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The ubiquity of PID controllers in the industry has remained mysterious until now. We provide here a mathematical explanation of this strange phenomenon by comparing their sampling with the the one of "intelligent" PID controllers, which…

Optimization and Control · Mathematics 2010-07-01 Brigitte D'Andrea Novel , Michel Fliess , Cédric Join , Hugues Mounier , Bruno Steux

A fractional order (FO) PID or FOPID controller is designed for an Automatic Voltage Regulator (AVR) system with the consideration of contradictory performance objectives. An improved evolutionary Non-dominated Sorting Genetic Algorithm…

Optimization and Control · Mathematics 2013-06-18 Indranil Pan , Saptarshi Das

We present a predictive feedback control method for a class of quasilinear hyperbolic systems with one boundary control input. Assuming exact model knowledge, convergence to the origin, or tracking at the uncontrolled boundary, are achieved…

Optimization and Control · Mathematics 2022-03-18 Timm Strecker , Ole Morten Aamo , Michael Cantoni

A simplified analysis is performed on the Bode-type filtering sensitivity trade-off integrals, which capture the sensitivity characteristics of the estimate and estimation error with respect to the process input and estimated signal in…

Systems and Control · Electrical Eng. & Systems 2022-04-11 Neng Wan , Dapeng Li , Lin Song , Naira Hovakimyan

We study a nonlinear, non-autonomous feedback controller applied to boundary control systems. Our aim is to track a given reference signal with prescribed performance. Existence and uniqueness of solutions to the resulting closed-loop…

Optimization and Control · Mathematics 2022-03-09 Marc Puche , Timo Reis , Felix Schwenninger

The PID controller is an elegant and versatile controller for set point tracking in double integrator systems of which mechanical systems evolving on Euclidean space constitute a large class. But since mechanical systems are typically…

Systems and Control · Electrical Eng. & Systems 2021-11-16 Rama Seshan , Ravi N Banavar , D. H. S. Maithripala , Arun D. Mahindrakar

An elementary mathematical example proves, thanks to the Routh-Hurwitz criterion, a result that is intriguing with respect to today's practical understanding of model-free control, i.e., an "intelligent" proportional controller (iP) may…

Systems and Control · Computer Science 2017-11-09 Cédric Join , Emmanuel Delaleau , Michel Fliess , Claude H. Moog

In this paper, we propose to use a nonlinear adaptive PID controller to regulate the joint variables of a mobile manipulator. The motion of the mobile base forces undue disturbances on the joint controllers of the manipulator. In designing…

Robotics · Computer Science 2022-07-12 Hadi Hajieghrary , Marc Peter Deisenroth , Yasemin Bekiroglu

This paper proposes a spectral-based tuning method for proportional-integral (PI) controllers in integrating-plus-dead-time (IPDT) systems. The design objective is to achieve unified exponential decay for both reference tracking and…

Systems and Control · Electrical Eng. & Systems 2025-07-03 Dhamdhawach Horsuwan

In this paper we propose a variation of the widely popular Interconnection-and-Damping-Assigment Passivity-Based Control (IDA-PBC) based on Poincare's Lemma to design output feedback globally stabilizing controllers for two dimensional…

Systems and Control · Electrical Eng. & Systems 2025-10-03 Rafael Cisneros , Leyan Fang , Wei He , Romeo Ortega

In this paper, we present a strictly negative imaginary state feedback control methodology for relative degree two negative imaginary systems such as flexible structures with collocated sensors and actuators. We show that by augmenting a…

Optimization and Control · Mathematics 2023-04-05 James Dannatt , Ian R. Petersen

In this study, a heuristic dynamic programming controller is proposed to control a boost converter. Conventional controllers such as proportional integral-derivative (PID) or proportional integral (PI) are designed based on the linearized…

Systems and Control · Electrical Eng. & Systems 2020-02-04 Sepehr Saadatmand , Pourya Shamsi , Mehdi Ferdowsi

This paper presents a learning-based control strategy for non-linear throttle valves with an asymmetric hysteresis, leading to a near-optimal controller without requiring any prior knowledge about the environment. We start with a carefully…

Systems and Control · Electrical Eng. & Systems 2024-07-18 Paul Daoudi , Bojan Mavkov , Bogdan Robu , Christophe Prieur , Emmanuel Witrant , Merwan Barlier , Ludovic Dos Santos

According to the well-known loop shaping method for the design of controllers, the performance of the controllers in terms of step response, steady-state disturbance rejection and noise attenuation and robustness can be improved by…

Systems and Control · Electrical Eng. & Systems 2023-01-02 Nima Karbasizadeh , S. Hassan HosseinNia

Modern fourth-generation storage ring light sources predominantly utilize digital I/Q-based proportional-integral (PI) feedback for their radio-frequency (RF) systems. This paper introduces a dedicated PI feedback model implemented in the…

Accelerator Physics · Physics 2026-01-12 Tianlong He , Wenshu Liang , Jincheng Xiao , Xin Huang

In this paper, a fractional order (FO) PI{\lambda}D\mu controller is designed to take care of various contradictory objective functions for an Automatic Voltage Regulator (AVR) system. An improved evolutionary Non-dominated Sorting Genetic…

Systems and Control · Computer Science 2013-01-08 Indranil Pan , Saptarshi Das

This paper uses the Continued Fraction Expansion (CFE) method for analog realization of fractional order differ-integrator and few special classes of fractional order (FO) controllers viz. Fractional Order Proportional-Integral-Derivative…

Systems and Control · Computer Science 2016-11-30 Anindya Pakhira , Saptarshi Das , Indranil Pan , Shantanu Das

This paper investigates real-time control strategies for dynamical systems that involve frictional contact interactions. Hybridness and underactuation are key characteristics of these systems that complicate the design of feedback…

Robotics · Computer Science 2016-11-28 Francois Robert Hogan , Alberto Rodriguez

Eduardo Sontag and coauthors studied Input-to-Output Stability (IOS) and the output asymptotic gain property. These notions changed control theory and recently had an impact on robust adaptive control through the Deadzone-Adapted…

Optimization and Control · Mathematics 2026-05-21 Iasson Karafyllis , Miroslav Krstic

The key idea of this contribution is the partial compensation of non-minimum phase zeros or unstable poles. Therefore the integer-order zero/pole is split into a product of fractional-order pseudo zeros/poles. The amplitude and phase…

Systems and Control · Electrical Eng. & Systems 2022-05-24 Benjamin Voß , Christoph Weise , Michael Ruderman , Johann Reger