Design Of Fractional Order Proportional-Integral-Derivative Controller Research Articles

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.

Fractional-order PID controller design via optimal selection strategy of frequency domain specifications

In this paper, a novel fractional-order Proportional-Integral Derivative (PID) controller design depending on optimal selection of frequency domain specifications is proposed for time delay systems. The frequency domain specification sets, namely, (i) phase margin and gain crossover frequency and (ii) phase margin and gain margin are determined so that the reference model is optimal according to three time domain performance indices, i.e. Integral Square Error (ISE), Integral Time Square Error (ITSE) and Integral Absolute Error (IAE). Here, the delayed Bode's ideal transfer function is employed in the reference model. Moreover, the stability region of the reference model is given via a theorem. In simulation studies, the proposed methodology is compared with other two different methods using the same frequency domain specifications. It is observed that the proposed optimal fractional-order PID controllers outperform according to the mentioned performance indices, and they also possess considerably acceptable performance in terms of other time domain specifications such as overshoot, settling time, etc.

Robust H[formula omitted]-PID control Stability of fractional-order linear systems with Polytopic and two-norm bounded uncertainties subject to input saturation

This paper deals a type of H∞ proportional–integral–derivative (PID) control mechanism for a type of structural uncertain fractional order linear systems by convex Polytopic and two-norm bounded uncertainties subject to input saturation which mainly focuses on the case of a fractional order α such that 0<α<1. The Gronwall–Bellman lemma and the sector condition of the saturation function are investigated for system stability analysis and stabilization. The main strategy of the presented strategy is to restore fractional order PID controller design under input saturation problem from static output feedback controller design. Unlike existing strategies, non-iterative strategy is used to get optimal output feedback based on the LMI. On the premise of a linear matrix inequality algorithm, the SOF control laws can be obtained. After that, the fractional-order PID controller is recovered from the SOF controller. A numerical example is provided in order to show the validity and superiority of the proposed method.

FOPID controller design for a perturbed PHWR system using enhanced crow search algorithm

The effectiveness of a control algorithm in the operation of a Pressurized Heavy Water Reactor (PHWR) relies upon its ability to counter the step back condition accurately. This paper presents an enhanced crow search algorithm for designing a fractional-order proportional integral derivative (FOPID) controller implemented in power control loop of a PHWR under step-back condition. The proposed controller is applied on eight different interval fractional transfer function models of PHWR derived using Edge theorem as well as eight step back conditions of PHWR. Simulation results reveal excellent reference tracking capability of the proposed controller. The effectiveness of the proposed controller has been proved by performing a comparison among different error performance indices with the existing controllers in the literature.

Tuning Rules for Fractional Order PID Controller Using Data Analytics

Flexibility and robust performance have made the FOPID (Fractional Order PID) controllers a better choice than PID (Proportional, Integral, Derivative) controllers. But the number of tuning parameters decreases the usage of FOPID controllers. Using synthetic data in available FOPID tuners leads to abnormal controller performances limiting their applicability. Hence, a new tuning methodology involving real-time data and overcomes the drawbacks of mathematical modeling is the need of the hour. This paper proposes a novel FOPID controller tuning methodology using machine learning algorithms. Feed Forward Back Propagation Neural Network (FFBPNN), Multi Least Squares Support Vector Regression (MLSSVR) chosen to design Machine Learning based Optimal Tuner (MLOT) can handle the interdependency between the controller parameters and multiple outputs for multiple inputs.The proposed tuner finds application in the control of power and energy systems. It can accomplish tracking, disturbance-rejection, and robustness controller performances, thus making FOPID controller design easier and accurate. Comparisons with existing FOPID tuning rules show better controller performances and easy tuning. Thus, this paper addresses a unique, real-time, model-free, easily tunable FOPID tuning methodology satisfying plant requirements.

Design of FOPID controller for higher order continuous interval system using improved approximation ensuring stability

This contribution deals with the design of a fractional-order proportional-integral-derivative (FOPID) controller through reduce-order modeling for continuous interval systems. First, a higher order interval plant (HOIP) is considered. The reduced-order interval plant (ROIP) for considered HOIP is derived by multipoint Padé approximation integrated with Routh table. Then, FOPID controller is designed for ROIP to satisfy the phase margin and gain cross over frequency. Thus obtained FOPID controller is implemented on HOIP also to validate the performance of designed FOPID on HOIP. A single-input-single-output (SISO) test system is taken up to elaborate the entire process of controller design. The outcomes affirm the validity of the designed FOPID controller. The designed FOPID controller produced stable results retaining the phase margin and gain cross-over frequency when implemented on HOIP. The results further proved that FOPID controller is working efficiently for ROIP and HOIP.

