6th International Conference On Electrical – Sofiane Bououden

2 PID Structure Table. 1. PID Basic Tuning Gains Rise time Overshoot Settling time Steady-state error oscillation Kp Decrease Increase Decrease Increase Ki Decrease Increase Increase Eliminate Increase Kd Decrease Decrease Decrease/Increase 3.2 Adaptive PID – Motivation This technique is the best choice for controlling system in real time, due to the adaptive gains, these gais are changing according to the envirmetal conditions, in general the adaptive case offers a good adaption to any changement in the system structure, due to the temperature and/or the pressure, and son on.

Below is some motivation behind using this technique: • fitting into different circumstance • Maintaining the automation working • Personal interest (IAS) In this paper, Gain-scheduling controller structure is used to update the gains KP, Ki and Kd accordingly (Fig. 3). A. Bounemeur et al. Fig. 3 Gain Scheduling technique 3.3 Procedures to Construct a Gain Scheduling Technique with PID Gains Below are the essential steps to construct a gain scheduling technique: • Identify the Scheduling Variable: • Divide the Operating Range into Regions: • Design PID Gains for Each Region: • Implement the Gain Scheduler: • Test and Validate Simulation Results Let’s consider a second-order nonlinear system given below: x¨ + c(x)x˙ + k(x)x = u (5) where: • c(x) = 1 + 0.5×2 Nonlinear damping.

• k(x) = 2 + x2: Nonlinear stiffness. • u: Control input. The simulation results are performed on Python: Libraries SciPy. We will design a gain-scheduled PID controller to regulate x(t) to a desired reference r(t). The scheduling variable will be x(t), and the gains Kp, Ki, Kd will depend on x(t). 4.1 Steps for Simulation 1. Use the system equation. 2. Define gains as a function of x(t). For example: Kp(x) = 2 − 0.5 | x | (6) Ki(x) = 1 + 0.2 | x | (7) Kd (x) = 0.5 + 0.1 | x | (8) Design and Analysis of an Adaptive PID Controller for a Class 3.

Simulate the closed-loop system with a gain-scheduled PID controller. 4. Compare the system response with and without gain scheduling (Fig. 4). Fig. 4.

Leopoldo Angrisani, Department of Electrical and Information Technologies Engineering, University of Napoli Federico II, Napoli, Italy Marco Arteaga, Departament de Control y Robótica, Universidad Nacional Autónoma de México, Coyoacán, Mexico Samarjit Chakraborty, Fakultät für Elektrotechnik und Informationstechnik, TU München, Munich, Germany Shanben Chen, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, China Tan Kay Chen, Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore Rüdiger Dillmann, University of Karlsruhe (TH) IAIM, Karlsruhe, Germany Haibin Duan, Beijing University of Aeronautics and Astronautics, Beijing, China Gianluigi Ferrari, Dipartimento di Ingegneria dell’Informazione, Sede Scientifica Università degli Studi di Parma, Parma, Italy Manuel Ferre, Centre for Automation and Robotics CAR (UPM-CSIC), Universidad Politécnica de Madrid, Madrid, Spain Faryar Jabbari, Department of Mechanical and Aerospace Engineering, University of California, Irvine, USA Limin Jia, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Janusz Kacprzyk, Intelligent Systems Laboratory, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Alaa Khamis, Department of Mechatronics Engineering, German University in Egypt El Tagamoa El Khames, New Cairo City, Egypt Torsten Kroeger, Intrinsic Innovation, Mountain View, USA Yong Li, College of Electrical and Information Engineering, Hunan University, Changsha, China Qilian Liang, Department of Electrical Engineering, University of Texas at Arlington, Arlington, USA Ferran Martín, Departament dʼEnginyeria Electrònica, Universitat Autònoma de Barcelona, Bellaterra, Spain Tan Cher Ming, College of Engineering, Nanyang Technological University, Singapore, Singapore Wolfgang Minker, Institute of Information Technology, University of Ulm, Ulm, Germany Pradeep Misra, Department of Electrical Engineering, Wright State University, Dayton, USA Subhas Mukhopadhyay, School of Engineering, Macquarie University, Sydney, NSW, Australia Cun-Zheng Ning, Department of Electrical Engineering, Arizona State University, Tempe, AZ, USA Toyoaki Nishida, Department of Intelligence Science and Technology, Kyoto University, Kyoto, Japan Luca Oneto, Department of Informatics, Bioengineering, Robotics and Systems Engineering, University of Genova, Genova, Italy Bijaya Ketan Panigrahi, Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, India Federica Pascucci, Department di Ingegneria, Università degli Studi Roma Tre, Rome, Italy Yong Qin, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Gan Woon Seng, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore Joachim Speidel, Institute of Telecommunications, University of Stuttgart, Stuttgart, Germany Germano Veiga, FEUP Campus, INESC Porto, Porto, Portugal Haitao Wu, Academy of Opto-electronics, Chinese Academy of Sciences, Beijing, China Walter Zamboni, Department of Computer Engineering, Electrical Engineering and Applied Mathematics, DIEM—Università degli studi di Salerno, Fisciano, Italy Kay Chen Tan, Department of Computing, Hong Kong Polytechnic University, Hong Kong, Hong Kong The book series Lecture Notes in Electrical Engineering (LNEE) publishes the latest developments in Electrical Engineering—quickly, informally and in high quality.

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