowledge of its parameters. To guarantee a suitable synchronization with the angle of the three-phase grid voltage we design an adaptive observer for such a signal requiring measurements only at the point of common coupling. Then we propose two alternative certainty-equivalent, adaptive phase-locked loops that ensure the angle estimation error goes to zero for almost all initial conditions. Although well-known, for the sake of completeness, we also present a PI controller with feedforward action that ensures the converter currents converge to an arbitrary desired value. Relevance of the theoretical results and their robustness to variation of the grid parameters are thoroughly discussed and validated in the challenging scenario of a converter connected to a grid with low short-circuit-ratio., Comment: 16 pages, 6 figures

Wind turbines are often controlled to harvest the maximum power from the wind, which corresponds to the operation at the top of the bell-shaped power coefficient graph. Such a mode of operation may be achieved implementing an extremum seeking data-based strategy, which is an invasive technique that requires the injection of harmonic disturbances. Another approach is based on the knowledge of the analytic expression of the power coefficient function, an information usually unreliably provided by the turbine manufacturer. In this paper we propose a globally, exponentially convergent on-line estimator of the parameters entering into the windmill power coefficient function. This corresponds to the solution of an identification problem for a nonlinear, nonlinearly parameterized, underexcited system. To the best of our knowledge we have provided the first solution to this challenging, practically important, problem., Comment: 9 figures, 23 pages

In this paper we are interested in the problem of adaptive state observation of linear time-varying (LTV) systems where the system and the input matrices depend on unknown time-varying parameters. It is assumed that these parameters satisfy some known LTV dynamics, but with unknown initial conditions. Moreover, the state equation is perturbed by an additive signal generated from an exosystem with uncertain constant parameters. Our main contribution is to propose a globally convergent state observer that requires only a weak excitation assumption on the system., Comment: 21 pages, 4 figures, detailed paper

In this paper we address the problem of adaptive state observation of affine-inthe-states time-varying systems with delayed measurements and unknown parameters. The development of the results proposed in the [Bobtsov et al. 2021a] and in the [Bobtsov et al. 2021c] is considered. The case with known parameters has been studied by many researchers (see [Sanz et al. 2019, Bobtsov et al. 2021b] and references therein) where, similarly to the approach adopted here, the system is treated as a linear time-varying system. We show that the parameter estimation-based observer (PEBO) design proposed in [Ortega et al. 2015, 2021] provides a very simple solution for the unknown parameter case. Moreover, when PEBO is combined with the dynamic regressor extension and mixing (DREM) estimation technique [Aranovskiy et al. 2016, Ortega et al. 2019], the estimated state converges in fixed-time with extremely weak excitation assumptions.

In this paper we propose a new parameter estimator that ensures global exponential convergence of linear regression models requiring only the necessary assumption of identifiability of the regression equation,which we show is equivalent to interval excitation of the regressor vector. Continuous and discrete-time versions of the estimators are given. An extension to--separable and monotonic--non-linear parameterizations is also given. The estimators are shown to be robust to additive measurement noise and--not necessarily slow--parameter variations. Moreover, a version of the continuous-time estimator that rejects sinusoidal disturbances with unknown internal model is given. The estimator is shown to be applicable to the classical model reference adaptive control problem relaxing the conspicuous assumption of known sign of the high-frequency gain. Simulation results that illustrate the performance of the estimator are given.

In this paper, we prove that it is possible to estimate online the parameters of a classical vector linear regression equation $ Y=\Omega \theta$, where $ Y \in \mathbb{R}^n,\;\Omega \in \mathbb{R}^{n \times q}$ are bounded, measurable signals and $\theta \in \mathbb{R}^q$ is a constant vector of unknown parameters, even when the regressor $\Omega$ is not persistently exciting. Moreover, the convergence of the new parameter estimator is global and exponential and is given for both continuous-time and discrete-time implementations. As an illustration example, we consider the problem of parameter estimation of a linear time-invariant system, when the input signal is not sufficiently exciting, which is known to be a necessary and sufficient condition for the solution of the problem with the standard gradient or least-squares adaptation algorithms., Comment: submitted to System and Control Letters

It is widely recognized that the existing parameter estimators and adaptive controllers for robot manipulators are extremely complicated to be of practical use. This is mainly due to the fact that the existing parameterization includes the complicated signal and parameter relations introduced by the Coriolis and centrifugal forces matrix. In an insightful remark of their seminal paper Slotine and Li suggested to use the parameterization of the power balance equation, which avoids these terms -- yielding significantly simpler designs. To the best of our knowledge, such an approach was never actually pursued in on-line implementations, because the excitation requirements for the consistent estimation of the parameters is ``very high". In this paper we use a recent technique of generation of ``exciting" regressors developed by the authors to overcome this fundamental problem. The result is applied to general Euler-Lagrange systems and the fundamental advantages of the new parameterization are illustrated with comprehensive simulations of a 2 degrees-of-freedom robot manipulator.

