Anton Pyrkin

Alexey Bobtsov, Anton Pyrkin, Romeo Ortega et al.

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.

Romeo Ortega, Nima Monshizadeh, Pooya Monshizadeh et al.

This note shows that the industry standard desired equilibrium for permanent magnet synchronous motors (i.e., maximum torque per Ampere) can be globally asymptotically stabilized with a PI control around the current errors, provided some viscous friction (possibly small) is present in the rotor dynamics and the proportional gain of the PI is suitably chosen. Instrumental to establish this surprising result is the proof that the map from voltages to currents of the incremental model of the motor satisfies some passivity properties. The analysis relies on basic Lyapunov theory making the result available to a wide audience.

Anton Pyrkin, Fernando Mancilla-David, Romeo Ortega et al.

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.

Anton Pyrkin, Alexey Vedyakov, Romeo Ortega et al.

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.

Alexey Bobtsov, Anton Pyrkin, Romeo Ortega et al.

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.

Alexey Bobtsov, Jose Guadalupe Romero, Romeo Ortega et al.

In this paper we present a radically new approach to design state observers for nonlinear systems, with particular emphasis on physical ones. Our objective is to obtain an algebraic relation between the unmeasurable part of the state and filtered versions of the systems inputs and outputs, which holds true for all $t \geq 0$. The latter qualifier should be contrasted with the usual asymptotic (or fixed/finite time) objective. The standing assumption for our design is the availability -- or possibility of constructing, via coordinate change -- state components with measurable derivatives. In the physical systems studied in the paper this condition is naturally satisfied. The next step in the design is the application of the Swapping Lemma to pull out from the dynamics the derivative of one of these signals. The design is completed replacing the latter by the measurable signals and arranging the remaining terms. The algebraic observer constitutes a refreshing major departure from classical asymptotic observer designs, even in the case of electrical motors and mechanical systems that have been exhaustively studied. Particularly notable is the fact that no observability or excitation condition is imposed for the construction of the algebraic observer.

Stanislav Kim, Anton Pyrkin, Oleg Borisov

A complete model of quadcopter motion for the task of dynamic positioning at a specified point is derived. Based on this model, two control algorithms are proposed. The first one generalizes previously obtained results to the case of a varying yaw angle. The second control algorithm addresses the above problem using a simplified regulator tuning methodology.

Stanislav Kim, Anton Pyrkin, Oleg Borisov

A complete model of the motion of a quadcopter along a smooth spatial trajectory is presented. Based on the model, a robust algorithm is proposed for controlling a quadcopter using measurements of linear coordinates and yaw angle. By introducing additional integrators, a dynamic control algorithm with a simplified controller tuning methodology is obtained. The control law is synthesized within the geometric approach, and its stability is proven. A realizable output-feedback version using an extended observer is also given. The results enable coordinated trajectory following in three-dimensional space despite unmeasured disturbances and incomplete state information.

Stanislav Kim, Anton Pyrkin, Oleg Borisov

The study addresses the problem of quadcopter motion control using output feedback. By applying a geometric approach, the quadcopter model is transformed into a normal form with a time-varying gain coefficient, which is subsequently made stationary through double integration of the control input. A robust output feedback control law is synthesised based on the extended observer method.

Anton Pyrkin, Alexey Bobtsov, Romeo Ortega et al.

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.

Alexey S. Matveev, Juan E. Machado, Romeo Ortega et al.

Voltage instability is a major threat in power system operation. The growing presence of constant power loads significantly aggravates this issue, hence motivating the development of new analysis methods for both existence and stability of voltage equilibria. Formally, this problem can be cast as the analysis of solutions of a set of nonlinear algebraic equations of the form $f(x)=0$, where $f:\mathbb{R}^n \mapsto \mathbb{R}^{n}$, and the associated differential equation $\dot x=f(x)$. By invoking advanced concepts of dynamical systems theory and effectively exploiting its monotonicity, we exhibit all possible scenarios for existence, uniqueness and stability, of its equilibria. We prove that, if there are equilibria, there is a distinguished one that is locally stable and attractive, and we give some physically-interpretable conditions such that it is unique. Moreover, a simple on-line procedure to decide whether equilibria exist of not, and to compute the distinguished one is proposed. In addition, we show how the proposed framework can be applied to long-term voltage stability analysis in AC power systems, multi-terminal high-voltage DC systems and DC microgrids.