Fractional Order PID Controller Research Articles

Robust FOPID Control of an After-Cooler Heat Exchanger with TES

In this paper the temperature control of an after-cooler heat exchanger (AHX) with Thermal Energy Storage (TES) is considered. The AHX can be modelled as a nonlinear system whose gain strongly depends on the operating point. This can cause the reduction of the phase margin which translates into the risk of excessive temperature overshoots. The generalized isodamping approach has been applied to design a fractional-order robust PID controller that guarantees the invariance of the phase margin despite the gain variations. Simulation results performed on a realistic model of the system demonstrate the effectiveness of the proposed design approach.

PID/FOPID Tuning Rule Based on a Second Order Inverse Response Process Model with Robustness Considerations

This paper deals with the design of a proportional-integral-derivative (PID) and fractional-order proportional-integral-derivative (FOPID) controller tuning rule for second-order controlled processes with inverse response. The design of the rules takes into account specific levels of robustness and performance for both load disturbance rejection and set-point tracking tasks. In the first step, the optimal parameters for both controllers are obtained from optimizations that seek to minimize the error in both control modes while maintaining the robustness constraint. Subsequently, fitting functions to the optimal parameters are sought to capture their behavior with the possibility of finding optimal parameters with the tuning rule designed between certain ranges of the model parameters. For FOPID and PID controllers, the rule IRM-RoT (Inverse Response Model Robust Tuning) have been developed. The performance of the controllers was compared using examples, and the results showed that fractional order controllers provide a novel solution for inverse response dynamics in process control.

Fractional Order PID Control of Propofol Dosage and Optimization in Lean and Obese Patients

This paper outlines the design of a fractional-order proportional–integral–derivative controller for regulating the induction phase of Propofol infusion in lean and obese patients. The obtained controller is implemented within the pharmacokinetic-pharmacodynamic model and the nonlinear Hill function to conduct closed-loop simulations. The latter are employed using a dataset comprising 24 patients to obtain clinical evaluation results. The design of the controller relies on a generic second-order plus dead time approximation model, which characterizes interpatient variability in response to Propofol infusion within the studied population. The fractional-order proportional–integral–derivative is tuned to achieve sufficient robustness margins ie phase margin, cutoff frequency, and the consideration of the iso-damping properties. The results show no undershoot and a smooth convergence to the desired value of the bispectral index, which indicates the depth of hypnosis.

Advancing Anesthesia Education: Training on Modeling and Control for Enhanced Patient Care

This paper introduces a training program focused on anesthesia modeling and control. The curriculum centers on the utilization of an open-source patient simulator and covers open-loop analysis, relative gain array analysis, and modeling for control purposes, preparing students for closed-loop anesthesia management. A decentralized approach to controller tuning is adopted, with emphasis on both standard PID and generalized fractional order PID controllers. Through practical exercises and simulations, students acquire essential skills to understand anesthesia modeling and control challenges effectively, contributing to improved patient outcomes in clinical practice.

First-Hand Design of a Fractional order PID for Controlling the Depth of Hypnosis during Induction

The integration of information technology and control engineering has significantly increased in the research field of clinical practice, including the management of medication dosing for general anesthesia. To achieve effective drug dosing, it is necessary to have appropriate controllers for closed loop control methods. A multitude of control mechanisms have been devised to manage hypnosis, with most of them based on pharmacokinetic-pharmacodynamic (PK-PD) models. This study presents a novel structure of a fractional order PID controller tuned for inducing hypnosis. The tuning algorithm uses a novel fractional order model instead of the classical PK-PD models. The main goal is to control the Bispectral Index by delivering Propofol during the hypnotic stage of anesthesia. Closed loop simulation results show that the proposed controller manages to ensure little undershoot and time to target for a nominal patient model. Robustness tests are also performed. The analysis shows that the proposed controller is suitable to maintain BIS signal within a safe operating range but fails to meet the time to target requirement for significant patient variability (greater than 2 orders of magnitude). Online adaptation rules are suggested as a solution.

