Right-half Plane Zeros Research Articles

A new technique for right half plane zero elimination from dynamics of a boost converter using magnetic coupling concept

PurposeControl-signal-to-output-voltage transfer function of the conventional boost converter has at least one right-half plane zero (RHPZ) in the continuous conduction mode which can restrict the open-loop bandwidth of the converter. This problem can complicate the control design for the load voltage regulation and conversely, impact on the stability of the closed-loop system. To remove this positive zero and improve the dynamic performance, this paper aims to suggest a novel boost topology with a step-up voltage gain by developing the circuit diagram of a conventional boost converter.Design/methodology/approachUsing a transformer, two different pathways are provided for a classical boost circuit. Hence, the effect of the RHPZ can be easily canceled and the voltage gain can be enhanced which provides conditions for achieving a smaller working duty cycle and reducing the voltage stress of the power switch. Using this technique makes it possible to achieve a good dynamic response compared to the classical boost converter.FindingsThe observations show that the phase margin of the proposed boost converter can be adequately improved, its bandwidth is largely increased, due to its minimum-phase structure through RHPZ cancellation. It is suitable for fast dynamic response applications such as micro-inverters and fuel cells.Originality/valueThe introduced method is analytically studied via determining the state-space model and necessary criteria are obtained to achieve a minimum-phase structure. Practical observations of a constructed prototype for the voltage conversion from 24 V to 100 V and various load conditions are shown.

Modeling, design and control of a modified flyback converter with ability of right-half-plane zero alleviation in continuous conduction mode

For fuel cell applications, a module-integrated dc/dc converter with the isolation capability is an important part of a power distribution system. It increases the low input voltage of a fuel cell to a desire high voltage and behaves as an interface connection circuit. There are several isolated dc/dc converters for connecting a fuel cell module to a power load. Among them, Flyback converter is a good candidate and widely used for fuel cell applications, due to its simple structure; however, the internal dynamics of a Flyback converter involves a right-half-plane zero (RHPZ), resulting in its performance degradation. Hence, the open-loop gain margin of a Flyback converter is small and its open-loop phase margin is negative, leading to difficulties for development of a voltage-mode controller. The major objective of the article is to address the aforementioned problems and present a new approach for eliminating them. To this end, a modified Flyback topology with ability of the RHPZ elimination is suggested and analyzed in this study and also, the superior performance of the modified converter is demonstrated in comparison with a classical Flyback converter. Then, the dynamical model of the designed circuit is derived using the averaging method and the design rules are determined. In addition, the theoretical model of the developed converter is validated via simulations and experiments. To keep the load voltage of this topology at a fixed value and, show its good performance for industrial applications, the type-II/III controllers are designed and the obtained simulated and practical results are introduced.

Combined feedback–feedforward control of Ćuk CCM converter for achieving fast transient response

The Ćuk converters operating in continuous conduction mode (CCM) can be preferred in applications such as microprocessor power delivery and pulsed load because these circuits have advantages of being able to step up/down, a small number of power components, and low input/output current ripples. However, they show poor transient performance due to right-half-plane-zeros (RHPZs) in the closed-loop transfer function of the Ćuk CCM converter. To enhance the transient response, a combined feedback–feedforward control for the Ćuk CCM converter is proposed. The proposed control scheme comprises a feedback control signal based on a Lyapunov function and a duty-ratio feedforward control signal. A Lyapunov-function-based controller (LBC) achieves fast dynamic response even under large-signal variations from the operating point. The duty ratio feedforward controller (DFFC) is developed to predict the effect of the disturbances and compensate it, while alleviating the burden of LBC. The proposed control logic makes the closed-loop system of the Ćuk CCM converter globally exponentially stable and thus provides a fast transient response even under large-signal variations. To construct the proposed controller, the authors make use of the large-signal averaged model of the Ćuk CCM converter, and consider the parasitic elements. To verify the proposed control scheme, numerical simulations and experimental tests are conducted.

