Cristina I. Muresan

Bio: Cristina I. Muresan is an academic researcher from Technical University of Cluj-Napoca. The author has contributed to research in topic(s): Control theory & PID controller. The author has an hindex of 14, co-authored 122 publication(s) receiving 1046 citation(s). Previous affiliations of Cristina I. Muresan include Core Laboratories.

A novel auto-tuning method for fractional order PI/PD controllers.

Abstract: Fractional order PID controllers benefit from an increasing amount of interest from the research community due to their proven advantages. The classical tuning approach for these controllers is based on specifying a certain gain crossover frequency, a phase margin and a robustness to gain variations. To tune the fractional order controllers, the modulus, phase and phase slope of the process at the imposed gain crossover frequency are required. Usually these values are obtained from a mathematical model of the process, e.g. a transfer function. In the absence of such model, an auto-tuning method that is able to estimate these values is a valuable alternative. Auto-tuning methods are among the least discussed design methods for fractional order PID controllers. This paper proposes a novel approach for the auto-tuning of fractional order controllers. The method is based on a simple experiment that is able to determine the modulus, phase and phase slope of the process required in the computation of the controller parameters. The proposed design technique is simple and efficient in ensuring the robustness of the closed loop system. Several simulation examples are presented, including the control of processes exhibiting integer and fractional order dynamics.

Development and implementation of an FPGA based fractional order controller for a DC motor

Abstract: Fractional calculus has been gaining more and more popularity in control engineering in numerous fields, including mechatronic applications. One of the most common applications in all mechatronic domains is the control of DC motors. Several control algorithms have been proposed for such motors, ranging from traditional PID algorithms, to the more sophisticated advanced methods, including fractional order controllers. Nevertheless, very little information regarding the implementation problems of such fractional algorithms exists today. The paper proposes a simple approach for designing a fractional order PI controller for controlling the speed of a DC motor. The resulting controller is implemented on an FPGA target and its performance is compared to other possible benchmarks. The experimental results show the efficiency of the designed fractional order PI controller. Beside the initial DC motor, two other different DC motors are also used in the experiments to demonstrate the robustness of the controller.

A Survey of Recent Advances in Fractional Order Control for Time Delay Systems

Abstract: Several papers reviewing fractional order calculus in control applications have been published recently. These papers focus on general tuning procedures, especially for the fractional order proportional integral derivative controller. However, not all these tuning procedures are applicable to all kinds of processes, such as the delicate time delay systems. This motivates the need for synthesizing fractional order control applications, problems, and advances completely dedicated to time delay processes. The purpose of this paper is to provide a state of the art that can be easily used as a basis to familiarize oneself with fractional order tuning strategies targeted for time delayed processes. Solely, the most recent advances, dating from the last decade, are included in this review.

Theoretical Analysis and Experimental Validation of a Simplified Fractional Order Controller for a Magnetic Levitation System

Abstract: Fractional order (FO) controllers are among the emerging solutions for increasing closed-loop performance and robustness. However, they have been applied mostly to stable processes. When applied to unstable systems, the tuning technique uses the well-known frequency-domain procedures or complex genetic algorithms. This brief proposes a special type of an FO controller, as well as a novel tuning procedure, which is simple and does not involve any optimization routines. The controller parameters may be determined directly using overshoot requirements and the study of the stability of FO systems. The tuning procedure is given for the general case of a class of unstable systems with pole multiplicity. The advantage of the proposed FO controller consists in the simplicity of the tuning approach. The case study considered in this brief consists in a magnetic levitation system. The experimental results provided show that the designed controller can indeed stabilize the magnetic levitation system, as well as provide robustness to modeling uncertainties and supplementary loading conditions. For comparison purposes, a simple PID controller is also designed to point out the advantages of using the proposed FO controller.

Tuning algorithms for fractional order internal model controllers for time delay processes

Abstract: This paper presents two tuning algorithms for fractional-order internal model control (IMC) controllers for time delay processes. The two tuning algorithms are based on two specific closed-loop control configurations: the IMC control structure and the Smith predictor structure. In the latter, the equivalency between IMC and Smith predictor control structures is used to tune a fractional-order IMC controller as the primary controller of the Smith predictor structure. Fractional-order IMC controllers are designed in both cases in order to enhance the closed-loop performance and robustness of classical integer order IMC controllers. The tuning procedures are exemplified for both single-input-single-output as well as multivariable processes, described by first-order and second-order transfer functions with time delays. Different numerical examples are provided, including a general multivariable time delay process. Integer order IMC controllers are designed in each case, as well as fractional-order IMC...

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Review of fractional PID controller

Abstract: Fractional calculus has been studied for over three centuries, and it has multifarious applications in science and engineering. This review investigates its progress since the first reported use of control systems, covering the fractional PID proposed by Podlubny in 1994, and is presenting a state-of-the-art fractional PID controller, incorporating the latest contributions in this field. It highlights developments in the field of fractional PID controllers, including their design and tuning, as well as explores their various versions. Software tools associated to the design of fractional PID controllers are also discussed.

Formulas For Natural Frequency And Mode Shape

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Design of a fractional order PID controller for hydraulic turbine regulating system using chaotic non-dominated sorting genetic algorithm II

Abstract: Fractional-order PID (FOPID) controller is a generalization of traditional PID controller using fractional calculus. Compared to the traditional PID controller, in FOPID controller, the order of derivative portion and integral portion is not integer, which provides more flexibility in achieving control objectives. Design stage of such an FOPID controller consists of determining five parameters, i.e. proportional, integral and derivative gains {Kp, Ki, Kd}, and extra integration and differentiation orders {λ,μ}, which has a large difference comparing with the conventional PID tuning rules, thus a suitable optimization algorithm is essential to the parameters tuning of FOPID controller. This paper focuses on the design of the FOPID controller using chaotic non-dominated sorting genetic algorithm II (NSGAII) for hydraulic turbine regulating system (HTRS). The parameters chosen of the FOPID controller is formulated as a multi-objective optimization problem, in which the objective functions are composed by the integral of the squared error (ISE) and integral of the time multiplied squared error (ITSE). The chaotic NSGAII algorithm, which is an incorporation of chaotic behaviors into NSGAII, is used as the optimizer to search true Pareto-front of the FOPID controller and designers can implement each of them based on objective functions priority. The designed chaotic NSGAII based FOPID controller procedure is applied to a HTRS system. A comparison study between the optimum integer order PID controller and optimum fractional order PID controller is presented in the paper. The simulation and some experimental results validate the superiority of the fractional order controllers over the integer controllers.