George C. Konstantopoulos

Stability and convergence analysis for a class of nonlinear passive systems

A systematic and general method that proves state boundedness and convergence to nonzero equilibrium for a class of nonlinear passive systems with constant external inputs is developed. First, making use of the method of linear-time-varying approximations, the boundedness of the nonlinear system states is proven. Next, taking advantage of the passivity property, it is proven that a suitable switching storage function can be always obtained to show convergence to the nonzero equilibrium by using LaSalles Invariance Principle. Numerical and simulation results illustrate the proposed theoretical analysis.

Generalized Nonlinear Stabilizing Controllers for Hamiltonian-Passive Systems With Switching Devices

A generalized nonlinear control scheme suitable to regulate any state variable at any desired reference value, for a class of nonlinear Hamiltonian-passive systems that includes switching power devices, is presented. The proposed controller acts as a special nonlinear oscillator, uses as feedback only the state variable that has to be regulated, renders the Hamiltonian-passive structure of the entire system, and regulates the nonlinear system to any nonzero desired equilibrium independently from its parameters and characteristics. Particularly, it is proven that under some common assumptions, the system states consisting of the controller states plus the original system states, are bounded for constant or piecewise constant external inputs. Under the same assumptions, it is established and proven that for these systems there exists a general, bounded, differentiable, nonincreasing storage function. Thus, LaSalles invariance principle can be directly applied to prove convergence to the desired equilibrium. Although this storage function can be really constructed as a suitably switching function, its explicit derivation is not necessary for the controller design; it is only needed to guess that such a storage function exists. This constitutes the main contribution of this brief since, in order to implement the proposed controller, one has simply to check whether some initial assumptions are satisfied. The simulation and experimental results conducted for the case of a dc-dc boost converter system with resistance-inductance load verify the proposed design approach.

Full-Scale Modeling, Control, and Analysis of Grid-Connected Wind Turbine Induction Generators With Back-to-Back AC/DC/AC Converters

A model-based dynamic analysis of a variable-speed wind generator system consisting of an induction generator connected to the grid through a full power frequency converter is conducted. To this end, a nonlinear modeling of the entire system is used in a manner that permits a novel controller design with common structure for both the generator- and grid-side converters. The proposed controller, acting directly on the duty-ratio inputs of the converters, ensures the boundedness of the duty-ratio signals in the permitted range although its structure is independent from the system parameters and open to different control objectives. Therefore, maximum power point tracking and power factor correction are easily implemented. Furthermore, the controller is proven to guarantee stability of the whole system under field- or near-field-oriented conditions without needing any flux measurement or estimation. Hence, the main contribution established by this approach is that a rigorous stability analysis taking into account the generator, converters, dc link, and controller dynamics is presented on the basis of a complete system modeling and controller design approach. The theoretical analysis and controller effectiveness are confirmed via extended simulation results for a commercial size 2-MW induction generator operating under varied wind speed conditions and are further validated on a similar system with real-time results.

Improved Synchronverters with Bounded Frequency and Voltage for Smart Grid Integration

Synchronverters are grid-friendly inverters that mimic conventional synchronous generators and play an important role in integrating different types of renewable energy sources, electric vehicles, energy storage systems, etc., to the smart grid. In this paper, an improved synchronverter is proposed to make sure that its frequency and voltage always stay within given ranges, while maintaining the function of the original synchronverter. Furthermore, the stability region characterized by the system parameters is analytically obtained, which guarantees that the improved synchronverter is always stable and converges to a unique equilibrium as long as the power exchanged at the terminal is kept within this area. Extensive OPAL-RT real-time simulation results are presented for the improved and the original self-synchronized synchronverters connected to a stiff grid and for the case when two improved synchronverters are connected to the same bus with one operating as a weak grid, to verify the theoretical development.

Experimental verification of an adaptive input shaping scheme for hoisting cranes

The aim of this paper is the presentation of an adaptive input shaping technique suitable for overhead cranes with hoisting mechanism. The main goal is the minimization of the remaining oscillations when the motion of the trolley and the hoisting of the load are performed simultaneously. While standard input shaping theory can be applied in its standard form in classical cranes, the shaper configuration when the load is hoisted is not profound. The adaptive version proposed calculates the parameters of the shaper online depending on the updated linearized model and the current rope length. Experimental results show the benefits of the proposed controller contrary to standard input shaping and to unshaped responses.