Dynamic Response and Stability Margin Improvement of Wireless Power Receiver Systems via Right-Half-Plane Zero Elimination

The series-series compensation topology is widely adopted in many wireless power transfer applications. For such systems, their wireless power receiver part typically involves a DC-DC converter with front-stage full-bridge diode rectifier, to process the high-frequency transmitted AC power into a DC output voltage for the load. It is recently reported that the current source nature of the series-series compensation will introduce right-half-plane (RHP) zeros into the small-signal transfer functions of the DC-DC converter of the wireless power receiver, which will severely affect the stability and dynamic response of the system. To resolve this issue, in this paper, it is proposed to adopt a different rectifier configuration for the system such that the input current to the DC-DC converter becomes controllable to eliminate the presence of RHP zeros of the small-signal transfer functions of the system. This rectifier can be applied to different wireless power receivers using the buck, buck-boost, or boost converters. As compared with the original wireless power receivers, the modified ones feature minimum-phase characteristics and hence ease the design of compensator. Theoretical and experimental results are provided. The comparative experimental results verify the elimination of the RHP zero, improved dynamic responses of reference tracking and against load disturbances, and a larger stability margin.

Analytical tuning of 2‐DOF smith predictor control scheme for DC‐DC boost converter: A process control perspective

AbstractStringent voltage regulation in a DC‐DC boost converter is a classical engineering problems in theory of power conversion. Voltage Mode Control (VMC) of boost converter is difficult for two principal reasons. First and foremost, of these two reasons, is the converter's non‐minimum phase (NMP) behavior that arises due to the presence of the dynamic right half plane zero (RHPZ) in control to output (c2o) transfer function in VMC. Second reason is the presence of parametric uncertainties* in converter during its continuous conduction mode (CCM) operation. This paper combines theory of smith predictor with boost converter for (i) analytically computing gains of PID controller, (ii) design of a low pass filter to deal with challenges posed by dynamic RHPZ. This two degrees of freedom (2‐DOF) control scheme is analytically derived as a function of the converter's parameters. Gains of PID controller, deduced in terms of circuit's parameter, are used in sequel for extensive simulation analysis of the converter's control loop. Results in this paper establish that the proposed 2‐DOF‐SP outperforms certain well known control schemes used in regulating output voltage and disturbance attenuation in boost converter.

Performance of MPPT-Based Minimum Phase Bipolar Converter for Photovoltaic Systems

The change in environmental conditions and dynamic loading distort the smooth and stable MPPT operation. Conventionally, boost and boost-derived converters are used for MPPT operations, which inherently display right half plane zero (RHPZ). The presence of RHPZ causes a transient undershoot and overshoot in the output voltages. A tradeoff between bandwidth and stability is another issue with such converters. In order to address these issues, a minimum-phase bipolar converter (MPBC) is proposed to facilitate the MPPT operation. The MPBC is derived by combining the Ćuk and SEPIC converters with some circuit modifications in both of them. These circuit modifications eliminate RHPZ from the proposed MPBC. Due to the minimum-phase behavior, the proposed MPBC can achieve high bandwidth with improved phase margin, which is required for the fast and stable MPPT operation. MPBC can operate at the high load current and provides wide operating ranges for the MPPT operation due to its buck and boost capabilities. The transient analysis of the proposed MPBC is carried out to compare its performance with the conventional bipolar converter. A 600-W scaled-down laboratory prototype is developed and implemented using Texas Instrument TMS320F28335 processor to validate the performance of the MPBC for photovoltaic systems.

Improved Controller and Design Method for Grid-Connected Three-Phase Differential SEPIC Inverter

Single-ended primary-inductor converter (SEPIC) based differential inverters (SEPIC-BDI) have received wide concerns in renewable energy applications due to their modularity, galvanic isolation, decreased power stages, continuous input current, and step up/down capability. However, its design still has several challenges related to component design, the existence of complex right half plane (RHP) zeros, and increased sensitivity to component mismatches. In this context, this paper presents an improved control and enhanced design method for the three-phase SEPIC-BDI for grid-tied applications. A generalized static linearization approach (SLA) is proposed to mitigate the low-order harmonics. It practically simplifies the control complexity and decreases the required control loops and sensor circuits. The mismatch between the SEPIC converters in each phase is highly mitigated due to the independent operation of the SLA in each phase and the output dc offset currents are reduced. The proposed enhanced design methodology modifies the SEPIC open-loop transfer function by moving the complex RHP zeros to the left half-plane (LHP). Therefore, a simple proportional-integral (PI) controller effectively maintains converter stability without adding higher-order compensators in the literature. Moreover, a straightforward integrator in the control loop eliminates the negative sequence harmonic component (NSHC) and provides a low computational burden. Simulations and experimental results based on 200V, 1.6 kW, 50 kHz prototype with silicon carbide (SiC) devices are provided to validate the effectiveness of the proposed work. The results show that the proposed controller and design method achieve pure output current waveforms at various operating points of the inverter and dc voltage variations.

