Comparative Study of Controller Scheme and Tuning Methods

For all first order plus time delay (FOPTD) systems, a fractional order PI (FOPI) or a traditional integer order PID (IOPID) controller can be designed to fulfill three design specifications: gain crossover frequency, phase margin, and a flat phase constraint simultaneously. In this paper, a guideline for choosing feasible or achievable gain crossover frequency and phase margin specifications, and a new FOPI/IOPID controller synthesis are proposed for all FOPTD systems. Using this synthesis scheme, the complete feasible region of the gain crossover frequency and phase margin can be obtained and visualized in the plane. With this region as the prior knowledge, all combinations of the phase margin and gain crossover frequency can be verified before the controller design. Only if the combination is chosen from this achievable region, the existence of the stabilizing and desired FOPI/IOPID controller design can be guaranteed. Especially, it is interesting to compare the areas of these two feasible regions for the IOPID controller and the FOPI controller. This area comparison reveals, for the first time, the potential advantages of one controller over the other in terms of achievable performances. As a basic step, a scheme for finding the stabilizing region of the FOPI/IOPID controller is presented first, and then a new scheme for designing a stabilizing FOPI/IOPID controller satisfying the given gain crossover frequency, phase margin and flat phase constraint is proposed in details. Thereafter, the complete information about the feasible region of gain crossover frequency and phase margin is collected. This feasible region for the FOPI controller is compared with that for the traditional IOPID controller. This area comparison shows the advantage of the FOPI over the traditional IOPID clearly. Simulation illustration is presented to show the effectiveness and the performance of the designed FOPI controller comparing with the designed IOPID controller following the same synthesis in this paper.

This paper displays an simple method for identification of controller for wind based Quadratic Boost Converter Inverter system. India, being the fourth largest wind power generator has attracted numerous researchers towards the improvement of wind energy conversion system. This paper also presents improved controller techniques for a Permanent Magnet Synchronous Generator (PMSG) coupled with Cascaded Quadratic Boost Converter (QBC) and Space Vector Modulation Inverter (SVMI). The digital simulation and execution of PMSG based wind turbine along with QBC and SVM Inverter is presented in a closed loop system. The performance of closed loop system is realized using Proportional Integral (PI) and Fractional Order Proportional Integral (FOPI) controllers. Initially, the AC power from PMSG wind turbine is rectified to DC using rectifier circuit. The DC power from the bridge rectifier is then boosted to the required level using quadratic boost converter. The output from QBC is then given to the SVM inverter. The closed loop investigations are carried with PI and FOPI controllers. The simulation results of both PI and FOPI controlled QBC are compared. The outcome of FOPI controller represents that the steady state error and settling time are reduced when compared to PI controlled closed loop Quadratic Boost Converter. The overall Matlab/simulink model is applied to undergraduate/postgraduate course as a educational tool and assessed thoroughly.

This paper proposes a low complexity control scheme for voltage control of a dynamic voltage restorer (DVR) in a three-phase system. The control scheme employs the fractional order, proportional-integral-derivative (FOPID) controller to improve on the DVR performance in order to enhance the power quality in terms of the response time, steady-state error and total harmonic distortion (THD). The result obtained was compared with fractional order, proportional-integral (FOPI), proportional-integral-derivative (PID) and proportional-integral (PI) controllers in order to show the effectiveness of the proposed DVR control scheme. A water cycle optimization algorithm (WCA) was utilized to find the optimal set for all the controller gains. They were used to solve four power quality issues; balanced voltage sag, balanced voltage swell, unbalanced voltage sag, and unbalanced voltage swell. It showed that one set of controller gain obtained from the WCA could solve all the power quality issues while the others in the literature needed an individual set of optimal gain for each power quality problem. To prove the concept, the proposed DVR algorithm was simulated in the MATLAB/Simulink software and the results revealed that the four optimal controllers can compensate for all the power quality problems. A comparative analysis of the results in various aspects of their dynamic response and %THD was discussed and analyzed. It was found that PID controller yields the most rapid performance in terms of average response time while FOPID controller yields the best performance in term of average % steady-state error. FOPI controller was found to provide the lowest THD percentage in the average %THD. FOPID did not differ much in average response from the PID and average %THD from FOPI; however, FOPID provided the most outstanding average steady-state error. According to the CBMA curve, the dynamic responses of all controllers fall in the acceptable power quality area. The total harmonic distortion (THD) of the compensated load voltage from all the controllers were within the 8% limit in accordance to the IEEE std. 519-2014.

