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 …

I and i

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Formulas For Natural Frequency And Mode Shape

The Viscosity can be imagined as the force that should be applied to a layer of fluid belonging to the plane fixed to the velocity of the layer placed at a fixed distance. For example a fluid flowing in a tube at different speeds: the minimum speed is in the edge of the section (due to friction) and the maximum speed is at the center. The viscosity in this example is that pressure which is exerted on the wall allows a constant speed on the whole section.

Non-newtonian fluids.

Explicit formula and graphs of few special functions are derived in the paper on the basis of various definitions of various fractional derivatives and various fractional integrals. Their applications are also reviewed in the paper.

/pdf/applications-of-fractional-calculus-1c2m93jo56.pdf

Applications of Fractional Calculus

Linear fractional order controllers; A survey in the frequency domain

The applicability of fractional calculus in system engineering outperforms classic identification techniques due to its ability to depict physical phenomena with increased accuracy. The present study explores the increased accuracy and flexibility of a fractional order model applied to an experimental smart beam depicting an airplane wing. The paper details the fractional order system identification of the beam and explores the possibility of realization of the model.

/pdf/different-fractional-order-models-for-an-experimental-smart-1qoway1947.pdf

Different fractional order models for an experimental smart beam system

Combine harvesters are considered challenging from control optimization point of view as they operate as factory on wheels, whereas multiple sub-systems with strong nonlinearities and dynamic interactions need to be managed simultaneously. The task of each sub-system is to execute its part with high performance under strongly varying operating conditions. The environment, from the machine itself, or from the outside area, is a strong disturbance to various interconnected control variables. A solution is provided here for the header height control problem, subject to external load disturbances coming from the field surface profile. The solution is versatile and enables multiple pathways to reached control structures ranging from simple PID tuners to predictive control. The simulated and field test results and their comparison indicates the feasibility of the proposed techniques in practice.

Versatile Solutions for the Combine Harvester Header Height Control Problem

This paper proposes the first MIMO closed-loop control of both anesthesia and hemodynamic system. The designed control strategies have been validated on a novel patient simulator. The aim of this paper is to evaluate the feasibility MIMO closed-loop control of anesthesia and hemodynamic variables taking into account the interaction (synergic and antagonistic) between subsystems. MPC control algorithm have been implemented and the results obtained reveal the feasibility of the patient simulator. The proposed methodology takes into account patient variability, is robust to subsystems interaction and meets the clinical objectives. The control algorithms are combined with the action of the anesthesiologist. Moreover, a disturbance signal to mimic surgical excitation has been introduced in the control architecture. The results given in this paper show the antagonistic effect in closed loop of the intervention from the anesthesiologist when additional bolus intake is present.

Closed-loop control of multi-drug infusion for anesthesia and hemodynamic management

In this paper, a novel approach to nonlinear control techniques based on material properties of handling objects in a class of nonlinear actuators is presented. A modified nonlinear fractional order sliding mode control is proposed with adaptation mechanisms to various material densities. The application domain of these techniques are well suited in agricultural, heavy-duty machines, including those featuring flexible joint manipulators. Experimental data indicates the feasibility of the proposed techniques in practice.

Control of Nonlinear Mechatronic Systems with Context-Dependent Varying Dynamics

This paper describes a novel automatic control toolbox, designed for non-experienced practitioners. Fractional order (FO) controllers are easily tuned with the main purpose of easy practical implementation. Experimental step data are required for the automatic FO controller tuning. An embedded system identification algorithm uses the step data to obtain a process model as a second order plus dead-time (SOPDT) system. Finally, the FO controller is computed based on the previously estimated SOPDT model in order to fulfil a set of user-imposed frequency domain performance specifications: phase margin, gain crossover frequency and gain margin maximization. Experimental step response data from a strongly nonlinear vertical take-off and landing unit have been used to design an FO controller using the toolbox. The experimental closed loop results validate the proposed toolbox. The end result is a user-friendly automatic fractional order controller tuning with endless possibilities of real-world applicability.

/pdf/a-novel-toolbox-for-automatic-design-of-fractional-order-pi-25fsvkyk.pdf

Isabela Roxana Birs

Papers

Different fractional order models for an experimental smart beam system

Versatile Solutions for the Combine Harvester Header Height Control Problem

Closed-loop control of multi-drug infusion for anesthesia and hemodynamic management

Control of Nonlinear Mechatronic Systems with Context-Dependent Varying Dynamics

A Novel Toolbox for Automatic Design of Fractional Order PI Controllers Based on Automatic System Identification from Step Response Data