Romeo Ortega

Johannes Schiffer, Daniele Zonetti, Romeo Ortega et al.

Microgrids have been identified as key components of modern electrical systems to facilitate the integration of renewable distributed generation units. Their analysis and controller design requires the development of advanced (typically model-based) techniques naturally posing an interesting challenge to the control community. Although there are widely accepted reduced order models to describe the dynamic behavior of microgrids, they are typically presented without details about the reduction procedure---hampering the understanding of the physical phenomena behind them. Preceded by an introduction to basic notions and definitions in power systems, the present survey reviews key characteristics and main components of a microgrid. We introduce the reader to the basic functionality of DC/AC inverters, as well as to standard operating modes and control schemes of inverter-interfaced power sources in microgrid applications. Based on this exposition and starting from fundamental physics, we present detailed dynamical models of the main microgrid components. Furthermore, we clearly state the underlying assumptions which lead to the standard reduced model with inverters represented by controllable voltage sources, as well as static network and load representations, hence, providing a complete modular model derivation of a three-phase inverter-based microgrid.

Bowen Yi, Romeo Ortega, Dongjun Wu et al.

In this paper we show that a slight modification to the widely popular interconnection and damping assignment passivity-based control method---originally proposed for stabilization of equilibria of nonlinear systems---allows us to provide a solution to the more challenging orbital stabilization problem. Two different, though related, ways how this procedure can be applied are proposed. First, the assignment of an energy function that has a minimum in a closed curve, i.e., with the shape of a Mexican sombrero. Second, the use of a damping matrix that changes "sign" according to the position of the state trajectory relative to the desired orbit, that is, pumping or dissipating energy. The proposed methodologies are illustrated with the example of the induction motor and prove that it yields the industry standard field oriented control.

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.

Nima Monshizadeh, Pooya Monshizadeh, Romeo Ortega et al.

In this paper, we examine the shifted passivity property of port-Hamiltonian systems. Shifted passivity accounts for the fact that in many applications the desired steady-state values of the input and output variables are nonzero, and thus one is interested in passivity with respect to the shifted signals. We consider port-Hamiltonian systems with strictly convex Hamiltonian, and derive conditions under which shifted passivity is guaranteed. In case the Hamiltonian is quadratic and state dependency appears in an affine manner in the dissipation and interconnection matrices, our conditions reduce to negative semidefiniteness of an appropriately constructed constant matrix. Moreover, we elaborate on how these conditions can be extended to the case when the shifted passivity property can be enforced via output feedback, thus paving the path for controller design. Stability of forced equilibria of the system is analyzed invoking the proposed passivity conditions. The utility and relevance of the results are illustrated with their application to a 6th order synchronous generator model as well as a controlled rigid body system.

Prasanna S. Gandhi, Pablo Borja, Romeo Ortega

Control of compliant mechanical systems is increasingly being researched for several applications including flexible link robots and ultra-precision positioning systems. The control problem in these systems is challenging, especially with gravity coupling and large deformations, because of inherent underactuation and the combination of lumped and distributed parameters of a nonlinear system. In this paper we consider an ultra-flexible inverted pendulum on a cart and propose a new nonlinear energy shaping controller to keep the pendulum at the upward position with the cart stopped at a desired location. The design is based on a model, obtained via the constrained Lagrange formulation, which previously has been validated experimentally. The controller design consists of a partial feedback linearization step followed by a standard PID controller acting on two passive outputs. Boundedness of all signals and (local) asymptotic stability of the desired equilibrium is theoretically established. Simulations and experimental evidence assess the performance of the proposed controller.

Romeo Ortega, Bowen Yi, Slobodan Vukosavic et al.

