Proportional-integral Compensator Research Articles

Dynamic analysis and comparison of the performance of linear and nonlinear controllers applied to a nonlinear non-interactive and interactive process

<p>This article presents an in-depth dynamic analysis and comparative evaluation of three distinct control strategies—proportional-integral (PI) compensator, linear quadratic regulator (LQR), and sliding mode control (SMC)—applied to a nonlinear process in two configurations: non-interactive system (NIS) and interactive system (IS). The primary objective was to optimize the regulation of fluid levels in a dual-tank system subject to external disturbances and varying operational conditions. The process dynamics were initially modeled using nonlinear differential equations, which were subsequently linearized to facilitate the design of the PI and LQR controllers. The PI compensator design was rooted in state-space representation and was tuned using the Ziegler-Nichols method to achieve the desired transient and steady-state performance. The LQR design employed optimal control theory, minimizing a quadratic cost function to derive the state feedback gain matrix, ensuring system stability by shifting the eigenvalues of the closed-loop system matrix into the left half of the complex plane. In contrast, the SMC leveraged the full nonlinear dynamics of the process, establishing a sliding surface to drive the system states toward a desired trajectory with robustness against model uncertainties and external disturbances. The SMC's performance was evaluated by analyzing the existence and stability of the sliding mode using the derived switching laws for the actuation signal. The comparative study was conducted through simulations in MATLAB/Simulink environments, where each controller's performance was assessed based on transient response, robustness to disturbances, and computational complexity. The results indicate that while the PI compensator and LQR provide satisfactory performance under linearized assumptions, the SMC demonstrates superior robustness and precision in managing the nonlinearities inherent in the IS configuration. This comprehensive analysis underscores the critical trade-offs between simplicity, computational overhead, and control efficacy when selecting appropriate control strategies for nonlinear, multi-variable processes.</p>

Simplified Nonlinear Current-Mode Control of DC-DC Cuk Converter for Low-Cost Industrial Applications.

This paper presents a robust nonlinear current-mode control approach for a pulse-width modulated DC-DC Cuk converter in a simple analog form. The control scheme is developed based on the reduced-state sliding-mode current control technique, in which a simplified equivalent control equation is derived using an averaged power converter model in continuous conduction mode. The proposed controller does not require an output capacitor current sensor and double proportional-integral compensators as in conventional sliding-mode current controllers; thus, the cost and complexity of the practical implementation is minimized without degrading the control performance. The simplified nonlinear controller rejects large disturbances, provides fast transient response, and maintains a constant switching frequency. The nonlinear control scheme is developed using an analog circuit with minimal added components, which is suitable for low-cost industrial applications. The control law derivation, control circuit design, controller gains selection, and stability analysis are provided. The proposed control methodology is verified via simulating the closed-loop nonlinear power converter model in MATLAB/SIMULINK under abrupt changes in load current and input voltage. The simulation results show that the proposed control scheme provides robust tracking performance, a low percentage overshoot, fast transient response, and a wide operating range. The maximum percentage overshoot and settling time of the closed-loop power converter response during line disturbance are 5.6% and 20 ms, respectively, whereas the percentage overshoot and settling time during load disturbance are 2.8% and 15 ms, respectively.

Chaos Elimination for a Buck Converter Using the Multi-Objective Grey Wolf Optimiser

Abstract A wide variety of nonlinear phenomena, such as bifurcation and chaos, have been observed in power electronics converters. Much research has been conducted on these behaviours in different converter topologies. The buck converter is known to exhibit chaotic behaviour in a wide parameter range, giving rise to unstable behaviours depending on the circuit parameters values. This paper investigates this bifurcation behaviour by varying the parameters of a voltage PI (Proportional Integral) controlled buck converter operating in continuous conduction mode, using a continuous-time model and constant frequency control signal. Furthermore, a novel and improved version of the PI compensation technique, designed using the multi-objective grey wolf optimiser (MOGWO), is proposed to stabilise the buck converter from chaotic state to periodic orbit.

