A Novel Fractional Order Fuzzy PID Controller and Its Optimal Time Domain Tuning Based on Integral Performance Indices

A novel fractional order (FO) fuzzy Proportional-Integral-Derivative (PID) controller has been proposed in this paper which works on the closed loop error and its fractional derivative as the input and has a fractional integrator in its output. The fractional order differ-integrations in the proposed fuzzy logic controller (FLC) are kept as design variables along with the input-output scaling factors (SF) and are optimized with Genetic Algorithm (GA) while minimizing several integral error indices along with the control signal as the objective function. Simulations studies are carried out to control a delayed nonlinear process and an open loop unstable process with time delay. The closed loop performances and controller efforts in each case are compared with conventional PID, fuzzy PID and PI{\lambda}D{\mu} controller subjected to different integral performance indices. Simulation results show that the proposed fractional order fuzzy PID controller outperforms the others in most cases.Comment: 30 pages, 20 figure

Handling packet dropouts and random delays for unstable delayed processes in NCS by optimal tuning of PIλDμ controllers with evolutionary algorithms

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.The issues of stochastically varying network delays and packet dropouts in Networked Control System (NCS) applications have been simultaneously addressed by time domain optimal tuning of fractional order (FO) PID controllers. Different variants of evolutionary algorithms are used for the tuning process and their performances are compared. Also the effectiveness of the fractional order PI(λ)D(μ) controllers over their integer order counterparts is looked into. Two standard test bench plants with time delay and unstable poles which are encountered in process control applications are tuned with the proposed method to establish the validity of the tuning methodology. The proposed tuning methodology is independent of the specific choice of plant and is also applicable for less complicated systems. Thus it is useful in a wide variety of scenarios. The paper also shows the superiority of FOPID controllers over their conventional PID counterparts for NCS applications.This work has been supported by the Board of Research in Nuclear Sciences (BRNS) of the Department of Atomic Energy (DAE), India, sanction no. 2009/36/62-BRNS, dated November 2009

An optimized fractional order PID controller for suppressing vibration of AC motor

Fractional order Proportional-Integral-Derivative (PID) controller is composed of a number of integer order PID controllers. It is more accurate to control the complex system than the traditional integer order PID controller. The values of parameters of the fractional order PID controller play a decisive role for the control effect. Because the fractional order PID controller added two adjustable parameters than the traditional PID controller, it is very difficult to tune parameters. So the Back Propagation (BP) neural network is selected to optimize the parameters of the fractional order PID controller in order to obtain the high performance. Then the optimized fractional order PID controller and the traditional PID controller are used to control AC motor speed governing system. And the vibration spectrum and stator current spectrum under different rotating speeds are compared and analyzed in detail. The results show that the optimized fractional order PID controller has better vibration suppression performance than the traditional PID controller. The reason is that the optimized fractional order PID controller changed the stator current component, and further changed the frequency components and the amplitude of the vibration signal of the motor

Controller Design for Fractional-Order Systems

In recent time, the application of fractional derivatives has become quite apparent in modeling mechanical and electrical properties of real materials. Fractional integrals and derivatives has found wide application in the control of dynamical systems, when the controlled system or/and the controller is described by a set of fractional order differential equations. In the present work a fractional order system has been represented by a higher integer order system, which is further approximated by second order plus time delay (SOPTD) model. The approximation to a SOPTD model is carried out by the minimization of the two norm of the actual and approximated system. Further, the effectiveness of a fractional order controller in meeting a set of frequency domain specifications is determined based on the frequency response of an integer order PID and a fractional order PID (FOPID) controller, designed for the approximated SOPTD model. The advent of fuzzy logic has led to greater flexibility in designing controllers for systems with time varying and nonlinear characteristics by exploiting the system observations in a linguistic manner. In this regard, a fractional order fuzzy PID controller has been developed based on the minimization different optimal control based integral performance indices. The indices have been minimized using genetic algorithms. Simulation results show that the fuzzy fractional order PID controller is able to outperform the classical PID, fuzzy PID and FOPID controllers

