Life at Low Reynolds Number

Load frequency control (LFC) is one of the essential process in interconnected power systems. To provide high quality, reliable and stable electrical power, designed controller should perform satisfactorily, i.e. suppress area frequency and tie-line power deviations. Within this scope, in this study, a high order differential feedback controller (HODFC) and a developed fractional high order differential feedback controller (FHODFC) are proposed for LFC problem in multi-area power systems for the first time. The gains of the HODFC and FHODFC are optimally tuned by particle swarm optimization (PSO) algorithm aiming to minimize integral of time weighted absolute error (ITAE) performance index. The superiority of the developed FHODFC are verified by comparing reported controller structures in the recent state-of-the-art literature and HODFC for two identical non-reheat thermal power system and two-area multi-source power system consisting of gas, thermal and hydro generation units with/without consideration of HVDC link. To test the robustness of the designed controllers, varying system parameters and loading conditions are investigated. The governor dead band (GDB) and generation rate constraint (GRC) limitations are also considered for the system under study to examine non-linearity handling success of the proposed controllers. Performance results indicate that the developed FHODFC provides better dynamic response and robustness than other published techniques under nonlinearities, random load pattern, and variations in system parameters and loading conditions.

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Design of an Optimized Fractional High Order Differential Feedback Controller for Load Frequency Control of a Multi-Area Multi-Source Power System With Nonlinearity

Classical fractional order controller tuning techniques usually establish the parameters of the controller by solving a system of nonlinear equations resulted from the frequency domain specifications like phase margin, gain crossover frequency, iso-damping property, robustness to uncertainty, etc. In the present paper a novel fractional order generalized optimum method for controller design using frequency domain is presented. The tuning rules are inspired from the symmetrical optimum principles of Kessler. In the first part of the paper are presented the generalized tuning rules of this method. Introducing the fractional order, one more degree of freedom is obtained in design, offering solution for practically any desired closed-loop performance measures. The proposed method has the advantage that takes into account both robustness aspects and desired closed-loop characteristics, using simple tuning-friendly equations. It can be applied to a wide range of process models, from integer order models to fractional order models. Simulation results are given to highlight these advantages.

https://www.mdpi.com/2227-7390/7/12/1166/pdf

Simplified Fractional Order Controller Design Algorithm

In this paper, a proportional-integral passivity-based controller (PI-PBC) is proposed to regulate the amplitude and frequency of the three-phase output voltage in a direct-current alternating-current (DC-AC) converter with an LC filter. This converter is used to supply energy to AC loads in hybrid renewable based systems. The proposed strategy uses the well-known proportional-integral (PI) actions and guarantees the stability of the system by means of the Lyapunov theory. The proposed controller continues to maintain the simplicity and robustness of the PI controls using the Hamiltonian representation of the system, thereby ensuring stability and producing improvements in the performance. The performance of the proposed controller was validated based on simulation and experimental results after considering parametric variations and comparing them with classical approaches.

https://www.mdpi.com/2079-9292/9/5/847/pdf

Nonlinear Voltage Control for Three-Phase DC-AC Converters in Hybrid Systems: An Application of the PI-PBC Method

This paper proposes a theoretical framework for generalization of the well established first order plus dead time (FOPDT) model for linear systems. The FOPDT model has been broadly used in practice to capture essential dynamic response of real life processes for the purpose of control design systems. Recently, the model has been revisited towards a generalization of its orders, i.e., non-integer Laplace order and fractional order delay. This paper investigates the stability margins as they vary with each generalization step. The relevance of this generalization has great implications in both the identification of dynamic processes as well as in the controller parameter design of dynamic feedback closed loops. The discussion section addresses in detail each of this aspect and points the reader towards the potential unlocked by this contribution.

Generalization of the FOPDT Model for Identification and Control Purposes

The beauty of the proportional-integral-derivative (PID) algorithm for feedback control is its simplicity and efficiency. Those are the main reasons why PID controller is the most common form of feedback. PID combines the three natural ways of taking into account the error: the actual (proportional), the accumulated (integral), and the predicted (derivative) values; the three gains depend on the magnitude of the error, the time required to eliminate the accumulated error, and the prediction horizon of the error. This paper explores the new meaning of integral and derivative actions, and gains, derived by the consideration of non-integer integration and differentiation orders, i.e., for fractional order PID controllers. The integral term responds with selective memory to the error because of its non-integer order λ , and corresponds to the area of the projection of the error curve onto a plane (it is not the classical area under the error curve). Moreover, for a fractional proportional-integral (PI) controller scheme with automatic reset, both the velocity and the shape of reset can be modified with λ . For its part, the derivative action refers to the predicted future values of the error, but based on different prediction horizons (actually, linear and non-linear extrapolations) depending on the value of the differentiation order, μ . Likewise, in case of a proportional-derivative (PD) structure with a noise filter, the value of μ allows different filtering effects on the error signal to be attained. Similarities and differences between classical and fractional PIDs, as well as illustrative control examples, are given for a best understanding of new possibilities of control with the latter. Examples are given for illustration purposes.