Elimination of the Voltage Output Fluctuations of a Vienna Active Rectifier-I Integrated Under Unsymmetrical Faults Based Wind Power Plant

In this article, a fault ride-through controller is proposed with the use of proportional-integral compensator and electronic sensors for riding-through alternative current faults in a wind power plant collection grid connected with a permanent magnet synchronous generator. Three parallel-connected wind energy conversion units supplying a direct current (DC) load are simulated and discussed. It is found that the sub-module will directly adjust the transmission of power and protect the generator from overheating, which can occur due to voltage fluctuation. Furthermore, a DC voltage controller is designed to ensure a stable closed-loop system, and the system stability is verified using bode plots. The dynamic response of the system is demonstrated with the use of power simulator (PowerSim, Rockville, USA) software to verify the reliability of the proposed rectifier topology.

Stability Analysis of the Dual Half-Bridge Series Resonant Inverter-Fed Induction Cooking Load Based on Floquet Theory

Induction heating (IH) applications aided power electronic control and becomes most attractive in recent years. Power control plays a vital role in any IH applications in which the stability of the converter is still a research hot spot due to variable frequency operation. In the proposed work, the stability of the converter is carried out based on the Floquet theory for dual-frequency half-bridge series inverter-fed multiload IH system. The dynamic behaviour of the converter is analyzed by developing a small-signal model of the converter. The system with a dynamic closed-loop controller results in poles and zeros lying outside the unit circle, which has poor closed-loop stability and up-down glitches in the frequency response plot. Hence, a proportional-integral (PI) compensator is used to mitigate the said issue, which results in a better response when compared with the open system and works satisfactorily. However, the system becomes unstable when the frequency is varied and the system also possesses a poor time domain response. Hence, the values of the controller gain are optimized with the Floquet theory, which is based on the Eigenvalues of the time domain model. For the optimized gains, the system possesses better stability for the variations in the switching frequency (20 kHz to 24 kHz), and also, the frequency response of the system is better with minimum time domain specifications. The performance of the system is simulated in MATLAB, and the response is noted for various switching frequencies in open loop, with a PI compensator, and with an optimized PI compensator. The output power is varied from 500 W to 18 W at load 1 and 250 W to 9 W at load 2. It is noted from the output response that the rise time is 0.0085 s, the peak time is 0.0001 s, and the peak overshoot is 0.1% with minimum steady-state error. Furthermore, the IH system is validated using a PIC16F877A microcontroller with the optimized PI controller, and the thermal image is recorded using a FLIR thermal imager.

Precise Luminous Flux and Color Control of Dimmable Red-Green-Blue Light-Emitting Diode Systems

A generic red, green, and blue (RGB) LED system encompasses complex interactions of power, heat, light, and color, which pose a major challenge for achieving precise control over luminance and color-mixing in high-quality lighting applications. In this article, new nonlinear empirical models of a practical RGB LED system with closed-loop control are formulated. They enable precise prediction of luminous flux and color coordinates by using the three distinct reference voltages as the control variables for independent current regulation across the RGB LED strings. The proposed empirical models are experimentally verified by using a hardware prototype of a dc–dc single-inductor three-output LED driver with proportional–integral compensators and time-interleaving control scheme. The measured values of luminous flux and color coordinates agree closely with the predicted values from the models.