The problem of parameter estimation 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.

In this brief note we present two new parameter identifiers whose estimates converge in finite time under weak interval excitation assumptions. The main novelty is that, in contrast with other finite-convergence time (FCT) estimators, our schemes preserve the FCT property when the parameters change. The previous versions of our FCT estimators can track the parameter variations only asymptotically. Continuous-time and discrete-time versions of the new estimators are presented, Comment: arXiv admin note: text overlap with arXiv:1908.05125

This paper considers the problem of frequency estimation for a multi-sinusoidal signal consisting of n sinuses in finite-time. The parameterization approach based on applying delay operators to a measurable signal is used. The result is the nth order linear regression model with n parameters, which depends on the signals frequencies. We propose to use Dynamic Regressor Extension and Mixing method to replace nth order regression model with n first-order regression models. Then the standard gradient descent method is used to estimate separately for each the regression model parameter. On the next step using algebraic equations finite-time frequency estimate is found. The described method does not require measuring or calculating derivatives of the input signal, and uses only the signal measurement. The efficiency of the proposed approach is demonstrated through the set of numerical simulations., Comment: 8 pages, 4 figures

In this paper we address the problems of flux and speed observer design for voltage-fed induction motors with unknown rotor resistance and load torque. The only measured signals are stator current and control voltage. Invoking the recently reported Dynamic Regressor Extension and Mixing-Based Adaptive Observer (DREMBAO) we provide the first global solution to this problem. The proposed DREMBAO achieve asymptotic convergence under an excitation condition that is strictly weaker than persistent excitation. If the latter condition is assumed the convergence is exponential.

In this paper we address the problem of state observation of linear time-varying systems with delayed measurements, which has attracted the attention of many researchers|see [7] and references therein. We show that, adopting the parameter estimationbased approach proposed in [3,4], we can provide a very simple solution to the problem with reduced prior knowledge., Comment: 3 pages, 6 figures

We consider the task of motion control for non-prehensile manipulation using parallel kinematics mechatronic setup, in particular, stabilization of a ball on a plate under unmeasured external harmonic disturbances. System parameters are assumed to be unknown, and only a ball position is measurable with a resistive touch sensor. To solve the task we propose a novel passivity-based output control algorithm that can be implemented for unstable linearized systems of an arbitrary relative degree. In contrast to previous works, we describe a new way to parametrize harmonic signal generators and an estimation algorithm with finite-time convergence. This scheme enables fast disturbance cancellation under control signal magnitude constraints., Comment: 11 pages, 11 figures, extended version of the paper accepted for IFAC WC 2020

We present the first solution to the problem of estimation of the state of multimachine power systems with lossy transmission lines. We consider the classical three-dimensional \fluxdecay" model of the power system and assume that the active and reactive power as well as the rotor angle and excitation voltage at each generator is available for measurement|a scenario that is feasible with current technology. The design of the observer relies on two recent developments proposed by the authors: a parameter estimation based approach to the problem of state estimation and the use of the dynamic regressor extension and mixing technique to estimate these parameters. Thanks to the combination of these techniques it is possible to overcome the problem of lack of persistent excitation that stymies the application of standard observer designs. Simulation results illustrate the performance of the proposed observer., Comment: 8 pages, 4 fugures

In this paper we propose a PI passivity-based controller, applicable to a large class of switched power converters, that ensures global state regulation to a desired equilibrium point. A solution to this problem was reported in \cite{HERetal} but it requires full state-feedback, which makes it practically unfeasible. To overcome this limitation we construct a state observer that is implementable with measurements that are available in practical applications. The observer reconstructs the state in finite-time, ensuring global convergence of the PI. The excitation requirement for the observer is very weak and is satisfied in normal operation of the converters. Simulation results illustrate the excellent performance of the proposed PI.

The problem of effective use of Phasor Measurement Units (PMUs) to enhance power systems awareness and security is a topic of key interest. The central question to solve is how to use this new measurements to reconstruct the state of the system. In this paper we provide the first solution to the problem of (globally convergent) state estimation of multimachine power systems equipped with PMUs and described by the fourth order flux-decay model. This work is a significant extension of our previous result, where this problem was solved for the simpler third order model, for which it is possible to recover algebraically part of the unknown state. Unfortunately, this property is lost in the more accurate fourth order model, significantly complicating the state observation task. The design of the observer relies on two recent developments proposed by the authors, a parameter estimation based approach to the problem of state estimation and the use of the Dynamic Regressor Extension and Mixing (DREM) technique to estimate these parameters. The use of DREM allows us to overcome the problem of lack of persistent excitation that stymies the application of standard parameter estimation designs. Simulation results illustrate the latter fact and show the improved performance of the proposed observer with respect to a locally stable gradient-descent based observer., Comment: 10 pages, 10 Figures

