Review of fractional PID controller

In recent years, it is remarkable to see the increasing number of studies related to the theory and application of fractional order controller (FOC), specially PI ? D ? controller, in many areas of science and engineering. Research activities are focused on developing new analysis and design methods for fractional order controllers as an extension of classical control theory. In this paper, a new tuning method for fractional order proportional and derivative (PD ?) or FO-PD controller is proposed for a class of typical second-order plants. The tuned FO-PD controller can ensure that the given gain crossover frequency and phase margin are fulfilled, and furthermore, the phase derivative w. r. t. the frequency is zero, i.e., the phase Bode plot is flat at the given gain crossover frequency. Consequently, the closed-loop system is robust to gain variations. The FOC design method proposed in the paper is practical and simple to apply. Simulation and experimental results show that the closed-loop system can achieve favorable dynamic performance and robustness.

A Fractional Order Proportional and Derivative (FOPD) Motion Controller: Tuning Rule and Experiments

Tuning fractional order proportional integral controllers for fractional order systems

Technical communique: Fractional order [proportional derivative] controller for a class of fractional order systems

In this paper, a fractional order PID controller is investigated for a position servomechanism control system considering actuator saturation and the shaft torsional flexibility. For actually implementation, we introduced a modified approximation method to realize the designed fractional order PID controller. Numerous simulation comparisons presented in this paper indicate that, the fractional order PID controller, if properly designed and implemented, will outperform the conventional integer order PID controller.

Fractional order PID control of a DC-motor with elastic shaft: a case study

Fractional order dynamic model could model various real materials more adequately than integer order ones and provide a more adequate description of many actual dynamical processes. Fractional order controller is naturally suitable for these fractional order models. In this paper, a fractional order PID controller design method is proposed for a class of fractional order system models. Better performance using fractional order PID controllers can be achieved and is demonstrated through two examples with a comparison to the classical integer order PID controllers for controlling fractional order systems.

A fractional order PID tuning algorithm for a class of fractional order plants

Many real world systems, including smart mechatronics systems, can be better characterized by dynamic systems of non-integer order. Using non-integer order or fractional order calculus, fractional order systems can be modeled more authentically. Due to the nature of the infinite dimensional model, proper approximations to fractional order differentiator (salpha, alpha isin Ropf) are fundamentally important. This paper contributed a new approximation scheme which is an extension of the well-established Oustaloup's approximation method. The benefits from using the proposed scheme are illustrated by numerical examples in both time and frequency domains

A Modified Approximation Method of Fractional Order System

As one of the main areas of value investing, the stock market attracts the attention of many investors. Among investors, market index movements are a focus of attention. In this paper, combining the efficient market hypothesis and the fractal market hypothesis, a stock prediction model based on mixed fractional Brownian motion (MFBM) and an improved fractional-order particle swarm optimization algorithm is proposed. First, the MFBM model is constructed by adjusting the parameters to mix geometric Brownian motion (GBM) and geometric fractional Brownian motion (GFBM). After that, an improved fractional-order particle swarm optimization algorithm is proposed. The position and velocity formulas of the fractional-order particle swarm optimization algorithm are improved using new fractional-order update formulas. The inertia weight in the update formula is set to be linearly decreasing. The improved fractional-order particle swarm optimization algorithm is used to optimize the coefficients of the MFBM model. Through experiments, the accuracy and validity of the prediction model are proven by combining the error analysis. The model with the improved fractional-order particle swarm optimization algorithm and MFBM is superior to GBM, GFBM, and MFBM models in stock price prediction.

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Stock Prediction Model Based on Mixed Fractional Brownian Motion and Improved Fractional-Order Particle Swarm Optimization Algorithm

Multivariate time series forecasting has long been a subject of great concern. For example, there are many valuable applications in forecasting electricity consumption, solar power generation, traffic congestion, finance, and so on. Accurately forecasting periodic data such as electricity can greatly improve the reliability of forecasting tasks in engineering applications. Time series forecasting problems are often modeled using deep learning methods. However, the deep information of sequences and dependencies among multiple variables are not fully utilized in existing methods. Therefore, a multivariate time series deep spatiotemporal forecasting model with a graph neural network (MDST-GNN) is proposed to solve the existing shortcomings and improve the accuracy of periodic data prediction in this paper. This model integrates a graph neural network and deep spatiotemporal information. It comprises four modules: graph learning, temporal convolution, graph convolution, and down-sampling convolution. The graph learning module extracts dependencies between variables. The temporal convolution module abstracts the time information of each variable sequence. The graph convolution is used for the fusion of the graph structure and the information of the temporal convolution module. An attention mechanism is presented to filter information in the graph convolution module. The down-sampling convolution module extracts deep spatiotemporal information with different sparsities. To verify the effectiveness of the model, experiments are carried out on four datasets. Experimental results show that the proposed model outperforms the current state-of-the-art baseline methods. The effectiveness of the module for solving the problem of dependencies and deep information is verified by ablation experiments.

https://www.mdpi.com/2076-3417/12/11/5731/pdf?version=1654580999

Chunna Zhao

Papers

A fractional order PID tuning algorithm for a class of fractional order plants

Fractional order PID control of a DC-motor with elastic shaft: a case study

A Modified Approximation Method of Fractional Order System

Stock Prediction Model Based on Mixed Fractional Brownian Motion and Improved Fractional-Order Particle Swarm Optimization Algorithm

Multivariate Time Series Deep Spatiotemporal Forecasting with Graph Neural Network