The design of a position observer for the interior permanent magnet synchronous motor is a challenging problem that, in spite of many research efforts, remained open for a long time. In this paper we present the first globally exponentially convergent solution to it, assuming that the saliency is not too large. As expected in all observer tasks, a persistency of excitation condition is imposed. Conditions on the operation of the motor, under which it is verified, are given. In particular, it is shown that at rotor standstill---when the system is not observable---it is possible to inject a probing signal to enforce the persistent excitation condition. {The high performance of the proposed observer, in standstill and high speed regions, is verified by extensive series of test-runs on an experimental setup.

Bowen Yi, Romeo Ortega, Weidong Zhang

In this paper we propose a new observer design technique for nonlinear systems. It combines the well-known Kazantzis-Kravaris-Luenberger observer and the recently introduced parameter estimation-based observer, which become special cases of it---extending the realm of applicability of both methods. A second contribution of the paper is the proof that these designs can be recast as particular cases of immersion and invariance observers---providing in this way a unified framework for their analysis and design. Simulation results of a physical system that illustrates the superior performance of the proposed observer compared to other existing observers are presented.

Pooya Monshizadeh, Juan E. Machado, Romeo Ortega et al.

We study a type of port-Hamiltonian system, in which the controller or disturbance is not applied to the flow variables, but to the systems power, a scenario that appears in many practical applications. A suitable framework is provided to model these systems and to investigate their shifted passivity properties, based on which, a stability analysis is carried out. The applicability of the results is illustrated with the important problem of stability analysis of electrical circuits with constant power loads.

Romeo Ortega, Bowen Yi, Jose Guadalupe Romero et al.

Immersion and Invariance is a technique for the design of stabilizing and adaptive controllers and state observers for nonlinear systems. In all these applications the problem considered is the stabilization of equilibrium points. Motivated by some modern applications we show that the technique can also be used to solve the problem of orbital stabilization, where the final objective is to generate periodic solutions that are attractive. The feasibility of our result is illustrated with some classical mechanical engineering and electronics examples.

Jose Guadalupe Romero, Romeo Ortega

A globally exponentially stable speed observer for mechanical systems was recently reported in the literature, under the assumptions of known (or no) Coulomb friction and no disturbances. In this note we propose and adaptive version of this observer, which is robust vis--a--vis constant disturbances. Moreover, we propose a new globally convergent speed observer that, besides rejecting the disturbances, estimates some unknown friction coefficients for a class of mechanical systems that contains several practical examples.

Daniele Zonetti, Romeo Ortega, Johannes Schiffer

The problem of primary control of high-voltage direct current transmission systems is addressed in this paper, which contains four main contributions. First, to propose a new nonlinear, more realistic, model for the system suitable for primary control design, which takes into account nonlinearities introduced by conventional inner controllers. Second, to determine necessary conditions - dependent on some free controller tuning parameters - for the existence of equilibria. Third, to formulate additional (necessary) conditions for these equilibria to satisfy the power sharing constraints. Fourth, to establish conditions for stability of a given equilibrium point. The usefulness of the theoretical results is illustrated via numerical calculations on a four-terminal example.

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.

Bowen Yi, Slobodan N. Vukosavic, Romeo Ortega et al.

Several heuristic procedures to estimate the rotor position of permanent magnet synchronous motors (PMSM) via signal injection have been reported in the literature. Using averaging theory, a framework to analyse such schemes has been recently proposed. However, to the best of our knowledge, no theoretical analysis of the performance of the conventional linear time invariant filtering methods, which are widely used as standard industrial practice, has been reported in the literature. The objective of this note is to propose a new method that, on one hand, is amenable to a rigorous theoretical analysis and, on the other hand, ensures an improved accuracy in the position estimation. An additional advantage of the new method is that it relies on the use of linear operators, implementable with simple computations. The effectiveness of the proposed scheme is assessed by experiments on an interior PMSM platform driven by a 521 V DC bus with 5-kHz PWM.