Voltage Control of PEM Fuel Cell in a DC Microgrid Using Optimal Artificial Rabbits Algorithm-Based Fractional Order PID Controller

Voltage Control of PEM Fuel Cell in a DC Microgrid Using Optimal Artificial Rabbits Algorithm-Based Fractional Order PID Controller

Analog real time tunable and configurable fractional order PID controller realization

Fractional-order controllers are modeled using irrational continuous-time transfer functions. Implementing these controllers in analogue form can be challenging, particularly if their parameters need to be adjusted in real-time. This paper presents an analogue implementation of a fractional PID controller that can be adjusted and configured in real-time. The controller can be configured as PIαDf, PIDβ, PIα, PDβ, Iα, Dβ. The signal within the proposed controller’s circuit stays analog and is not converted into discrete values. A prototype of the controller is tested. The results of the frequency and time domain validations indicated similarity between the theoretical, simulated and experimental measurements.

Fractional-Order PID Optimal Tuning Rule based on a FOPDT Process Model with Robustness Constraints

This paper introduces a tuning rule design for fractional order PID controllers. The design is based on a first order plus dead time model for the controlled process. The control problem presented, requires minimizing the integrated absolute error for each control mode, then making a different set of rules for set-point and load-disturbance response. For the proposed optimization, a robustness constraint based on the maximum value of the sensitivity function has been considered so that the tuned controllers have an optimal performance and guarantee the stability of the control system at the time of implementation. By performing a curve fitting process towards the optimal controller parameters, the Model based Robust Tuning rule was designed and its improvement over other tuning methods is validated through examples.

Intermediate Tuning Proposal for Fractional Order PID Controllers with Balanced Servo/Regulation Operation

Many tuning rules for controllers consider each operating mode separately, including servo-control and regulatory-control. This paper considers the problem where an optimal controller for one of these modes has to operate in a different mode than the one for which it was tuned. A weighted performance degradation index is analyzed and an intermediate tuning rule is proposed for fractional-order PID controllers, taking into account a robustness constraint. This rule serves as a proposal for further research on the application of this methodology in the design of tuning rules for FOPID controllers.

Application of Fractional-order PID controllers in a Greenhouse Climate Control System

A model-based Fractional Order Proportional-Integral-Derivative (FOPID) control design method is applied to a multivariable greenhouse climate control system. A multivariable transfer function model of the greenhouse system, obtained via model Identification experiment, provides plant’s model information for control design. The fractional controller is tuned using the conventional Biggest Log-modulus Tuning (BLT) method associated with integer order PID controllers. However, unlike the conventional PID case, the controller gains are first computed using internal model control design procedure. This produces preliminary values of controller parameters. The FOPID controller gains are further tuned using a single detuning factor (F) until a biggest log modulus of 2N dB is obtained where N is the number of loops in the MIMO system. Simulation studies, using MATLAB and Simulink, show that good compromise between performance and robustness is achievable for both temperature and humidity regulation in a greenhouse control application.

FOPID Controller Design for a Buck Converter System Using a Novel Hybrid Cooperation Search Algorithm with Pattern Search for Parameter Tuning

This research introduces a novel metaheuristic algorithm, OCSAPS, representing an upgraded cooperation search algorithm (CSA) version. OCSAPS incorporates opposition-based learning (OBL) and pattern search (PS) algorithms. The proposed algorithm's application aims to develop a fractional order proportional-integral-derivative (FOPID) controller tailored for a buck converter system. The efficacy of the proposed algorithm is assessed by statistical boxplot and convergence response analyses. Furthermore, the performance of the OCSAPS-based FOPID-controlled buck converter system is benchmarked against CSA, Harris hawk optimization (HHO), and genetic algorithm (GA). This comparative analysis encompasses transient and frequency responses, performance indices, and robustness analysis. The outcomes of this comparison highlight the distinctive advantages of the proposed approach-based system. Moreover, the proposed approach's performance was compared with six other approaches used to control buck converter systems similarly regarding both time and frequency domain responses. Overall, the findings underscore the efficacy of the OCSAPS algorithm as a robust solution for designing FOPID controllers in buck converter systems.

