Hector Chiacchiarini

BIFURCATIONS AND HOPF DEGENERACIES IN NONLINEAR FEEDBACK SYSTEMS WITH TIME DELAY

An application of the well-developed frequency-domain approach to detect oscillations in nonlinear feedback systems with time delay is presented. The method depends on an early proof of the Hopf bifurcation theorem known as the Graphical Hopf Theorem (GHT). Several nondegeneracy conditions are included to apply the GHT in nonlinear systems with time delay. The singular conditions corresponding to degeneracies, which include static and dynamic bifurcations, as well as some special cases of degenerate Hopf bifurcations and multiple crossings, are also discussed. Two Single-Input Single-Output (SISO) feedback systems with odd nonlinearities are presented as examples to show that the proposed technique and a standard simulation method have very good agreement in the results, yet the GHT is much simpler in calculation. The first one shows an application of the GHT under classical Hopf conditions while the second emphasizes the presence of degenerate Hopf bifurcations and multiple crossings. For both examples, and others which have appeared recently in the literature, a considerable simplification of the formulas for recovering periodic solutions is also provided in this paper.

Predictive functional control based on fuzzy model: magnetic suspension system case study

Abstract Fuzzy model based predictive functional controller (FPFC) is applied to the magnetic suspension system—a pilot plant for magnetic bearing. High quality control requirements are short settle time with a-periodical step response and zero steady-state error. Open loop unstable process was stabilised with linear lead compensator. The FPFC was used as a cascade controller. Due to some model uncertainties, the Takagi–Sugeno fuzzy model of stabilised system was obtained using fuzzy identification. Comparing to PID, it improved quality and robustness performance. With its computational efficiency, it proved to be ideal solution for high sampling frequency systems.

High-Performance Control of a DC–DC Z-Source Converter Used for an Excitation Field Driver

The electromechanical interface is a synchronous machine, because its field winding permits direct management of the magnetization during speed variations. For systems with a common dc-link for the drive and excitation converters, the efficiency is increased if the excitation drive has boosting capability. It is shown that with the proposed control strategy the Z-source converter is suitable for this application, becoming a better alternative than the typically used buck converter. The Z-source converter, in combination with the proposed multiloop control law, can achieve the desired voltage reference swing and high-performance tracking. An analytical comparison between the dominant losses of the buck topology, typically used in FESS, and the Z-source converter shows that the latter has higher efficiency for this application. The parameters of the converter prototype were experimentally identified and used to implement the proposed controller. The control strategy uses the two duty cycles as manipulated variables, one to allow tracking fast changes in the reference signal and the other to adapt the system to the slow changes. The combined action on both inputs contribute to the compensation of the nonminimum phase response of the Z-converter. Experimental results show the potential of the controller for tracking typical FESS application waveforms.

Predictive Functional Control Based on Fuzzy Model: Comparison with Linear Predictive Functional Control and PID Control

The implementation of the fuzzy predictive functional control (FPFC) on the magnetic suspension system is presented in the paper. The magnetic suspension system was in our case the pilot plant for magnetic bearing and is an open-loop unstable process, therefore a lead compensator was used to stabilize it. The high quality control requirements were a-periodical step response and zero steady-state error. Adding the integrator to a feedback causes overshoot. The solution to the problem was cascade control with fuzzy predictive functional controller in the outer loop. To cope with the unknown model parameters and the nonlinear nature of the magnetic system, a fuzzy identification based on FNARX model was used. After successful validation the obtained fuzzy model was used for controller design. The FPFC is compared with a cascade linear predictive functional control (PFC) and PID control. The results we obtained with the FPFC are very promising and hardly comparable with conventional control techniques.

Paper: Variable structure control with a second-order sliding condition: Application to a steam generator

A method for the design of second-order sliding mode controllers is developed for a class of nonlinear systems. The key idea is the necessity of nullifying both the auxiliary output as well as its time derivative when the system is sliding. It is found that if the auxiliary output has a strong vector relative degree one, it is possible to design a continuous control input. This allows the application of the sliding mode control to systems that do not allow discontinuous control signals generated by the classical variable structure control. Robustness of the controllers is analyzed and dynamic bounds for the uncertainty are found for a class of nonlinear systems. The design technique could be extended to nth-order sliding controllers, though the complexity of the calculations increases and the robustness bounds become more restrictive. The application of the technique to a drum-type steam generating unit to solve a robust tracking problem is presented.