Sine Cosine Algorithm Assisted FOPID Controller Design for Interval Systems Using Reduced-Order Modeling Ensuring Stability

The focus of present research endeavor was to design a robust fractional-order proportional-integral-derivative (FOPID) controller with specified phase margin (PM) and gain cross over frequency (ωgc) through the reduced-order model for continuous interval systems. Currently, this investigation is two-fold: In the first part, a modified Routh approximation technique along with the matching Markov parameters (MPs) and time moments (TMs) are utilized to derive a stable reduced-order continuous interval plant (ROCIP) for a stable high-order continuous interval plant (HOCIP). Whereas in the second part, the FOPID controller is designed for ROCIP by considering PM and ωgc as the performance criteria. The FOPID controller parameters are tuned based on the frequency domain specifications using an advanced sine-cosine algorithm (SCA). SCA algorithm is used due to being simple in implementation and effective in performance. The proposed SCA-based FOPID controller is found to be robust and efficient. Thus, the designed FOPID controller is applied to HOCIP. The proposed controller design technique is elaborated by considering a single-input-single-output (SISO) test case. Validity and efficacy of the proposed technique is established based on the simulation results obtained. In addition, the designed FOPID controller retains the desired PM and ωgc when implemented on HOCIP. Further, the results proved the eminence of the proposed technique by showing that the designed controller is working effectively for ROCIP and HOCIP.

Fractional order PID control for steer-by-wire system of emergency rescue vehicle based on genetic algorithm

Aiming at dealing with the difficulty for traditional emergency rescue vehicle (ECV) to enter into limited rescue scenes, the electro-hydraulic steer-by-wire (SBW) system is introduced to achieve the multi-mode steering of the ECV. The overall structure and mathematical model of the SBW system are described at length. The fractional order proportional-integral-derivative (FOPID) controller based on fractional calculus theory is designed to control the steering cylinder’s movement in SBW system. The anti-windup problem is considered in the FOPID controller design to reduce the bad influence of saturation. Five parameters of the FOPID controller are optimized using the genetic algorithm by maximizing the fitness function which involves integral of time by absolute value error (ITAE), peak overshoot, as well as settling time. The time-domain simulations are implemented to identify the performance of the raised FOPID controller. The simulation results indicate the presented FOPID controller possesses more effective control properties than classical proportional-integral-derivative (PID) controller on the part of transient response, tracking capability and robustness.

Multi‐objective robust fuzzy fractional order proportional–integral–derivative controller design for nonlinear hydraulic turbine governing system using evolutionary computation techniques

AbstractThe present paper proposes a novel multi‐objective robust fuzzy fractional order proportional–integral–derivative (PID) controller design for nonlinear hydraulic turbine governing system (HTGS) by using evolutionary computation techniques. The fuzzy fractional order PID (FOPID) controller takes closed loop error and its fractional derivative as inputs and performs fuzzy logic operations. Then, it produces the output through the fractional order integrator. The predominant advantages of the proposed controller are its capability to handle complex nonlinear processes like HTGS in heuristic manner, due to fuzzy incorporation and extending an additional flexibility in tuning the order of fractional derivative/integral terms to enhance the closed loop performance. The present work formulates the optimal tuning problem of fuzzy FOPID controller for HTGS as a multi‐objective one instead of a traditional single‐objective one towards satisfying the conflicting criteria such as less settling time and minimum damped oscillations simultaneously to ensure the improved dynamic performance of HTGS. The multi‐objective evolutionary computation techniques such as non‐dominated sorting genetic algorithm‐II (NSGA‐II) and modified NSGA‐II have been utilized to find the optimal input/output scaling factors of the proposed controller along with the order of fractional derivative/integral terms for HTGS system under no load and load turbulence conditions. The performance of the proposed fuzzy FOPID controller is compared with PID and FOPID controllers. The simulations have been conducted to test the tracking capability and robust performance of HTGS during dynamic set point changes for a wide range of operating conditions and model parameter variations, respectively. The proposed robust fuzzy FOPID controller has ensured better fitness value and better time domain specifications than the PID and FOPID controllers, during optimization towards satisfying the conflicting objectives such as less settling time and minimum damped oscillations simultaneously, due to its special inheritance of fuzzy and FOPID properties.

Design of FOPID controller for fractional-order plants with experimental verification

In this paper, a design method is proposed for a robust stabilizing fractional order proportional integral derivative (FOPID) controller for One Non-Integer Order Plus Time Delay plant (NIOPTD-I). The NIOPTD-I model is obtained after reducing the higher order continuous time process model. The FOPID controller is designed by using stability boundary locus method, which satisfies user defined frequency domain specifications phase margin and the gain crossover frequency. A robust control system is designed against gain variations by achieving flat phase condition which is due to zero slope at the gain crossover frequency of the phase plot. Thus robust stabilizing FOPID controller for NIOPTD-I fractional order plant is designed. The applicability of the proposed method is illustrated with simulation example and experimental validation with the liquid level control system.

Optimal fractional order PID design via Tabu Search based algorithm

This paper presents an optimization method based on the Tabu Search Algorithm (TSA) to design a Fractional-Order Proportional-Integral-Derivative (FOPID) controller. All parameter computations of the FOPID employ random initial conditions, using the proposed optimization method. Illustrative examples demonstrate the performance of the proposed FOPID controller design method.