The main objective of this paper is to allow renewable energy sources (RES) to actively participate within hybrid microgrid by proposing a new control system based on fractional order proportional integral (FOPI) controller. Fractional order proportional integral controller is a classical proportional integral (PI) in which the integral part is a fraction instead of integer numbers. The paper introduces a hybrid photovoltaic (PV), wind turbine and battery storage system connected to a three-phase grid. Three types of controller are considered and compared for a hybrid renewable energy system (HRES), namely, FOPI, PI, and the fractional order integral control (FIC). For the PV resource, maximum power point tracking (MPPT) controller was designed using the incremental conductance plus integral regulator technique. A DC/DC boost converter was utilized to connect the renewable energy resources to a point of common coupling. MATLAB/Simulink is adopted to perform the simulation results of the developed HRES. The results show that the FOPI controller outperforms other controllers under several operating conditions. The paper also includes experimental results from a prototype real scale.

Design proportional–integral–derivative (PID) controllers for unstable first-order plus time delay (FOPTD) and unstable second-order plus time delay (SOPTD) systems with/without a zero is proposed by direct synthesis method. For unstable FOPTD system, a series PID controller is considered. The derivative time of series PID controller is made equal to 0.5 times time delay to cancel the numerator zero with the pole of the loop transfer function (product of process transfer function and controller transfer function). The reduced characteristic equation is compared with the desired characteristic equation to get PI settings. The conventional PID controller parameters are obtained from series PID controller. For unstable SOPTD systems, PID controller with a first-order lead/lag compensator is considered. The controllers designed by the proposed method are implemented on various transfer function models, nonlinear model equations of bioreactor and on inverted pendulum (IP) set-up to show the efficiency of the proposed method. The performance of the proposed controllers is compared with the controllers reported in the recent literature in terms of IAE. The robustness of the controller is determined by the maximum magnitude of sensitivity function, phase margin and gain margin.

In this paper, two fractional order proportional integral controllers are designed to improve the performance and robustness for a class of fractional order systems which can better model many real systems such as bioengineering systems. For comparison between the fractional order proportional integral controllers and the traditional integer order PID (IOPID) controller, the IOPID controller is also designed following the same proposed tuning specifications. Unfortunately, the designed IOPID controller can not meet the required spcification. However, the designed fractional order proportional integral (FOPI) and fractional order [proportional integral] (FO[PI]) controllers both can satisfy all the three specifications proposed. From the simulation results presented, it can be seen that both the FOPI and FO[PI] controllers designed work efficiently. Furthermore, we can observe that the FO[PI] controller outperforms the FOPI controller following the proposed design schemes for the fractional order systems considered.

This paper proposes the design of gray wolf optimizer (GWO) algorithm-based fractional order proportional integral (FOPI) controller for power factor correction (PFC) using interleaved dc–dc single ended primary inductance converter converter with improved performance characteristics such as speed, accuracy, and stability. The detailed analysis and modeling of the proposed converter are presented. The optimal parameters of FOPI controller are obtained using GWO algorithm to improve the speed of response of the system. FOPI controller provides better performance in terms of robustness and stability since it has one more adjustable parameter than the conventional proportional integral (PI) controller. The cascade control strategy is implemented for the proposed converter with GWO-based FOPI controller as inner current and outer voltage controllers for PFC and load voltage regulation. The performance characteristics of the proposed system are analyzed and compared with conventional and other optimization techniques using MATLAB/Simulink software. A prototype of the proposed converter controlled by TMS320C2000 microcontroller for an output power of 200 W is tested and validated with the simulation results. The proposed system is used for powering devices like robots in critical applications such as military, space craft, etc., where stability, speed, and accuracy are major concerns.