Stanislav Aranovskiy, Romeo Ortega, Rafael Cisneros

This paper deals with the problem of control of partially known nonlinear systems, which have an open-loop stable equilibrium, but we would like to add a PI controller to regulate its behavior around another operating point. Our main contribution is the identification of a class of systems for which a globally stable PI can be designed knowing only the systems input matrix and measuring only the actuated coordinates. The construction of the PI is done invoking passivity theory. The difficulties encountered in the design of adaptive PI controllers with the existing theoretical tools are also discussed. As an illustration of the theory, we consider port--Hamiltonian systems and a class of thermal processes.

Joel Ferguson, Alejandro Donaire, Romeo Ortega et al.

Interconnection and damping assignment, passivity-based control (IDA-PBC) has proven to be a successful control technique for the stabilisation of many nonlinear systems. In this paper, we propose a method to robustify a system which has been stabilised using IDA-PBC with respect to constant, matched disturbances via the addition of integral action. The proposed controller extends previous work on the topic by being robust against the damping of the system, a quantity which may not be known in many applications.

Bowen Yi, Romeo Ortega, Weidong Zhang

In this paper we propose an energy pumping-and-damping technique to regulate nonholonomic systems described by kinematic models. The controller design follows the widely popular interconnection and damping assignment passivity-based methodology, with the free matrices partially structured. Two asymptotic regulation objectives are considered: drive to zero the state or drive the systems total energy to a desired constant value. In both cases, the control laws are smooth, time-invariant, state-feedbacks. For the nonholonomic integrator we give an almost global solution for both problems, with the objectives ensured for all system initial conditions starting outside a set that has zero Lebesgue measure and is nowhere dense. For the general case of higher-order nonholonomic systems in chained form, a local stability result is given. Simulation results comparing the performance of the proposed controller with other existing designs are also provided.

Bowen Yi, Romeo Ortega, Houria Siguerdidjane et al.

Probing signal injection is a well-established technique to extract additional information from a weakly (or non) observable dynamical system. Using averaging theory, a framework to analyse such schemes for general nonlinear systems has been recently proposed in [Combes et. al., 2016], where it is shown that the signal injection may be used to generate a new high frequency component of the systems output that can be used for state observation or controller design. A key step for the success of this technique is the implementation of a filter to reconstruct this virtual output from the measurement of the overall systems output. The main contribution of this paper is to propose a new filter with guaranteed convergence properties that outperforms the classical designs. The method is applied to a general class of electromechanical systems, and its performance is assessed via simulations and experiments on the benchmark example of a 1-dof magnetic levitation system.

Bowen Yi, Romeo Ortega, Houria Siguerdidjane et al.

In this paper we address the problem of sensorless control of the 1-DOF magnetic levitation system. Assuming that only the current and the voltage are measurable, we design an adaptive state observer using the technique of signal injection. Our main contribution is to propose a new filter to identify the virtual output generated by the signal injection. It is shown that this filter, designed using the dynamic regressor extension and mixing estimator, outperforms the classical one. Two additional features of the proposed observer are that (i) it does not require the knowledge of the electrical resistance, which is also estimated on-line and (ii) exponential convergence to a tunable residual set is guaranteed without excitation assumptions. The observer is then applied, in a certainty equivalent way, to a full state-feedback control law to obtain the sensorless controller, whose performance is assessed via simulations and experiments.

Joel Ferguson, Alejandro Donaire, Romeo Ortega et al.

In this paper we present a method to robustify energy-shaping controllers for port-Hamiltonian (pH) systems by adding an integral action that rejects unknown additive disturbances. The proposed controller preserves the pH structure and, by adding to the new energy function a suitable cross term between the plant and the controller coordinates, it avoids the unnatural coordinate transformation used in the past. This paper extends our previous work by relaxing the requirement that the systems Hamiltonian is strictly convex and separable, which allows the controller to be applied to a large class of mechanical systems, including underactuated systems with non-constant mass matrix. Furthermore, it is shown that the proposed integral action control is robust against unknown damping in the case of fully-actuated 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.

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.