Multilevel Thresholding for Image Segmentation Using an Improved Electromagnetism Optimization Algorithm

Image segmentation is considered one of the most important tasks in image processing, which has several applications in different areas such as; industry agriculture, medicine, etc. In this paper, we develop the electromagnetic optimization (EMO) algorithm based on levy function, EMO-levy, to enhance the EMO performance for determining the optimal multi-level thresholding of image segmentation. In general, EMO simulates the mechanism of attraction and repulsion between charges to develop the individuals of a population. EMO takes random samples from search space within the histogram of image, where, each sample represents each particle in EMO. The quality of each particle is assessed based on Otsu’s or Kapur objective function value. The solutions are updated using EMO operators until determine the optimal objective functions. Finally, this approach produces segmented images with optimal values for the threshold and a few number of iterations. The proposed technique is validated using different standard test images. Experimental results prove the effectiveness and superiority of the proposed algorithm for image segmentation compared with well-known optimization methods

Applications of fractional calculus in electrical and computer engineering

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of several systems. This article illustrates several applications of fractional calculus in science and engineering. It has been recognized the advantageous use of this mathematical tool in the modeling and control of many dynamical systems. In this perspective, this paper investigates the use of FC in the fields of controller tuning, electrical systems, digital circuit synthesis, evolutionary computing, redundant robots, legged robots, robotic manipulators, nonlinear friction and financial modeling.N/

Motion control of unmanned ground vehicle using artificial intelligence

The aim of this thesis is to solve two problems: the. trajectory tracking and navigation, for controlling the motion of unmanned ground vehicles (UGV). Such vehicles are usually used in industry for assisting automated production process or delivery services to improve and enhance the quality and efficiency. With regard to the trajectory tracking problem, the main task is to design a new method that is capable of minimising trajectory-tracking errors in UGV. To achieve this, a comprehensive mathematical model needs to be established that contains kinematic and dynamic characteristics beside actuators. In addition, different trajectories need to be generated and applied individually as a reference input, i.e. continuous gradient trajectories such as linear, circular and lemniscuses or a non-continuous gradient trajectory such as a square trajectory. The design method is based on a novel fractional order proportional integral derivative (FOPID) control strategy, which is proposed to control the movement of UGV to track given trajectories. Two FOPID controllers are required in this design. The first FOPID is constructed in order to control the orientation of UGV. The second FOPID controller is to control the speed of UGV. The particle swarm optimization (PSO) algorithm is used to obtain the optimal parameters for both controllers. The significance of the proposed method is that an observable improvement has been achieved in terms of minimising trajectory-tracking errors and reducing control efforts, especially in continuous gradient trajectories. The stability of the proposed controllers is investigated based upon Nyquist stability criterion. Moreover, the robustness of the controllers is examined in the presence of disturbances to demonstrate the effectiveness of the controllers under certain harsh conditions. The influence from external disturbances has been represented by square pulses and sinusoidal waves. The drawback of this method, however, a highly trajectory tracking error is observed in non-continuous gradient trajectories due to the sharpness of the rotation at the corners of a square trajectory. To overcome this drawback, a new controller, abbreviated as (NN-FOPID), has been proposed based on a combination of neural networks and the FOPID. The purpose is to minimise the trajectory tracking error of non-continuous trajectories, in particular. The Levenberg-Marquardt (LM) algorithm is used to train the NN-FOPID controller. The neural networks’ cognitive capacities have made the system adaptable to respond effectively to the variants in trajectories. The obtained results by using NN-FOPID have shown a significant improvement of reducing errors of trajectory tracking and increasing control efforts over the results by FOPID. The other task is to solve the navigation problem of UGV in static and dynamic environments. This can be conducted by firstly constructing workspace environments that contain multiple dynamic and static obstacles. The dynamic obstructing obstacles can move in different velocities. The static obstacles can be randomly positioned in the workspace and all obstacles are allowed to have different sizes and shapes. Secondly, a UGV can be placed in any initial posture on the condition that it has to reach a given destination within the boundaries of the workspace. Thirdly, a method based on fuzzy inference systems (FIS) is proposed to control the motion of the UGV. The design of FIS is based on fuzzification, inference engine and defuzzification processes. The navigation task is divided into obstacle avoidance and target reaching tasks. Consequently, two individual FIS controllers are required to drive the actuators of the UGV, one is to avoid obstacles and the other is to reach a target. Both FIS controllers are combined through a switching mechanism to select the obstacle avoidance FIS controller if there is an obstacle, otherwise choosing reaching target FIS. The simulation results have confirmed the effectiveness of the proposed design in terms of obtaining optimal paths with shortest elapsed time. Similarly, a new method is proposed based on an adaptive neurofuzzy inference system (ANFIS) to guide the UGV in unstructured environments. This method combines the advantages of adaptive leaning and inference fuzzy system. The simulation results have demonstrated adequate achievements in terms of obtaining shortest and feasible paths whilst avoiding static obstructing obstacles and hence reaching the specified targets speedily. Finally, a UGV is constructed to investigate the overall performance of the proposed FIS controllers practically. The architecture of the UGV consists of three ultrasonic sensors, a magnetic compass and two quadratic decoders that they are interfaced with an Arduino microcontroller to read the sensory information. The Arduino, who acts as a slave microcontroller is serially connected with a master Raspberry Pi microcontroller. Raspberry Pi and Arduino communicate with each other based on a proposed hierarchical algorithm. Three case studies are introduced to demonstrate the effectiveness and the validation of the proposed FIS controllers and the UGV’s platform in real-time