Control transition mode from voltage control to MPPT for PV generators in isolated DC microgrids

The integration of photovoltaic (PV) power sources on a large scale into grid-tied and islanded solutions is now a reality. Despite the fluctuating characteristics of solar energy, the direct current (DC) nature of PV sources is highly compatible with DC microgrids compared with AC solutions. However, as more PV sources are being installed, challenges related to the control of DC microgrids are also increasing, especially for islanded applications. To ensure an appropriate transition from the maximum power point to DC bus voltage regulation of DC microgrids, novel control strategies must be designed, and this aspect is particularly critical when these grids operate without energy storage systems. We therefore propose a new control strategy for a PV generator for islanded DC microgrids without storage systems. Our approach allows for smooth switching from the maximum power point mode to the voltage control regulation mode (V control) when the available PV power is excessive, thus limiting the generated PV power and returning to maximum power point operation when all the available power is required. This allows us to control a DC microgrid without a storage system and provides a new alternative that offers a cost-effective solution for rural and deprived regions. Our solution combines the maximum power point tracking algorithm with a proportional integral compensator for V control and minimises undervoltage/overvoltage problems in the DC bus. The behaviour of the isolated DC microgrid under different conditions, for example in the case of transitions, perturbations, and different types of loads, is also studied and verified. The performance of the proposed control strategy is confirmed by several simulation and experimental tests.

Simplified Control Structure of Fuzzy Logic and Kalman Filter for Induction Motor Drive

The paper deals with the utilization of Kalman filter and fuzzy logic control in induction motor drive with direct torque control (DTC). In order to lower ripple of stator current vector in DTC drive, pulse width modulation technique with high switching frequency is applied. However, the performance of the DTC also depends on the accuracy of both stator resistance and stator current vector. In the paper, the stator resistance and stator current components are assumed to be distorted by Gaussian noises. In order to reduce the effect of noises especially at low speed and very low speed regions, a simple Kalman filter is applied for filtering current components, and fuzzy logic theory is used to increase the flexibility of proportional-integral (PI) compensator in the speed controller of the drive structure. Simulations are implemented in conditions of high-level noises of stator current and stator resistance, and a wide range of load torque. An ITAE-based criterion is utilized to evaluate the performance of drive structures. Results confirmed the expected dynamic properties of the proposed drive structure. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

Robust Passivity-Based Control Scheme for 1.26 KW Proton Exchange Membrane Fuel Cell Under Temperature and Load Variations

Abstract The model-based system engineering (MBSE) is based on simplified mathematical models that reflect the dynamic behavior of the systems. These are most of the time nonlinear and need control schemes taking in consideration of exogenous perturbations. The main contribution of this article is the design of a robust passivity-based sliding mode control scheme for a 1.26 KW proton exchange membrane fuel cell (PEMFC). The uncertainties considered in this article are temperature and load variation. The fuel cell (FC) reference current is adapted in a linear transformation by introducing a temperature sensor. This information is present in most of commercial PEMFC and not used in the closed-loop system. Moreover, the proposed approach cancels the errors caused by the average approach modeling and the observer (the part, which replaces current sensor). Robustness against load variation is assured via a proportional integral compensation of the incremental value of load resistance. The performance of the controller and the effectiveness of our approach is shown through the simulation with matlab-simulink software.

A 6.78 MHz Single-Stage Wireless Power Transmitter Using a 3-Mode Zero-Voltage Switching Class-D PA

A 6.78 MHz single-stage transmitter (TX) using a reconfigurable regulating class-D power amplifier (PA) for wireless power transfer (WPT) applications is presented. Based on a 3-mode modulation scheme, the TX achieves power regulation and transmission with only one power stage. A discontinuous-conduction-mode (DCM) zero-voltage switching (ZVS) scheme is adopted to reduce switching loss. A control loop is set to regulate the output voltage of the WPT receiver (RX) by automatically adjusting the transmitting power. With dual-loop control and a proportional-integral (PI) compensation scheme, the loop achieves tight regulation and fast response. The controller is implemented digitally to benefit from the AirFuel <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">®</sup> embedded Bluetooth communication link. The PA was fabricated with a high-voltage 0.35 μm CMOS process, and the digital controller with a standard 0.35 μm CMOS process, respectively. Measurement results show that the output voltage of the RX was correctly regulated to 11.7 V under a load change of 50mA to 500mA, and the WPT system could deliver a maximum power of 7.3 W to the RX over a distance of 4.0 cm, and achieved TX to RX peak efficiency of 57.3%.