Harmonic distortion reduction in power inverters

The output voltage of PWM power inverters shows harmonic distortion due to several causes; the main ones are the modulation algorithm, nonlinearities due to the output filter, dead times, voltage drops across the switches and modulation of the dc bus voltage. The distortion is more evident when using low dc bus voltages. As a result, motors driven by these inverters have important torque pulsations. This work proposes to reduce the distortion produced by dead times and voltage drops across the switches, using a simple algorithm that recalculates the width of each PWM pulse, preserving the ideal area. The algorithm takes advantage of the fact that the dead times are not always necessary, but only when the load current changes its sign. By simulation, the THD was reduced from 18% to 0.29% in a single-phase inverter. The proposed algorithm only needs products and sums, so it is suitable for being implemented on a DSP with low processing load. Experimental results were obtained from a non-optimized laboratory prototype, showing a reduction of the THD from 17.9% to 0.59%.

Synthesis of Sinusoidal Waveform References Synchronized With Periodic Signals

This paper proposes a novel method to generate a sinusoidal waveform synchronized with any measurable periodic signal whose frequency is within a given neighborhood. The synthesized sinusoidal signal could be used as a reference current for certain applications of parallel active power filters or any other where such synchronization would be necessary (e.g., ac/dc converters for renewable energy resources, power factor correctors, power supplies, UPS, etc.) The method is based on the behavior of a dynamical system and avoids employing the usual combination of phase-locked loop (PLL) and lookup table found in most parallel active filters synthesizing a sinusoidal source current (a table also means using significant storage memory). The novel method produces two high-quality sinusoidal waveforms that are in quadrature and is applicable to those parallel active filters whose control methodology is in the reference frame, or alternatively, it produces three sinusoidal waveforms shifted 120 degrees for designs that work in the frame. Here, a th order implementation is described, including a proof of convergence. For its most simple implementation , simulated and experimental results are included.

Nonlinear analog controller for a buck converter: theory and experimental results

The design of a switching power supply (buck DC-DC converter) with regulated output voltage for a wide range of current consumption is considered. The control objective is to regulate the output voltage despite the existence of current load variations with bounded time derivative. A variable-structure technique is used to design a continuous time controller. A discrete and an analog version of the same controller are compared. Laboratory experiences are performed to obtain conclusions about the real performance of the proposed controller with satisfactory results.

A Novel Feedback/Feedforward Control Strategy for Three-Phase Voltage-Source Converters

In this paper a novel control strategy for voltage source converters (VSCs) is introduced. The proposed strategy consists of a nonlinear feedback controller based on feedback linearization plus a feedforward compensation of the load current. In our proposal an energy function and a quadrature current are considered as outputs, such that zero dynamics is avoided. In this way, a full linearization is obtained via nonlinear transformation and feedback. In order to improve the performance of the whole system and to diminish the output capacitor size an estimate of the load current is feed forwarded. The estimate is calculated by using a nonlinear reduced order observer. Simulation results are presented in order to validate the proposal. These results include performance in presence of parameters uncertainties and noisy measurements. In addition, a comparison with other controllers introduced by other researchers is carried on.

Predictive control based on fuzzy model: a case study

The implementation of the fuzzy predictive functional control (FPFC) on the magnetic suspension system is presented. The magnetic suspension system is in our case the pilot plant for magnetic bearing and is an open-loop unstable process, therefore a lead compensator is used to stabilize it. The high quality control requirements include a periodical step response and zero steady-state error. Adding the integrator to a feedback causes overshoot. The solution to the problem is a cascade control with fuzzy predictive functional controller in the outer loop. To cope with the unknown model parameters and the nonlinear nature of the magnetic system, a fuzzy identification based on the FNARX model is used. After a successful validation the obtained fuzzy model is used for the controller design. The FPFC is compared with a cascade PID control. The results obtained with the FPFC are very promising and comparable with the conventional control techniques.