Overshoot Damping and Dynamics Improvement in Wireless Power Transfer Systems via Receiver-Side Controller Design

Buck converters have been extensively used for output regulation in the receiver of series–series compensated wireless power transfer (WPT) systems. Nonetheless, there are two major challenges in the controller design of this class of WPT systems. First, due to the current-source nature and finite dc-link capacitance, a right-half-plane (RHP) zero exists in the WPT receiver, reducing its stability margin and causing limited system dynamics. Second, this RHP zero can cause an overshoot issue in the WPT system. Without proper treatment, this overshoot may largely increase the voltage/current stress of the system and even cause catastrophic failure. However, existing solutions to the above two issues suffer from long communication delays or significantly compromised output regulation, degrading system performance. In this article, the slow dynamics and the overshoot issue of the WPT system are elaborated in theory and a solution is proposed by adding a feedforward path of the dc-link voltage in the receiver's controller. No communication is involved in the proposed control method, and only trivial computation is added to the controller. The proposed method is examined on a WPT prototype. The experimental results show that the two issues of the WPT system can be simultaneously solved by the proposed method while the output regulation of the system is not compromised.

Hybrid Tuning of a Boost Converter PI Voltage Compensator by Means of the Genetic Algorithm and the D-Decomposition

In this paper the D-decomposition technique is investigated as a source of non-linear boundaries used with the Genetic Algorithm (GA) search of a PI voltage compensator gains of the boost converter operating in Continuous Conduction Mode (CCM). The well known and appreciated boost converter has been chosen as a test object due to its right-half plane zero in the control-to-output (c2o) voltage transfer function. The D-decomposition, as a technique relying on the frequency sweeping, clearly indicates not only the global stability but, in its extended version, regions satisfying the required gain (GM) and phase (PM) margins. Such results are in form of easy to interpret functions KI=f(KP). The functions are easy to convert to the GA constraints. The GA search, with three different performance indexes as the fitness functions, is applied to a control structure with time delays basing on identified c2o voltage transfer functions. The identification took place in an experiment and in simulation. Outcomes of the identification are compared to mathematically derived formula taking into account certain parasitics. A complete set of practically useful mathematical formulas together with their validation in simulation and experiment is included.

Design of a switched‐capacitor boost converter utilizing magnetic coupling with capability of right‐half plane zero elimination

The dynamic operation of the conventional boost converters is limited in the continuous conduction mode, due to the presence of at least one right-half plane (RHP) zero in their control transfer function which can limit the open-loop bandwidth of the converter. This problem complicates the control design for the output voltage regulation and conversely influences the closed-loop system stability. To cancel this problem, a new step-up boost converter using the magnetic coupling and the switched capacitor (SC) is presented. In the proposed converter the effect of the RHP zero can be successfully eliminated, the voltage transfer ratio can be enhanced and the circumstances are provided to reach a small operating duty cycle as well as stress reduction of the diodes and power switch. Using the averaging technique, the state-space model of the converter is analytically studied and the essential conditions are given for achieving a minimum-phase structure. Based on the mentioned advantage, a simple classical PI controller for the output voltage regulation is designed. To confirm the theoretical analysis of the proposed converter, simulations and practical results are presented. Also, the performance of the proposed converter is compared with the other boost converters without RHP zero.

Internal Model Power Synchronization Control of a PV-Based Voltage-Source Converter in Weak-Grid and Islanded Conditions

The power synchronization control strategy for grid-connected voltage-source converters (VSCs) provides an operation similar to synchronous machines. It is able to avoid the instability caused by a standard phase-locked loop in integration into weak grids. However, the non-minimum phase phenomenon in the developed dynamics places a fundamental limitation on the ac system's stability. This paper proposes a one-degree-of-freedom internal-model-based control methodology. It introduces a control approach to incorporate the dynamics of the system's nominal model in the control structure. It also rectifies the unwanted effects of the right-half plane zeros. The explicit incorporation of the model enhances the tracking capabilities of the controller in a PV-based VSC. Besides, this article shows that a single-loop of control will suffice to regulate active and reactive power. Validating results are generated via a hardware-in-the-loop system based on a Xilinx Zynq-7000 SoC field-programmable gate array (FPGA). Furthermore, experimental results are conducted for low-power prototyping to examine the satisfactory performance of the proposed control architecture.