Wind Power Frequency Control in Doubly FED Induction Generator Using CFMPC-FOPID Controller Scheme

Because the majority of wind turbines operate in maximum output power tracking mode, power system frequency cannot be supported. However, if the penetration rate of wind power increases, the system inertia related to frequency modulation may decrease. In addition, frequency stability will be severely affected in the event of significant disturbances to the system load. Due to the high penetration of wind power in isolated power systems, this study suggests a coordinated frequency management approach for emergency frequency regulation. In order to prevent the phenomenon of load frequency control in doubly fed induction generators (DFIGs), a unique efficient control scheme is developed. The Cascaded Fractional Model Predictive Controller coupled with Fractional-Order PID controller (CFMPC-FOPID) is developed to provide the DFIG system with an efficient reaction to changes in load and system parameters. The proposed controller must have a robust tendency to respond quickly in terms of minimum settling time, undershoot, and overshoot. Nonlinear feedback controllers are designed using frequency deviations and power imbalances to achieve the reserve power distribution between generators and DFIGs in a variety of wind speed conditions. It makes upgrading quick and easy. In Matlab/Simulink, a simulation model is built to test the viability of the suggested approach.

A Comparative Study between Fractionalized and Fractional Order PID Controllers for Control of a Stable System Based on Particle Swarm Optimization Algorithm

A Comparative Study between Fractionalized and Fractional Order PID Controllers for Control of a Stable System Based on Particle Swarm Optimization Algorithm

Optimal Design of Fractional-Order PID Controllers for a Nonlinear AWS Wave Energy Converter Using Hybrid Jellyfish Search and Particle Swarm Optimization

In this study, a nonlinear Archimedes wave swing (AWS) energy conversion system was employed to enable the use of irregular sea waves to provide useful electricity. Instead of the conventional PI controllers used in prior research, this study employed fractional-order PID (FOPID) controllers to control the back-to-back configuration of AWS. The aim was to maximize the energy yield from waves and maintain the grid voltage and the capacitor DC link voltage at predetermined values. In this study, six FOPID controllers were used to accomplish the control goals, leading to an array of thirty parameters required to be fine-tuned. In this regard, a hybrid jellyfish search optimizer and particle swarm optimization (HJSPSO) algorithm was adopted to select the optimal control gains. Verification of the performance of the proposed FOPID control system was achieved by comparing the system results to two conventional PID controllers and one FOPID controller. The conventional PID controllers were tuned using a recently presented metaheuristic algorithm called the Coot optimization algorithm (COOT) and the classical particle swarm optimization algorithm (PSO). Moreover, the FOPID was also tuned using the well-known genetic algorithm (GA). The system investigated in this study was subjected to various unsymmetrical and symmetrical fault disturbances. When compared with the standard COOT-PID, PSO-PID, and GA-FOPID controllers, the HJSPSO-FOPID results show a significant improvement in terms of performance and preserving control goals during system instability

Enhancing the transient stability of interconnected power systems by designing an adaptive fuzzy-based fractional order PID controller

The reliable and efficient operation of the electrical energy transmission system heavily relies on maintaining stability as a key requirement. Interconnected power systems often experience low-frequency oscillations (LFOs), which have the potential to initiate instability and, subsequently, necessitate careful attention and investigation. To tackle this issue, researchers have focused on various controllers, including Fractional-Order Proportional-Integral-Derivative (FOPID) controllers. The FOPID controller, with its increased number of design parameters, has proven to be more successful than the traditional PID controller in various engineering applications. However, determining the optimal parameters for the controller becomes more challenging due to the increased design space. Moreover, the performance of fixed-gain FOPID controllers may be degraded when confronted with highly nonlinear and uncertain controlled objects such as power systems. This issue is primarily attributed to the static nature of fixed-gain FOPID controllers. To overcome these challenges associated with fixed-gain FOPID controllers and to instill an adaptive quality, this article introduces a novel power system control methodology. This adaptive approach combines a FOPID control strategy with a fuzzy logic system and is denoted as EOA-AFFOPID. The proposed adaptive controller dynamically tunes its coefficients through a fuzzy block, which significantly improves the overall performance of the control system. To establish a performance benchmark, we have also created an alternative controller, named EOA-FOPID, a version of the optima FOPID controller with fixed coefficients. The proposed methodology is applied to multi-machine interconnected power systems equipped with Static Synchronous Series Compensators (SSSCs), and comparative evaluations are conducted with other popular recent control strategies. The comparisons demonstrate the effectiveness of the EOA-AFFOPID control strategy in damping system fluctuations and achieving significant performance improvements in terms of different metrics including overshoot, undershoot, and settling time.