The self-excited induction generator (SEIG) is widely applied in the wind energy conversion system (WECS) to enhance power generation. The power generation from WECS is varied in terms of varying wind speed. Hence, to improve the working of SEIG-based WECS, the multi-stage coati optimized proportional integral (CPI) fractional order proportional integral derivative (FOPID) controller is proposed in this work. The proposed coati optimized proportional integral - fractional order proportional integral derivative controls the SEIG’s grid side converter and generator side converter. The coati optimization algorithm optimizes the controller parameters of a proposed multi-state controller. The proposed CPI-FOPID controls both the voltage at the grid side converter and the current at a generator side converter. Moreover, the pitch angle of the wind turbine (WT) is controlled by the fuzzy-based tilt integral derivative (F-TID) controller. The proposed work will be implemented on the Matlab/Simulink platform, and the THD of 0.63% has proven the efficacy of the proposed methodology.

This study aims to determine the improvement effect on the delay margin if fractional-order proportional integral (PI) controller is used in the control of a single-area delayed load frequency control (LFC) system. The delay margin of the system with fractional-order PI control has been obtained for various fractional integral orders and the effect of them has been shown on the delay margin as a third controller parameter. Furthermore, the stability of the system that is either under or over the delay margin is examined by generalized modified Mikhailov criterion. The stability results obtained have been confirmed numerically in time domain. It is demonstrated that the proposed controller for delayed LFC system provides more flexibility on delay margin according to integer-order PI controller.

The main causes of frequency instability or oscillations in islanded microgrids are unstable load and varying power output from distributed generating units (DGUs). An important challenge for islanded microgrid systems powered by renewable energy is maintaining frequency stability. To address this issue, a proportional integral derivative (PID) controller is designed in this article. Firstly, islanded microgrid model is constructed by incorporating various DGUs and flywheel energy storage system (FESS). Further, considering first order transfer function of FESS and DGUs, a linearized transfer function is obtained. This transfer function is further approximated into first order plus time delay (FOPTD) form to design PID control strategy, which is efficient and easy to analyze. PID parameters are evaluated using the Chien-Hrones-Reswick (CHR) method for set point tracking and load disturbance rejection for 0% and 20% overshoot. The CHR method for load disturbance rejection for 20% overshoot emerges as the preferred choice over other discussed tuning methods. The effectiveness of the discussed method is demonstrated through frequency analysis and transient responses and also validated through real time simulations. Moreover, tabulated data presenting tuning parameters, time domain specifications and comparative frequency plots, support the validity of the proposed tuning method for PID control design of the presented islanded model.

The first- and second-order fractional-order proportional integral (FOPI) controllers based on the Al-Alaoui operator and the continued fraction expansion method are designed and applied to the closed-loop control system of a resonant optical gyro. The phase margin method is used to tune the control parameters. The characteristics of the unit step responses of the integer order proportional integral (IOPI) and the FOPI controllers are calculated and compared. Responses to perturbations at different positions of the closed-loop control system are simulated. Results show that for the resonant optical gyro, the FOPI closed-loop control system has much better unit-step-response performance and noise-resistance ability than the IOPI control system, which is important for improving the dynamic response characteristics and the robustness of the gyro’s feedback system and enhancing the detection ability of the gyro. Experiments on a resonant optical gyro experimental system also verify the advantages of the FOPI controller in step response and bias stability.

ABSTRACTThe use of robust design techniques such as the one based on and for tuning proportional integral (PI) and proportional integral derivative (PID) controllers have been limited to address a small set of processes. This work addresses the problem by considering a wide set of possible plants, both first- and second-order continuous-time systems with time delays and zeros, leading to PI and PID controllers. The use of structured uncertainties to handle neglected dynamics allows to expand the range of processes to be considered. The proposed approach takes into account the robustness of the controller with respect to these structured uncertainties by using the small-gain theorem. In addition, improved performance is sought through the minimisation of an upper bound to the closed-loop system norm. A Lyapunov–Krasovskii-type functional is used to obtain delay-dependent design conditions. The controller design is accomplished by means of a convex optimisation procedure formulated using linear matrix inequalities. In order to illustrate the flexibility of the approach, several examples considering recycle compensation, reduced-order controller design and a practical implementation are addressed. Numerical experiments are provided in each case to highlight the main characteristics of the proposed design method.

