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This book aims to propose the implementation and application of Fractional Order Systems (FOS). It is well known that FOS can be utilized in control applications and systems modeling, and their effectiveness has been proven in many theoretical works and simulation routines. A further and mandatory step for FOS real world utilization is their hardware implementation and applications on real systems modeling. With this viewpoint, introductory chapters are included on the definition of stability region of Fractional Order PID Controller and Chaotic FOS, followed by the practical implementation based on Microcontroller, Field Programmable Gate Array, Field Programmable Analog Array and Switched Capacitor. Another section is dedicated to FO modeling of Ionic Polymeric Metal Composite (IPMC). This new material will have applications in robotics, aerospace and biomedicine.

This paper presents a parameter formula connecting the well-known proportional-integral-derivative (PID) control and the active disturbance rejection control (ADRC). On the one hand, this formula gives a quantitative lower bound to the bandwidth of the extended state observer (ESO) used in ADRC, implying that the ESO is not necessarily of high gain. On the other hand, enlightened by the design of ADRC, a new PID tuning rule is provided, which can guarantee both strong robustness and nice tracking performance of the closed-loop systems under the PID control. Moreover, it is proved that the ESO can be rewritten as a suitable linear combination of the three terms in PID, which can give a better estimate for the system uncertainty than the single integral term in the PID controller. Theoretical results are verified also by simulations in the paper.

In this paper, we present a fuzzy PID control system as a combination of a fuzzy PID controller and a fuzzy control process, which is represented by a fuzzy control differential equation in linear form. We use the concepts of the generalized Hukuhara differentiability and the fuzzy integral of fuzzy-valued functions to study some qualitative properties for this system in the space of fuzzy numbers. We also study the existence and uniqueness result for solutions of fuzzy PID control differential equations under some suitable conditions. A number of examples are also provided to illustrate the results of the theory.

The conventional PID controller has static parameters that cannot be changed at different operating conditions. As a result, the term ‘adaptive PID controller’ has appeared to solve this problem. This controller can be tuned using intelligent techniques such as Fuzzy Logic Control, Neural Network Control, or Adaptive Neuro-Fuzzy Inference Systems. However, the choice of the suitable parameters for these intelligent controllers has a direct effect on their performance. Metaheuristics algorithms—with their powerful performance, speed, and optimal parameter selection—can be applied for choosing controller parameters efficiently. In this paper, a hybrid of genetic algorithm and particle swarm optimization is proposed to tune the parameters of different adaptive PID controllers. To evaluate the performance of the proposed hybrid optimization method on the different adaptive PID controllers, these controllers are applied to control the operation of one of the most difficult chemical processes, the divided wall distillation column. The proposed column used in this work separates a ternary mixture of ethanol, propanol, and n-butanol. Our proposed hybrid optimization technique is compared with the genetic algorithm, and simulation results show that our proposed hybrid genetic-particle swarm technique outperforms genetic algorithm for different disturbances.

Although the classical PID（proportional-integral-derivative） controller is most widely and successfully used in engineering systems which are typically nonlinear with various uncertainties, almost all the existing investigations on PID controller focus on linear systems. The aim of this paper is to present a theory on PID controller for nonlinear uncertain systems, by giving a simple and analytic design method for the PID parameters together with a mathematic proof for the global stability and asymptotic regulation of the closed-loop control systems. To be specific, we will construct a 3-dimensional manifold within which the three PID parameters can be chosen arbitrarily to globally stabilize a wide class of second order nonlinear uncertain dynamical systems, as long as some knowledge on the upper bound of the derivatives of the nonlinear uncertain function is available.We will also try to make the feedback gains as small as possible by investigating the necessity of the manifold from which the PID parameters are chosen, and to establish some necessary and sufficient conditions for global stabilization of several special classes of nonlinear uncertain systems.

A PID controller design using an internal model control (IMC) approach is a well-established method for controller tuning in a DC-DC boost converter. This study introduces an innovative implementation of a novel indirect Internal Model Control (IMC) strategy for PID controller design, tailored specifically for a DC-DC boost converter. While the indirect IMC approach has been documented in prior research, its application to boost converters signifies a substantial contribution to the field. The proposed method simplifies the tuning process by focusing exclusively on the plant shifting parameter ψ, thereby eliminating the need for an IMC filter. Optimal tuning is achieved through the Grey Wolf Optimization (GWO) method, which enhances the controller’s stability, robustness, and transient response in the presence of disturbances commonly encountered in boost converter operation. Extensive simulations are performed in a MATLAB Simulink environment to compare the performance of the GWO-based indirect IMC-PID controller with traditional PID and IMC-PID designs. Performance is assessed based on transient response parameters and performance indices, such as IAE, ISE, ITAE, and ITSE. Results reveal that the GWO-optimized indirect IMC-PID controller significantly outperforms conventional controllers, demonstrating enhanced servo and regulatory behaviors.