ON Effect of Right-Half-Plane Zero Present in Buck Converters With Input Current Source in Wireless Power Receiver Systems

In wireless power receiver systems, the buck converter is widely used to step down the higher rectified voltage derived from the wireless receiver coil, to a lower output voltage for the immediate battery charging process. In this article, the presence and effect of the right-half-plane (RHP) zeros found in the small-signal inductor-current-to-duty-ratio and output-voltage-to-duty-ratio transfer functions of the buck converter in the wireless power receiver system on the control performance, are investigated. It is found and mathematically proved that the RHP zeros are introduced by the current source nature of the system attributed to the series-series compensation and finite dc-link capacitance. The RHP zero not only results in nonmonotonic open-loop dynamic response but also complicates the design of feedback control and causes potential closed-loop instability. Theoretical and experimental results are provided to validate the presence of the RHP zeros and their effect on open-loop and closed-loop dynamic responses.

Dynamic enhancement of interleaved step-up/step-down DC–DC converters using passive damping networks

In this paper, a passive damping network between two stages of a cascaded DC–DC boost/buck interleaved converter was proposed to enhance the dynamic behavior. By this damping network, the right-half plane zeros in converter’s transfer function are sufficiently departed from the left half-plane, which leads to more damped transient behavior. A frequency analysis illustrated the dynamic enhancement in the proposed converter. To validate the theoretical model under different related circumstances, experimental results are presented through implementing a prototype setup.

A novel strategy for indirect control of peak dc-link voltage of grid-connected qZS inverter fed through renewable energy sources

This paper presents a novel strategy to indirectly control the peak dc-link voltage (PDV) of grid-connected quasi-Z-source (qZS) inverter supplied with renewable energy sources (RES). The method is directed to indirectly determine and regulate the pulsating PDV through the qZS network capacitor voltages. The small signal model is developed by representing ac- and dc-sides separately. The ac-side control is designed with higher bandwidth to avoid interference from dc-side. The dc-side control utilizes shoot-through duty ratio to PDV transfer function and controller is designed to minimize the effect of its right-half-plane zero (RHPZ) characteristics. The gating signals are realized through maximum constant boost control in conjunction with one-sixth of third harmonic injection. The strategy is implemented through MATLAB/Simulink and is verified experimentally with real-time simulations (RTSs) in OPAL-RT.

A Critical analysis of Non-ideal Quasi Z Source Inverter considering with parasitic resistances

This paper describes the perfect small signal mathematical modeling of a non-ideal quasi-Z-source inverter (q-ZSI) by considering the parasitic resistances of capacitors and inductors. In this work, the detailed transfer function model of the system is derived mathematically by using state-space averaging method under continuous conduction mode (CCM). The deduced transfer function model exhibits the non-minimum phase of a system in the capacitor voltage-to-control transfer function due to the presence of Right-Half-Plane (RHP) zeros. The RHP zeros could impose a limitation on the controller design. Therefore, the effect of parasitic resistances of passive elements on system dynamics is analyzed with the frequency response plots such as Bode plot, Root locus and Pole-Zero maps. This analysis helps to frame the guidelines for selecting the pertinent values of passive components and their parasitic resistances. The system stability and dynamic response of the presented small signal model are compared with circuit model and validated in Mat lab/Simulink environment

A Critical Analysis of Non-ideal Quasi Z Source Inverter Considering with Parasitic Resistances

This paper describes the perfect small signal mathematical modeling of a non-ideal quasi-Z-source inverter (q-ZSI) by considering the parasitic resistances of capacitors and inductors. In this work, the detailed transfer function model of the system is derived mathematically by using state-space averaging method under continuous conduction mode (CCM). The deduced transfer function model exhibits the non-minimum phase of a system in the capacitor voltage-to-control transfer function due to the presence of Right-Half-Plane (RHP) zeros. The RHP zeros could impose a limitation on the controller design. Therefore, the effect of parasitic resistances of passive elements on system dynamics is analyzed with the frequency response plots such as Bode plot, Root locus and Pole-Zero maps. This analysis helps to frame the guidelines for selecting the pertinent values of passive components and their parasitic resistances. The system stability and dynamic response of the presented small signal model are compared with circuit model and validated in Mat lab/Simulink environment

