Discrete-time implementation and experimental validation of a fractional order PD controller for vibration suppression in airplane wings

Vibrations in airplane wings have a negative impact on the quality and safety of a flight. For this reason, active vibration suppression techniques are of extreme importance. In this paper, a smart beam is used as a simulator for the airplane wings and a fractional order PD controller is designed for active vibration mitigation. To implement the ideal fractional order controller on the smart beam unit, its digital approximation is required. In this paper, a new continuous-to-discrete-time operator is used to obtain the discrete-time approximation of the ideal fractional order PD controller. The efficiency and flexibility, as well as some guidelines for using this new operator, are given. The numerical examples show that high accuracy of approximation is obtained and that the proposed method can be considered as a suitable solution for obtaining the digital approximation of fractional order controllers. The experimental results demonstrate that the designed controller can significantly improve the vibration suppression in smart beams

Managing temporary workers in higher education: still at the margin?

Purpose – To evaluate whether “numerical flexibility” – specifically a form of temporary and precarious employment – hourly-paid part-time teaching in the UK higher education sector – adds strategic value and demonstrates good practice. Design/methodology/approach – The study is based on new evidence drawn from five case study organisations in which a range of managers was interviewed in depth. Findings – Analysis identifies a continuum of strategies from integration into the main workforce through to “deepened differentiation”. Although integration is somewhat problematic when applied to a diverse group, differentiation seems predicated on a defensive, risk management approach designed to further marginalise this activity. Also, differentiation fails to address the aspirations of many employees, creating tensions between institutional strategy and the needs of academic heads. Research limitations/implications – The number of case studies is limited. These case studies were selected because they had the most proactive strategies on this issue, which infers that the majority of employers in HE have not been rather less strategic or proactive. Practical implications – The paper is of particular value to HR professionals considering the use of numerical flexibility approaches. It also contributes to the academic debate on the strategic value of such approaches. Originality/value – The paper explores a neglected but important area of the workforce. The paper notes that some supposed benefits of numerical flexibility might be illusory, such as the deployment of allegedly “cheap and disposable” substitute workers which may be offset by unintentional consequences including rigidities in an organisation's human resource systems

A NEW APPROACH FOR DIRECT DISCRETIZATION OF FRACTIONAL ORDER OPERATOR IN DELTA DOMAIN

The fractional order system (FOS) comprises fractional order operator. In order to obtain the discretized version of the fractional order system, the first step is to discretize the fractional order operator, commonly expressed as s±m, 0 < m < 1. The fractional order operator can be used as fractional order differentiator or integrator, depending upon the values of . In general, there are two approaches for discretization of fractional order operator, one is indirect method of discretization and another is direct method of discretization. The direct discretization method capitalizes the method of formation of generating function where fractional order operator s±mis expressed as a function of Z in the shift operator parameterization and continued fraction expansion (CFE) method is then utilized to get the corresponding discrete domain rational transfer function. There is an inherent problem with this discretization method using shift operator parameterization (discrete Z-domain). At fast sampling time, the discretized version of the continuous time operator or system should resemble that of the continuous time counterpart if the sampling theorem is satisfied. At very high sampling rate, the shift operator parameterized system fails to provide meaningful information due to its numerical ill conditioning. To overcome this problem, Delta operator parameterization for discretization is considered in this paper, where at fast sampling rate, the continuous time results can be obtained from the discrete time experiments and therefore a unified framework can be developed to get the discrete time results and continuous time results hand to hand. In this paper a new generating function is proposed to discretize the fractional order operator using the Gauss-Legendre 2-point quadrature rule. Additionally, the function has been expanded using the CFE in order to obtain rational approximation of the fractional order operator. The detailed mathematical formulations along with the simulation results in MATLAB, with different fractional order systems are considered, in order to prove the newness of this formulation for discretization of the FOS in complex Delta domain

Reconnection–less Reconfigurable Fractional–Order Current–Mode Integrator Design with Simple Control

A design of a fractional-order (FO) integrator is introduced for operation of resulting solution in the current mode (CM). The solution of the integrator is based on the utilization of RC structures, but in comparison to other RC structure based FO designs, the proposed integrator offers the electronic control of the order. Moreover, the control of the proposed integrator does not require multiple specific and accurate values of the control voltages/currents in comparison to the topologies based on the approximation of the FO Laplacian operator. The electronic control of a gain level (gain adjustment) of the proposed integrator is available. The paper offers the results of Cadence IC6 (spectre) simulations and more importantly experimental measurements to support the presented design. The proposed integrator can be used to build various FO circuits as demonstrated by the utilization of the integrator into a structure of a frequency filter in order to provide FO characteristics

Bipedal Locomotion: A Fractional CPG for Generating Patterns

Proceedings of the 10th Conference on Dynamical Systems Theory and ApplicationsThere has been an increase interest in the study of animal locomotion. Many models for the generation of locomotion patterns of different animals, such as centipedes, millipedes, quadrupeds, hexapods, bipeds, have been proposed. The main goal is the understanding of the neural bases that are behind animal locomotion. In vertebrates, goal-directed locomotion is a complex task, involving the central pattern generators located somewhere in the spinal cord, the brainstem command systems for locomotion, the control systems for steering and control of body orientation, and the neural structures responsible for the selection of motor primitives. In this paper, we focus in the neural networks that send signals to the muscle groups in each joint, the so-called central pattern generators (CPGs). We consider a fractional version of a CPG model for locomotion in bipeds. A fractional derivative) Dα f (x), with α non-integer, is a generalization of the concept of an integer derivative, where α = 1 The integer CPG model has been proposed by Golubitsky, Stewart, Buono and Collins, and studied later by Pinto and Golubitsky. It is a four cells model, where each cell is modelled by a system of ordinary differential equations. The coupling between the cells allows two independent permutations, and, as so, the system has D2 symmetry. We consider 0 < α ≤ 1 and we compute, for each value of α, the amplitude and the period of the periodic solutions identified with two legs' patterns in bipeds. We find the amplitude and the period increase as α varies from zero up to one