Comprehensive Design and Implementation of a Modified Synchronous Reference Frame Vector Control Method for High Power Three Phase PWM Rectifier

Three-phase PWM rectifiers have been used widely due to their benefits such as unity power factor, sinusoidal input current and also low-ripple output DC voltage. Among control methods, vector control method in the synchronous reference frame through proportional–integral compensators directly controls the input current. However, the effect of non-ideal grid voltage like harmonic polluted voltage was not investigated. In this paper, firstly, comprehensive design and digital implementation of modified vector control method with simple structure is proposed. Secondly, the effect of the grid voltage distortion is considered and a solution based on resonant controllers is also proposed. Thirdly, all of the designs and dynamic assessments of the overall control system are performed in z domain to consider overall delay, comprehensively. Finally, extend simulations and experimental verifications on a high power 30 kW rectifier are done. The results not only show the significant decrease of THD value of the input current but also, simple structure for digital implementation is verified. All of these validate the effectiveness of the proposed control methods and design procedure.

Stability Effect of Control Weight on Multiloop COT-Controlled Buck Converter With PI Compensator and Small Output Capacitor ESR

Multiloop constant on-time (COT) controlled buck converter uses two weight resistors for sensing inductor current and detecting output voltage in its inner loop. When an output capacitor with a small equivalent series resistance (ESR) is employed, the converter will suffer the risk of instability due to different weight settings of inductor current and output voltage using a proportional-integral (PI) compensation gain in the outer voltage loop. However, no attention has been paid for their stability effects, which are important for designing the inner loop and outer voltage loop. To address these issues, a piecewise linear model is established for multiloop COT-controlled buck converter. Circuit parameter-related bifurcation behaviors and control weight-related dynamical distributions are explored to demonstrate these stability effects. Furthermore, by deriving an approximate discrete model, a control weight-related stability criterion is expressed explicitly, from which stability boundaries for dividing the normally stable and abnormally unstable operation parameter regions are thereby yielded. Besides, control weight-related transient performances under different circuit parameter settings are analyzed. Finally, PSIM circuit simulations and hardware circuit experiments verify the theoretical analysis well.

Small Signal Modeling and Design Analysis for Boost Converter With Valley V 2 Control

Recently, it has been reported that valley V 2 control can be applied to boost converters. However, the actual transient performance and design methodology are not clear due to insufficient knowledge about its small signal model. In this article, a small signal model of valley V 2 controlled boost converter is proposed by combining average method and sampled-data method, which is simple and accurate to half the switching frequency. Then, design guidance focused on dynamical performance and stability is provided. Moreover, compensator for the valley V 2 controlled boost converter is discussed. The proposed small signal model and design guidelines are verified with experimental results. Results first indicate that for the valley V 2 controlled boost converter, the inductor current information is contained in the control loop because of the discontinuous output voltage ripple, which is totally different from that in V 2 controlled buck converter. Also, the equivalent series resistance as well as the duty ratio will affect the transient performance to some extent. Moreover, just by using the simple proportional integral compensator, the valley V 2 controlled boost converter can be compensated, and it possesses fast transient performance. As for the stability issues, the ramp compensation is useful to eliminate the instability, improving the stability margin.