The German PID-NET registry was founded in 2009, serving as the first national registry of patients with primary immunodeficiencies (PID) in Germany. It is part of the European Society for Immunodeficiencies (ESID) registry. The primary purpose of the registry is to gather data on the epidemiology, diagnostic delay, diagnosis, and treatment of PIDs. Clinical and laboratory data was collected from 2,453 patients from 36 German PID centres in an online registry. Data was analysed with the software Stata® and Excel. The minimum prevalence of PID in Germany is 2.72 per 100,000 inhabitants. Among patients aged 1-25, there was a clear predominance of males. The median age of living patients ranged between 7 and 40 years, depending on the respective PID. Predominantly antibody disorders were the most prevalent group with 57% of all 2,453 PID patients (including 728 CVID patients). A gene defect was identified in 36% of patients. Familial cases were observed in 21% of patients. The age of onset for presenting symptoms ranged from birth to late adulthood (range 0-88 years). Presenting symptoms comprised infections (74%) and immune dysregulation (22%). Ninety-three patients were diagnosed without prior clinical symptoms. Regarding the general and clinical diagnostic delay, no PID had undergone a slight decrease within the last decade. However, both, SCID and hyper IgE- syndrome showed a substantial improvement in shortening the time between onset of symptoms and genetic diagnosis. Regarding treatment, 49% of all patients received immunoglobulin G (IgG) substitution (70%-subcutaneous; 29%-intravenous; 1%-unknown). Three-hundred patients underwent at least one hematopoietic stem cell transplantation (HSCT). Five patients had gene therapy. The German PID-NET registry is a precious tool for physicians, researchers, the pharmaceutical industry, politicians, and ultimately the patients, for whom the outcomes will eventually lead to a more timely diagnosis and better treatment.

Owing to nonlinear structure and uncertain load demand characteristics, expert and intelligent automatic generation control (AGC) is inevitable for coherent operation and control of electric power system. Hence, in this paper, to mitigate the frequency and power deviations efficiently under sudden load demand conditions, a novel fractional-order fuzzy PID (FOFPID) controller is suggested in AGC of restructured multi-area multi-source hydrothermal power systems. The parameters of FOFPID controller are optimized by utilizing bacterial foraging optimization algorithm. The controller is implemented on restructured two- and three-area systems. It is observed that the advocated method shows superiority over fuzzy PID, fractional-order PID and conventional PID control schemes. Energy storage units such as redox flow batteries (RFB) which show extremely long charge–discharge life cycle and outstanding quick response to alleviate the system oscillations under disturbances have further been incorporated into the studied systems to analyze their efficacy in boosting AGC performance. Analysis of results reveals that with RFB, system transient performance improves significantly. It is also observed that the obtained results satiate the AGC requirement under different power transactions taking place in a deregulated market in the presence/absence of appropriate generation rate constraint treated for thermal and hydro plants. Finally, the robustness of the presented approach is demonstrated against the wide variations in the system parameters and initial loading condition.

Covers PID control systems from the very basics to the advanced topics This book covers the design, implementation and automatic tuning of PID control systems with operational constraints. It provides students, researchers, and industrial practitioners with everything they need to know about PID control systems—from classical tuning rules and model-based design to constraints, automatic tuning, cascade control, and gain scheduled control.  PID Control System Design and Automatic Tuning using MATLAB/Simulink introduces PID control system structures, sensitivity analysis, PID control design, implementation with constraints, disturbance observer-based PID control, gain scheduled PID control systems, cascade PID control systems, PID control design for complex systems, automatic tuning and applications of PID control to unmanned aerial vehicles. It also presents resonant control systems relevant to many engineering applications. The implementation of PID control and resonant control highlights how to deal with operational constraints. Provides unique coverage of PID Control of unmanned aerial vehicles (UAVs), including mathematical models of multi-rotor UAVs, control strategies of UAVs, and automatic tuning of PID controllers for UAVs Provides detailed descriptions of automatic tuning of PID control systems, including relay feedback control systems, frequency response estimation, Monte-Carlo simulation studies, PID controller design using frequency domain information, and MATLAB/Simulink simulation and implementation programs for automatic tuning Includes 15 MATLAB/Simulink tutorials, in a step-by-step manner, to illustrate the design, simulation, implementation and automatic tuning of PID control systems Assists lecturers, teaching assistants, students, and other readers to learn PID control with constraints and apply the control theory to various areas. Accompanying website includes lecture slides and MATLAB/ Simulink programs PID Control System Design and Automatic Tuning using MATLAB/Simulink is intended for undergraduate electrical, chemical, mechanical, and aerospace engineering students, and will greatly benefit postgraduate students, researchers, and industrial personnel who work with control systems and their applications.