https://www.mdpi.com/2227-7390/7/6/530/pdf

Back to Basics: Meaning of the Parameters of Fractional Order PID Controllers

This paper presents an improved locomotion for an N-link swimming artificial eukaryotic flagellum (AEF) microrobot using a fractional order approach for both the navigation waveform and control. The proposed locomotion is tested on a simulator of the robot, developed in the MATLAB/Simulink environment, which allows to select different modes of swimming and control strategies, as well as evaluate the performance of the locomotion in terms of propulsion, power efficiency or tracking. Different robust fractional order proportional-derivative (PD$^{\mu }$) controllers are designed in order to reduce the effects of the load variation of the actuator of each link depending on its position along the flagellum. For comparison purposes, three-parameter integer order controllers are also designed. Simulation results are given in order to show the benefits of the proposed locomotion in comparison with classical waveforms and previous results.

Improved Locomotion of an AEF Swimming Robot Using Fractional Order Control

Cardiovascular diseases (CVDs) remain the leading cause of death worldwide, according to recent reports from the World Health Organization (WHO). This fact encourages research into the cardiovascular system (CVS) from multiple and different points of view than those given by the medical perspective, highlighting among them the computational and mathematical models that involve experiments much simpler and less expensive to be performed in comparison with in vivo or in vitro heart experiments. However, the CVS is a complex system that needs multidisciplinary knowledge to describe its dynamic models, which help to predict cardiovascular events in patients with heart failure, myocardial or valvular heart disease, so it remains an active area of research. Firstly, this paper presents a novel electrical model of the CVS that extends the classic Windkessel models to the left common carotid artery motivated by the need to have a more complete model from a medical point of view for validation purposes, as well as to describe other cardiovascular phenomena in this area, such as atherosclerosis, one of the main risk factors for CVDs. The model is validated by clinical indices and experimental data obtained from clinical trials performed on a pig. Secondly, as a first step, the goodness of a fractional-order behavior of this model is discussed to characterize different heart diseases through pressure–volume (PV) loops. Unlike other models, it allows us to modify not only the topology, parameters or number of model elements, but also the dynamic by tuning a single parameter, the characteristic differentiation order; consequently, it is expected to provide a valuable insight into this complex system and to support the development of clinical decision systems for CVDs.

/pdf/cardiovascular-circulatory-system-and-left-carotid-model-a-23tzuhh9.pdf

Cardiovascular Circulatory System and Left Carotid Model: A Fractional Approach to Disease Modeling

Performance Study of Propulsion of N-link Artificial Eukaryotic Flagellum Swimming Microrobot Within a Fractional Order Approach: From Simulations to Hardware-in-the-loop Experiments

Ionic polymer-metal composites (IPMCs) are electrically driven materials that undergo bending deformations in the presence of relatively low external voltages, exhibiting a great potential as actuators in applications in soft robotics, microrobotics, and bioengineering, among others. This paper presents an artificial eukaryotic flagellum (AEF) swimming robot made up of IPMC segments for the study of planar wave generation for robot propulsion by single and distributed actuation, i.e., considering the first flagellum link as an actuator or all of them, respectively. The robot comprises three independent and electrically isolated actuators, manufactured over the same 10 mm long IPMC sheet. For control purposes, a dynamic model of the robot is firstly obtained through its frequency response, acquired by experimentally measuring the flagellum tip deflection thanks to an optical laser meter. In particular, two structures are considered for such a model, consisting of a non-integer order integrator in series with a resonant system of both non-integer and integer order. Secondly, the identified models are analyzed and it is concluded that the tip displacement of each actuator or any IPMC point is characterized by the same dynamics, which remains unchanged through the link with mere variations of the gain for low-frequency applications. Based on these results, a controller robust to gain variations is tuned to control link deflection regardless of link length and enabling the implementation of a distributed actuation with the same controller design. Finally, the deflection of each link is analyzed to determine whether an AEF swimming robot based on IPMC is capable of generating a planar wave motion by distributed actuation.

/pdf/modeling-and-control-of-ipmc-based-artificial-eukaryotic-k72z4yti.pdf

Cristina Nuevo-Gallardo

Papers

Back to Basics: Meaning of the Parameters of Fractional Order PID Controllers

Improved Locomotion of an AEF Swimming Robot Using Fractional Order Control

Cardiovascular Circulatory System and Left Carotid Model: A Fractional Approach to Disease Modeling

Performance Study of Propulsion of N-link Artificial Eukaryotic Flagellum Swimming Microrobot Within a Fractional Order Approach: From Simulations to Hardware-in-the-loop Experiments

Modeling and Control of IPMC-Based Artificial Eukaryotic Flagellum Swimming Robot: Distributed Actuation