Model Predictive Control of an Indirect Matrix Converter with Active Damping Capability

In this paper, a model predictive control (MPC) scheme is proposed to control indirect matrix converter (IMC), which is used for three phase-to-three phase direct power conversion. IMC is composed of back-to-back connected conventional current source rectifier (CSR) and voltage source inverter (VSI) without any intermediate energy storage component between them. The aim in the control of CSR side is generally to have unity power factor with relatively low total harmonic distortion (THD) and the aim in the control of VSI side is to be able to synthesize sinusoidal load currents with desired peak value and frequency. Imposed source current MPC technique in abc frame is used for the rectifier side and cost function evaluation process calculates three-phase supply current errors respect to its reference. Supply currents for next sampling interval are predicted using the discrete form of input filter model. The peak value of sinusoidal supply current reference is generated from the error in load current space vector using a PI compensator. This generated reference is synchronized with supply voltage by the multiplication of Proportional-Integral (PI) compensator output value and instantaneous three-phase supply voltage. An active damping technique, which does not require to select an optimum value for fictitious damping resistor, is also included in the proposed control scheme in order to mitigate the resonance phenomenon of lightly damped input LC filter to suppress the higher order harmonics in supply currents. Load currents with desired peak and frequency are also obtained by imposing sinusoidal currents in abc frame. The cost function for VSI stage evaluates output load current error. Load current predictions are obtained by using the discrete form of load model. These two cost functions are combined into a single cost function without any weighting factor since both error terms are in the same nature. The switching state that minimizes this pre-defined cost function among the 24-valid switching combinations of IMC is selected and applied to converter. The proposed model predictive control with active damping method shows good performance in terms of THD levels in supply currents even at low current demands from supply side. The proposed model predictive control method combined with active damping strategy guarantees unity power factor operation and draws sinusoidal load currents at desired peak and frequency.

Disturbance Observer-Based Fuzzy Adapted S-Surface Controller for Spatial Trajectory Tracking of Autonomous Underwater Vehicle

A new adaptive robust control scheme combining the disturbance-observer-based control (DOBC) with fuzzy adapted S-Surface control is proposed for trajectory tracking control of autonomous underwater vehicle. The main contribution of the proposed method is that control configuration does not require the bounds of uncertainty of the vehicle to be known and disturbances effect can be estimated and rejected. The proposed control law is mainly composed of three parts: a feed forward control along with disturbance estimator, S-Surface control and single input adaptive fuzzy proportional-integral (PI) compensator. The nominal feed forward controller specifies desired closed loop dynamics with extravagance from known preferred acceleration vector. Meanwhile, the disturbance observer and adaptive fuzzy PI control term to compensate the unknown effects that are disturbances and unmodeled dynamics. An additional term as S-Surface control assures fast convergence due to a nonlinear expression in to surface and also enhance stability of the underwater vehicle in oceanic environment. Moreover, the disturbance observer enhances the robustness performance of the adaptive fuzzy system for disturbances that cannot be modeled by fuzzy logic. The stability of closed loop controlled system is proven to be guaranteed according to Lyapunov theory. Finally, numerical simulation results illustrate the effectiveness and robustness of the proposed control method.

Design method considering the frequency band of the disturbance in the DC link voltage control system of hybrid electric vehicle driving systems

AbstractDC link voltage variable systems with DC/DC converter are used in hybrid electric vehicles for improving the power of the system by boosting the DC link voltage. Voltage feedback control using only proportional compensator has been proposed as a control method for the DC/DC converter. The control system can be easily designed, but there is a possibility that a steady‐state error occurs in the DC link voltage. In this paper, a proportional integral compensator is proposed to eliminate the steady‐state error of the DC link voltage in DC link voltage feedback controllers. In addition, when designing the gain of the compensator, the frequency band of the disturbance is considered. The proposed method is verified through experiments on the downsizing model.

An Instantaneous Event-Triggered Hz–Watt Control for Microgrids

This paper proposes a distributed control scheme to compensate for droop-induced frequency deviations in autonomous microgrids. In this scheme, no extra direct frequency control and proportional-integral compensation are employed to remove the frequency deviations; that is, the deviations are compensated instantaneously. To reduce the communication burden, the scheme is then equipped with a need-based (event-triggered) data exchange strategy. An event-triggering mechanism is introduced, which highly reduces the amount of communications in both transient and steady-state stages and ensures that the intervals between consecutive communication instants are positive (i.e., the system is Zeno-free). Stability and equilibrium analyses of the resultant system considering the whole system dynamics are provided, as well. Effectiveness of the proposed controller for different cases is verified by simulating a microgrid in MATLAB/SimPowerSystems software environment.