Bounded droop controller for parallel operation of inverters

In this paper, the stability of parallel-operated inverters in the sense of boundedness is investigated. At first, the non-linear model of parallelled inverters with a generic linear or non-linear load is obtained by using the generalised dissipative Hamiltonian structure and then the robust droop controller, recently proposed in the literature for parallel operation of inverters, is implemented in a way to produce a bounded control output. The proposed controller is called the bounded droop controller (BDC). It introduces a zero-gain property and can guarantee the boundedness of the closed-loop system solution. Therefore, for the first time, the closed-loop stability in the sense of boundedness is guaranteed for parallelled inverters feeding generic non-linear/linear loads. The controller structure is further improved to increase its robustness with respect to initial conditions, numerical errors or external disturbances while maintaining the stability property. Moreover, the controller is tuned to avoid any possible limit cycles in the voltage dynamics. Real-time simulation results for two single-phase inverters operated in parallel loaded with a non-linear load are presented to verify the effectiveness of the proposed BDC.

Bounded Nonlinear Stabilizing Speed Regulators for VSI-Fed Induction Motors in Field-Oriented Operation

A new nonlinear controller design is developed for speed regulation of voltage source inverter (VSI)-driven induction motors. The proposed controller directly provides the duty-ratio input of the VSI in the permitted range to ensure linear modulation, is fully independent from the system parameters and suitably regulates the motor speed and the stator flux to the desired values. Considering the complete nonlinear model of the converter-motor system and applying advanced nonlinear methods, boundedness of the full system states is proven. Furthermore, exploiting the Hamiltonian-passive structure of the system, state convergence to the equilibrium is shown using LaSalles Invariance Principle. Though the controller design is developed in the frame of the field-oriented control methodology, stability holds true even without accurate field orientation guaranteeing an effective performance in cases where parameter variations occur. Extensive simulation results on an industrial size system are conducted to evaluate the proposed controller performance, under rapid changes of the reference speed or load torque as well as system parameter variations. In addition, a lab size induction motor system is experimentally tested. In all cases, the system response shows fast convergence to the equilibriums after limited transients, thus verifying the theoretical results.

Advanced Integrated Modeling and Analysis for Adjustable Speed Drives of Induction Motors Operating With Minimum Losses

The nonlinear induction motor model is appropriately integrated by incorporating the dynamics of the power electronic converter in a manner that permits the design of stable field-oriented control (FOC) operating with minimum losses. As already proven, the challenging issue of operating the induction machine with minimum copper losses requires a varying rotor flux opposed to the standard FOC technique, which keeps the rotor field magnitude constant and tracks the electric torque to the desired level. To this end, exploiting the Hamiltonian structure of the developed motor/converter model, an innovated nonlinear controller is proposed that guarantees the technical limits of the converter (linear modulation) and simultaneously operates under FOC at steady state to achieve accurate speed regulation with varying rotor flux according to the minimal losses requirements. Under these circumstances, the conventional FOC stability analysis does not hold anymore, and therefore for the first time, a new rigorous analysis is provided that proves stability and convergence to the desired equilibrium for the complete closed-loop motor converter system. Finally, the theoretical contribution is examined in comparison to the traditional FOC operation by simulations obtained for an industrial size induction motor, while it is further evaluated by real-time results of a motor with similar parameters.

PLL-Less Nonlinear Current-Limiting Controller for Single-Phase Grid-Tied Inverters: Design, Stability Analysis, and Operation Under Grid Faults

A nonlinear controller for single-phase grid-tied inverters, that can operate under both a normal and a faulty grid with guaranteed closed-loop stability, is proposed. The proposed controller acts independently from the system parameters, does not require a phase-locked loop, and can achieve the desired real power regulation and unity power factor operation. Based on nonlinear input-to-state stability theory, it is analytically proven that the inverter current always remains below a given value, even during transients, independently from grid variations or faults (short circuit or voltage sag). The desired performance and stability of the closed-loop system are rigorously proven since the controller has a structure that does not require any switches, additional limiters, or monitoring devices for its implementation. Therefore, nonlinear stability of a grid-tied inverter with a given current-limiting property is proven for both normal and faulty grid conditions. The effectiveness of the proposed approach is experimentally verified under different operating conditions of the grid.

Bounded Integral Control of Input-to-State Practically Stable Nonlinear Systems to Guarantee Closed-Loop Stability

A fundamental problem in control systems theory is that stability is not always guaranteed for a closed-loop system even if the plant is open-loop stable. With the only knowledge of the input-to-state (practical) stability (ISpS) of the plant, in this note, a bounded integral controller (BIC) is proposed which generates a bounded control output independently from the plant parameters and states and guarantees closed-loop system stability in the sense of boundedness. When a given bound is required for the control output, an analytic selection of the BIC parameters is proposed and its performance is investigated using Lyapunov methods, extending the result for locally ISpS plant systems. Additionally, it is shown that the BIC can replace the traditional integral controller (IC) and guarantee asymptotic stability of the desired equilibrium point under certain conditions, with a guaranteed bound for the solution of the closed-loop system. Simulation results of a DC/DC buck-boost power converter system are provided to compare the BIC with the IC operation.