Johannes Schiffer, Petros Aristidou, Romeo Ortega

The increasing penetration of power-electronic-interfaced devices is expected to have a significant effect on the overall system inertia and a crucial impact on the system dynamics. In the future, the reduction of inertia will have drastic consequences on protection and real-time control and will play a crucial role in the system operation. Therefore, in a highly deregulated and uncertain environment, it is necessary for Transmission System Operators to be able to monitor the system inertia in real time. We address this problem by developing and validating an online inertia estimation algorithm. The estimator is derived using the recently proposed dynamic regressor extension and mixing procedure. The performance of the estimator is demonstrated via several test cases using the 1013-machine ENTSO-E dynamic model.

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.

Juan E. Machado, José Arocas-Pérez, Wei He et al.

This paper proposes a nonlinear, adaptive controller to increase the stability margin of a direct-current (DC) small-scale electrical network containing a constant power load, whose value is unknown. Due to their negative incremental impedance, constant power loads are known to reduce the effective damping of a network, leading to voltage oscillations and even to network collapse. To tackle this problem, we consider the incorporation of a controlled DC-DC power converter between the feeder and the constant power load. The design of the control law for the converter is based on the use of standard Passivity-Based Control and Immersion and Invariance theories. The good performance of the controller is evaluated with numerical simulations.

Joel Ferguson, Alejandro Donaire, Romeo Ortega et al.

In this paper, we present a method of applying integral action to enhance the robustness of energy shaping controllers for underactuated mechanical systems with matched disturbances. Previous works on this problem have required a number of technical assumptions to be satisfied, restricting the class of systems for which the proposed solution applies. The design proposed in this paper relaxes some of these technical assumptions.

Lei Wang, Fulvio Forni, Romeo Ortega et al.

The main objective of this paper is to propose an alternative procedure to carry out one of the key steps of immersion and invariance stabilising controller design. Namely, the one that ensures attractivity of the manifold whose internal dynamics contains a copy of the desired system behaviour. Towards this end we invoke contraction theory principles and ensure the attractivity of the manifold rendering it horizontally contractive. The main advantage of adopting this alternative approach is to make more systematic the last step of the design with more explicit degrees of freedom to accomplish the task. The classical case of systems in feedback form is used to illustrate the proposed controller design.

Alejandro Donaire, Romeo Ortega, Jose Guadalupe Romero

To extend the realm of application of the well known controller design technique of interconnection and damping assignment passivity-based control (IDA-PBC) of mechanical systems two modifications to the standard method are presented in this article. First, similarly to [1], it is proposed to avoid the splitting of the control action into energy-shaping and damping injection terms, but instead to carry them out simultaneously. Second, motivated by [2], we propose to consider the inclusion of generalised forces, going beyond the gyroscopic ones used in standard IDA-PBC. It is shown that several new controllers for mechanical systems designed invoking other (less systematic procedures) that do not satisfy the conditions of standard IDA-PBC, actually belong to this new class of SIDA-PBC.

Daniele Zonetti, Romeo Ortega, Abdelkrim Benchaib

The problem of modeling and control of multi-terminal high-voltage direct-current transmission systems is addressed in this paper, which contains five main contributions. First, to propose a unified, physically motivated, modeling framework - based on port-Hamiltonian representations - of the various network topologies used in this application. Second, to prove that the system can be globally asymptotically stabilized with a decentralized PI control, that exploits its passivity properties. Close connections between the proposed PI and the popular Akagi's PQ instantaneous power method are also established. Third, to reveal the transient performance limitations of the proposed controller that, interestingly, is shown to be intrinsic to PI passivity-based control. Fourth, motivated by the latter, an outer-loop that overcomes the aforementioned limitations is proposed. The performance limitation of the PI, and its drastic improvement using outer-loop controls, are verified via simulations on a three-terminals benchmark example. A final contribution is a novel formulation of the power flow equations for the centralized references calculation.