Improving DC Microgrid Dynamic Performance Using a Fast State-Plane-Based Source-End Controller

DC microgrids interconnect load-end converters and distributed renewable energy sources within efficient and reliable networks that can operate independently from the main grid. When load-side converters tightly regulate their output voltages, they behave as constant power loads (CPLs) from the standpoint of the source-end converters. CPLs can cause instability within the network, including large voltage drops or oscillations in the dc bus during transients, which can lead to the collapse of the dc bus. Traditionally, the stability of CPL-loaded dc microgrids relies on the addition of passive elements, usually leading to increase in dc-bus capacitance. In these scenarios, source-end converter controllers are usually linear dual-loop proportional-integral compensators, which exhibit a limited dynamic response. State-plane-based controllers have been proposed to improve the dynamic response of stand-alone power converters loaded by CPLs. However, the operation of these converters in the context of a microgrid, where they interact with other converters of slower response, has not been studied thoroughly. This work proposes the use of a fast state-plane controller to replace one of the system's source-side controllers in order to improve three aspects of the microgrid operation: resiliency under CPL's changes, load transient voltage regulation, and voltage transient recovery time. Since the converter is operating within a microgrid, the controller incorporates a traditional droop rule to enable current sharing with the rest of the converters of the network. The system performance improvement is analyzed mathematically for a linear model, and a parametric analysis is performed for a more detailed model. Simulations and experimental results of a microgrid with three converters feeding a CPL are provided for different transients.

Adaptive Backstepping Control Design for Uncertain Non-smooth Strictfeedback Nonlinear Systems with Time-varying Delays

This paper is concerned with the problem of adaptive neural tracking control for uncertain non-smooth nonlinear time-delay systems with a class of lower triangular form. Based on Filippov’s theory, the bounded stability and asymptotic stability are extended to the ones for the considered systems, which provides the theory foundation for the subsequent adaptive control design. In the light of Cellina approximate selection theorem and smooth approximation theorem for Lipschitz functions, the system under investigation is first transformed into an equivalent system model, based on which, two types of controllers are designed by using adaptive neural network (NN) algorithm. The first designed controller can guarantee the system output to track a target signal with bounded error. In order to achieve asymptotic tracking performance, the other type of controller with proportional-integral(PI) compensator is then proposed. It is also noted that by exploring a novel Lyapunov-Krasovskii functional and designing proper controllers, the singularity problem frequently encountered in adaptive backstepping control methods developed for time-delay nonlinear systems with lower triangular form is avoided in our design approach. Finally, a numerical example is given to show the effectiveness of our proposed control schemes.

A Novel Current Predictive Control Based on Fuzzy Algorithm for PMSM

The fast and stable current inner loop in the permanent-magnet synchronous motor (PMSM) control system is the key factor that ensures the torque control performance of the motor. The deadbeat model predictive control strategy can achieve fast dynamic response, but it depended on the accurate mathematical model of the motor. When the model parameter in the predictive controller has mismatched with real system, the static error or oscillations will occur in the steady state. Therefore, a novel current predictive control based on the fuzzy algorithm is proposed in this paper. The novel control strategy contained a predictive controller, a proportional-integral (PI) compensation link, a magnetic flux observer, and a fuzzy controller. According to the operation state of the motor and the model parameter mismatch of the controller, the fuzzy algorithm can adjust the effect of compensation link by weight coefficient in real time. The dynamic performance of the proposed method is guaranteed compared with the traditional deadbeat predictive current control based on the space vector pulsewidth modulation (SVPWM). When the model parameter mismatch of controller is occurred, the weight of the PI compensation link is enhanced, and the static error or oscillation of the motor system can be eliminated.