Right-Half-Plane Zero Elimination of Boost Converter Using Magnetic Coupling With Forward Energy Transfer

Control-to-output transfer function of the classical boost converter in continuous conduction mode contains a right-half-plane (RHP) zero that limits its frequency response. In this paper, to eliminate this zero and enhance the dynamic performance, a forward path for energy transfer to output within the on interval of the power switch is provided using the magnetic coupling. This approach simply eliminates the RHP zero by introducing an inductor coupled to the boost inductor, a diode, and a capacitor into the classical boost topology. In addition, the provided forward path enhances the voltage gain, which makes it possible to achieve a smaller operating duty cycle and reduced voltage stress for the power switch in applications with large voltage conversion ratios. Using this approach does not complicate the control structure, and a traditional single-loop voltage control scheme can be used to regulate the output voltage. The proposed approach is analytically examined by obtaining the averaged state-space model of the resulting converter, and a criterion to eliminate the RHP zero is presented. Experimental results from an implemented laboratory prototype for 48- to 200-V voltage conversion and 100-W nominal power are provided.

New results on the robust stability of control systems with a generalized disturbance observer

AbstractA generalized disturbance observer‐based (GDOB) control system and its robust stability are studied in this paper. One feature of this new GDOB scheme is that an inverse of the nominal plant in the standard DOB is no longer required. Thus, it is applicable to both minimum‐phase (MP) and non‐minimum‐phase (NMP) plants. New conditions for robust stability are derived for two cases: plants with no right half plane (RHP) zero and plants with no RHP pole, which are in a perfect dual form. The duality reveals that the robust stability for a plant with RHP zeros is met when the Q‐filter has a sufficiently large constant. This is fundamentally different from well‐known results for a MP plant. The stability conditions indicate that the robustness against large uncertainties not only can be achieved by a well‐selected Q‐filter, but also by the reduction of mismatch between a compensated plant and a desired model. The obtained stability results provide guidelines for the control system design. This is illustrated by three examples.

Sliding Mode Control Based on Internal Model for a Non-minimum phase Buck and Boost Converter

This work presents the application of different schemes to control a non-minimum phase Buck-Boost converter. Three control schemes are used. The first controller presented is a PI controller, the second one is Sliding Mode Control and the third one is a combination of two control schemes, Internal Model Control and Sliding Mode Control. The controllers are designed from a Right-Half Plane Zero (RHPZ) reduced order model. The RHPZ model is converted, using Taylor approximation, in a First Order Plus Dead Time (FOPDT) model and after that, the controllers are obtained. The performance of the SMC-IMC is compared against to a PI controller and a SMC. The simulation results show that SMC-IMC improves the converter response, reducing the chattering and presenting better robustness for load changes

Fixed Switching Frequency Digital Sliding-Mode Control of DC-DC Power Supplies Loaded by Constant Power Loads with Inrush Current Limitation Capability

This paper proposes a digital sliding-mode controller for a DC-DC boost converter under constant power-loading conditions. The controller has been designed in two steps: the first step is to reach the sliding-mode regime while ensuring inrush current limiting; and the second one is to move the system to the desired operating point. By imposing sliding-mode regime, the equivalent control and the discrete-time large-signal dynamic model of this system are derived. The analysis shows that unlike with a resistive load, the boost converter under a fixed-frequency digital sliding-mode current control with external voltage loop open and loaded by a constant power load, is unstable. Furthermore, as with a resistive load, the system presents a right-half plane zero in the control-to-output transfer function. After that, an outer controller is designed in the z-domain for system stabilization and output voltage regulation. The results show that the system exhibits good performance in startup in terms of inrush current limiting and in transient response due to load and input voltage disturbances. Numerical simulations from a detailed switched model are in good agreement with the theoretical predictions. An experimental prototype is implemented to verify the mathematical analysis and the numerical simulation, which results in a perfect agreement in small-signal and steady-state behavior but also in a small discrepancy in the current limitation due a small propagation delay. Some efficient solutions have been proposed to mitigate the inrush current in the experimental results.