We propose a novel decentralized mixed algebraic and dynamic state observation method for multi-machine power systems with unknown inputs and equipped with Phasor Measurement Units (PMUs). More specifically, we prove that for the third-order flux-decay model of a synchronous generator, the local PMU measurements give enough information to reconstruct algebraically the load angle and the quadrature-axis internal voltage. Due to the algebraic structure a high numerical efficiency is achieved, which makes the method applicable to large scale power systems. Also, we prove that the relative shaft speed can be globally estimated combining a classical Immersion and Invariance (I&I) observer with - the recently introduced - dynamic regressor and mixing (DREM) parameter estimator. This adaptive observer ensures global convergence under weak excitation assumptions that are verified in applications. The proposed method does not require the measurement of exogenous inputs signals such as the field voltage and the mechanical torque nor the knowledge of mechanical subsystem parameters., Comment: 10 pages, 11 figures

In this paper we propose a new state observer design technique for nonlinear systems. It consists of an extension of the recently introduced parameter estimation-based observer, which is applicable for systems verifying a particular algebraic constraint. In contrast to the previous observer, the new one avoids the need of implementing an open loop integration that may stymie its practical application. We give two versions of this observer, one that ensures asymptotic convergence and the second one that achieves convergence in finite time. In both cases, the required excitation conditions are strictly weaker than the classical persistent of excitation assumption. It is shown that the proposed technique is applicable to the practically important examples of multimachine power systems and chemical-biological reactors., Comment: 13 pages, 8 figures

We present some new results on the dynamic regressor extension and mixing parameter estimators for linear regression models recently proposed in the literature. This technique has proven instrumental in the solution of several open problems in system identification and adaptive control. The new results include: (i) a unified treatment of the continuous and the discrete-time cases; (ii) the proposal of two new extended regressor matrices, one which guarantees a quantifiable transient performance improvement, and the other exponential convergence under conditions that are strictly weaker than regressor persistence of excitation; and (iii) an alternative estimator ensuring parameter estimation in finite-time that retains its alertness to track time-varying parameters. Simulations that illustrate our results are also presented., Comment: 8 pages, 7 figures, under review in IEEE TAC

One of the most widely studied dynamical systems in nonlinear control theory is the levitated ball. Several full-state feedback controllers that ensure asymptotic regulation of the ball position have been reported in the literature. However, to the best of our knowledge, the design of a stabilizing law measuring only the current and the voltage - so-called sensorless control - is conspicuous by its absence. Besides its unquestionable theoretical interest, the high cost and poor reliability of position sensors for magnetic levitated systems, makes the problem of great practical application. Our main contribution is to provide the fist solution to this problem. Instrumental for the development of the theory is the use of parameter estimation-based observers, which combined with the dynamic regressor extension and mixing parameter estimation technique, allow the reconstruction of the magnetic flux. With the knowledge of the latter it is shown that the mechanical coordinates can be estimated with suitably tailored nonlinear observers. Replacing the observed states, in a certainty equivalent manner, with a full information asymptotically stabilising law completes the sensorless controller design. Simulation results are used to illustrate the performance of the proposed scheme., Comment: 8 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1711.02733

The problem of designing a flux observer for magnetic field electromechanical systems from noise corrupted measurements of currents and voltages is addressed in this paper. Imposing a constraint on the systems magnetic energy function, which allows us to construct an algebraic relation between fluxes and measured voltages and currents that is independent of the mechanical coordinates, we identify a class of systems for which a globally convergent adaptive observer can be designed. A new adaptive observer design technique that effectively exploits the aforementioned algebraic relation is proposed and successfully applied to the practically important examples of permanent magnet synchronous motors and magnetic levitation systems.

In this paper we address the problem of state observation for sensorless control of nonlinear magnetic levitation systems, that is, the regulation of the position of a levitated object measuring only the voltage and current of the electrical supply. Instrumental for the development of the theory is the use of parameter estimation-based observers, which combined with the dynamic regressor extension and mixing parameter estimation technique, allow the reconstruction of the magnetic flux. With the knowledge of the latter it is shown that the mechanical coordinates can be estimated with suitably tailored nonlinear observers. Replacing the observed states, in a certainty equivalent manner, with a full information globally stabilising law completes the sensorless controller design. We consider one and two-degrees-of-freedom systems that, interestingly, demand totally different mathematical approaches for their solutions. Simulation results are used to illustrate the performance of the proposed schemes.

This paper deals with the problem of identification of photovoltaic arrays' maximum power extraction point---information that is encrypted in the current-voltage characteristic equation. We propose a new parameterisation of the classical five parameter model of this function that, combined with the recently introduced identification technique of dynamic regressor extension and mixing, ensures a fast and accurate estimation of all unknown parameters. A concavity property of the current-voltage characteristic equation is then exploited to directly identify the desired voltage operating point. Realistic numerical examples via computer simulations are presented to assess the performance of the proposed approach., Comment: This paper is submitted to th International Journal of Adaptive Control and Signal Processing