Fractional Order Modeling and Control of an Articulated Robotic Arm

This paper presents a fractional order system modeling of a robotic arm and the development of a Fractional Order PID (FOPID) controller applied to the system. The controller technique originated from non-integer calculus, which improves the robotic arm's overall stability and positioning. The robotic arm system is modeled using the non-integer order technique in order to improve system accuracy. Thus, a non-integer order Proportional Integral Derivative (PID) control method is implemented to stabilize the plant positioning. Using MATLAB/Simulink the FOPID controller simulations were confirmed and compared to the Integer Order PID (IOPID) controller for tracking the robotic arm positioning. Simulation outcomes imply that the proposed non-integer controller increases the system stability and position with/without external disturbances being present in the environment.

Design and Optimization of Precision Fertilization Control System Based on Hybrid Optimized Fractional-Order PID Algorithm

In order to mitigate time-varying, lag, and nonlinearity impacts on fertilization systems and achieve precise control of liquid conductivity, we propose a novel hybrid-optimized fractional-order proportional-integral-derivative (PID) algorithm. This algorithm utilizes a fuzzy algorithm to tune the five parameters of the fractional-order PID algorithm, employs the Smith predictor for structural optimization, and utilizes Wild Horse Optimizer, improved by genetic algorithms, to optimize fuzzy rules. We conducted MATLAB simulations, precision experiments, and stability tests on this controller. MATLAB simulation results, along with precision experiment results, indicate that compared to PID controllers, Smith predictor-optimized PID controllers, and fuzzy-tuned fractional-order PID controllers, the proposed controller has the narrowest steady-state conductivity range, the shortest settling time, and the lowest overshoot, showcasing excellent overall dynamic performance. Stability test results demonstrate that the controller maintains stable operation under different pressure conditions. Therefore, this control system from our study achieves superior control effectiveness, providing a viable approach for the control of nonlinear time-delay systems.

Robust stabilization of interval fractional‐order plants with an interval time delay by fractional‐order proportional integral derivative controllers

AbstractThis paper concentrates on presenting a reliable procedure to compute the stabilizing region of fractional‐order proportional integral derivative (FOPID) controllers for interval fractional‐order plants having an interval time delay. An interval fractional‐order plant is defined as a fractional‐order transfer function whose denominator and numerator coefficients are all uncertain and lie in specified intervals. Also, an interval time delay points to a delay term whose value varies in a specific interval. The D‐decomposition technique and the value set concept are employed to determine the stabilizing region of FOPID controllers. In this study, first, a theorem is presented to compute the boundary of the value sets of systems having interval time day. Then, a lemma is provided for robust stability analysis of the given closed‐loop control system. For a convenient use of the paper results, an algorithm is proposed to solve the problem of robustly stabilizing interval fractional‐order plants with an interval time delay using FOPID controllers. Finally, four examples are provided to illustrate the proposed procedure.

Application of Fractional-Order PID Controller to Improve Stability of a Single-Machine Infinite-Bus System

Application of Fractional-Order PID Controller to Improve Stability of a Single-Machine Infinite-Bus System

Working Performance Improvement of a Novel Independent Metering Valve System by Using a Neural Network-Fractional Order-Proportional-Integral-Derivative Controller

In recent years, reducing the energy consumption in a hydraulic excavator has received deep attention in many studies. The implementation of the novel independent metering valve system (NIMV) has emerged as a promising solution in this regard. However, external factors such as noise, throttling loss, and leakage have negative influences on the tracking precision and energy saving in the NIMV system. In this paper, a novel control method, simple but effective, called a neural network-fractional order-proportional-integral-derivative controller is developed for the NIMV system. In detail, the fractional order-proportional-integral-derivative (FOPID) controller is used to improve the precision, stability, and fast response of the control system due to the inclusion of non-integer orders in the proportional, integral, and derivative terms. Along with that, the auto-tuning algorithm of the neural network controller is applied for adjusting five parameters in the FOPID controller under noise, throttling loss, and leakage. In addition, the proposed controller alleviates the amount of calculation for the system by using model-free control. To verify the effectiveness of the proposed controller, the simulation and experiment are conducted on the AMESim/MATLAB and a real test bench. As a result, the proposed controller not only operates the NIMV system accurately in the target trajectory but also reduces energy consumption, saving up 23.33% and 29.25% compared to FOPID and PID in the experimental platform, respectively.