Frequency instability of an isolated microgrid (IMG) often arises due to load variations and uncertain power outputs of renewable sources. This contribution addresses the frequency instability issue by designing a Padula and Visioli (PV) tuned proportional-integral-derivative (PID) controller for IMG. The considered IMG model is novel due to the integration of eco-friendly generation sources, including a biogas turbine generator (BTG) and a biodiesel engine generator (BEG), along with other distributed generation units (DGUs) and energy storage devices (ESDs). In this contribution, mathematical modeling of considered units is derived as first-order model. Further, an overall transfer function of the IMG system is obtained using first-order transfer functions of IMG components and system dynamics. Thus, the obtained transfer function is then approximated into a first-order plus time delay (FOPTD) model to facilitate a simpler PID control design. PID controller parameters are computed using PV method for set point (SP) and load disturbance (LD) modes, keeping maximum sensitivity as a constraint. Various PID controller i.e. PID-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PV</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>SP</i>1.4</sub>, PID-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PV</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>SP</i>2.0</sub>, PID-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PV</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>LD</i>1.4</sub>, and PID-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PV</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>LD</i>2.0</sub> is designed for SP and LD modes. The efficacy of PID control design is tested by analyzing its impact on frequency deviation and mitigation of error with acceptable transient response for SP and LD mode. A comparative study is also performed based on tabulated data featuring error indices, time domain indicators, control efforts, and frequency plots to validate PV method-based PID control designs for IMG. Moreover, the real-time simulator, i.e., OPAL-RT, is utilized to further validate the efficacy of the PID controller in frequency error mitigation of the considered IMG model.

One of the key drivers in gaining the cost-effective, reliable and low-downtime Operation system for major Oil Fields is implementation of Water Injection System (WIS) with capability of online-automated regulation and control. This Paper outlines an application of Proportional, Integral, Derivative (PID) control loop algorithm for Decentralized WIS (with direct injection from Water Source wells to Injection wells by means of high capacity ESP's) used in West Qurna-2 oilfield located in Iraq, operated by LUKOIL. PID control loop algorithm has being used in the industry for the years, but not commonly applied as integral component of Water Injection System allowing to maintain optimal equipment modes. Such limited PID deployment is explained by complexity of operational parameters synchronizing for every Water Injection System component. The decentralized Water Injection System at the West Qurna 2 project is common and united pipeline system for every WellPad that provides water transfer from Water source wells (3-5 wells per WellPad) to injection wells (3-6 wells per WellPad) with line pressure of 70-130 Barg by means of high-capacity ESP equipped with VSD. Water injection process is regulated by controlling both the conventional ESP parameters (frequency, flow rate, motor current and load, Intake and discharge pressures), line pressure, required injection rate by means of flow control valves, and implemented PID control loop algorithm. This paper discusses the techniques of PID control loop algorithm application as the tool for: –Pipeline protection against high pressure without full shutdown of water injection process and–ESP automated regulation to ensure operation inside Recommended Operated Range (ROR) and smoothening of ESP mode when any changes in the system happen (i.e. shutdown of other water source well ESP's at the same WellPad or shutdown of injection well) with immediate feedback to Operator Control Room. Implemented approach allows to decrease number of ESP shutdowns and avoid high jumping of ESP loads that consequently leads to maximizing of ESP run life. Comparative examples and case studies of submersible equipment operation results before and after the application of PID regulation are specified. Mainly by implementing PID regulation and control stable and smooth operation of equipment and ESP's used for WIS (direct injection from Water Source Well to Injection Well) has been achieved. New approach for PID application as a tool for pipeline overpressure protection has been formed, which allowed to reduce Capital Expenses for the WIS construction works. Specified case can be used as example for further development and projects in the oil and gas industry.

In recent years, the switched reluctance machine (SRM) represents a contemporary competitive technology in the fields of automotive and aeronautics, because their growing needs for electric drives with a frequent and important high-speed variation. This paper presents an application of the fractional order control of the speed of switched reluctance motor for its application used for electric and hybrid vehicles. It also presents a comparative study between the speed control with the fuzzy logic controller (FLC) regulator and the fractional order proportional integral control. The numerical simulations showed that the speed control with the designed fractional order proportional integral control realise a better dynamic behaviour of the motor, a better speed and a good accommodation to the disturbances of the load. The application of the fractional order proportional integral (FOPI) controller achieved a high performance and a longer lifetime to SRM than the results obtained by a fuzzy logic controller.