Intelligent active force control of human hand tremor using smart actuator

Patients suffering from Parkinson’s disease (PD) experience tremor which may generate a functional disability impacting their daily life activities. In order to provide a non-invasive solution, an active tremor control technique is proposed to suppress a human hand tremor. In this work, a hybrid controller which is a combination of the classic Proportional-Integral (PI) control and Active Force Control (AFC) strategy was employed. A test-rig is utilized as a practical test and verification platform of the controller design. A linear voice coil actuator (LVCA) was utilized as the main active suppressive element to control the tremor of hand model in collocation with the sensor. In order to validate the AFC scheme in real-time application, an accelerometer was used to obtain the measured values of the parameter necessary for the feedback control action. Meanwhile, a laser displacement sensor was used to quantify the displacement signal while hand shaking. To optimize the controller parameters, three different optimization techniques, namely the genetic algorithm (GA), particle swarm optimization (PSO) and differential evolution (DE) techniques were incorporated into the hybrid PI+AFC controller to obtain a better performance in controlling tremor of the system. For the simulation study, two different models were introduced to represent the human hand in the form of a mathematical model with four degree-of-freedom (4 DOF) biodynamic response (BR) and a parametric model as the plant model. The main objective of this investigation is to optimize the PI and AFC parameters using three different types of intelligent optimization techniques. Then, the parameters that have been identified were tested through an experimental work to evaluate the performance of controller. The findings of the study demonstrate that the hybrid controller gives excellent performance in reducing the tremor error in comparison to the classic pure PI controller. Based on the fitness evaluation, the AFC-based scheme enhances the PI controller performance roughly around 10% for all optimization techniques. Besides that, an intelligent mechanism known as iterative learning control (ILC) was incorporated into the AFC loop (called as AFCAIL) to find the estimated mass parameter. In addition, a sensitivity analysis was presented to investigate the performance and robustness of the voice coil actuator with the proposed controller in real-time environment. The results prove that the AFCAIL controller gives an excellent performance in reducing the hand tremor error in comparison with the classic P, PI and hybrid PI+AFC controllers. These outcomes provide an important contribution towards achieving novel methods in suppressing hand tremor by means of intelligent control