On fuzzy semi δ – V continuity in fuzzy δ – V topological space

New concepts of fuzzy semi δ – V and fuzzy semi δ – Λ sets were introduced in the work „On fuzzy semi δ – Λ sets and fuzzy semi δ – V sets V – 6” by the authors (J. Trip. Math. Soc., 6, 81 – 88 (2004)). It was shown that the family of all fuzzy semi δ – V sets forms a fuzzy supra topological space on X denoted by ( X, FS δV ). The aim of this paper is to introduce the concept of fuzzy semi δ – V continuity in a fuzzy δ – V topological space. Finally, some properties, preservation theorems, etc., are studied.Нові поняття нечітких напів δ - V та нечітких напів δ - Λ множин введено у роботі авторів „On fuzzy semi δ - Λ sets and fuzzy semi δ - V sets V - 6" (J. Trip. Math. Soc. - 2004. - 6. - C. 81 - 88). Було показано, що сім'я усіх нечітких напів δ - V множин формує нечіткий супра-топологічний простір в X, що позначається як ( X, FS δ V ). Метою даної статті є введення поняття нестійкої напів δ - V неперервності у нестійкому δ - V топологічному просторі. Також досліджено деякі її властивості, наведено теорему про збереження та інші питання

Performance analysis of robust stable PID controllers using dominant pole placement for SOPTD process models

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordThis paper derives new formulations for designing dominant pole placement based proportionalintegral-derivative (PID) controllers to handle second order processes with time delays (SOPTD). Previously, similar attempts have been made for pole placement in delay-free systems. The presence of the time delay term manifests itself as a higher order system with variable number of interlaced poles and zeros upon Pade approximation, which makes it difficult to achieve precise pole placement control. We here report the analytical expressions to constrain the closed loop dominant and nondominant poles at the desired locations in the complex s-plane, using a third order Pade approximation for the delay term. However, invariance of the closed loop performance with different time delay approximation has also been verified using increasing order of Pade, representing a closed to reality higher order delay dynamics. The choice of the nature of non-dominant poles e.g. all being complex, real or a combination of them modifies the characteristic equation and influences the achievable stability regions. The effect of different types of non-dominant poles and the corresponding stability regions are obtained for nine test-bench processes indicating different levels of open-loop damping and lag to delay ratio. Next, we investigate which expression yields a wider stability region in the design parameter space by using Monte Carlo simulations while uniformly sampling a chosen design parameter space. The accepted data-points from the stabilizing region in the design parameter space can then be mapped on to the PID controller parameter space, relating these two sets of parameters. The widest stability region is then used to find out the most robust solution which are investigated using an unsupervised data clustering algorithm yielding the optimal centroid location of the arbitrary shaped stability regions. Various time and frequency domain control performance parameters are investigated next, as well as their deviations with uncertain process parameters, using thousands of Monte Carlo simulations, around the robust stable solution for each of the nine test-bench processes. We also report, PID controller tuning rules for the robust stable solutions using the test-bench processes while also providing computational complexity analysis of the algorithm and carry out hypothesis testing for the distribution of sampled data-points for different classes of process dynamics and non-dominant pole types.KH acknowledges the support from the University Grants Commission (UGC), Govt. of India under its Basic Scientific Research (BSR) schem

Transformation of LQR weights for Discretization Invariant Performance of PI/PID Dominant Pole Placement Controllers

This is the author accepted manuscript. The final version is available from Cambridge University Press via the DOI in this record.Linear quadratic regulator (LQR), a popular technique for designing optimal state feedback controller is used to derive a mapping between continuous and discrete-time inverse optimal equivalence of proportional integral derivative (PID) control problem via dominant pole placement. The aim is to derive transformation of the LQR weighting matrix for fixed weighting factor, using the discrete algebraic Riccati equation (DARE) to design a discrete time optimal PID controller producing similar time response to its continuous time counterpart. Continuous time LQR-based PID controller can be transformed to discrete time by establishing a relation between the respective LQR weighting matrices that will produce similar closed loop response, independent of the chosen sampling time. Simulation examples of first/second order and first-order integrating processes exhibiting stable/unstable and marginally-stable open-loop dynamics are provided, using the transformation of LQR weights. Time responses for set-point and disturbance inputs are compared for different sampling time as fraction of the desired closed-loop time constant.University Grants Commission (UGC), Government of IndiaESIF ERDF Cornwal

Hybrid numerical scheme for time-evolving wave fields

Many problems in geophysics, acoustics, elasticity theory, cancer treatment, food process control and electrodynamics involve study of wave field synthesis (WFS) in some form or another. In the present work, modelling of wave propagation phenomena is studied as a static problem, using finite element method and treating time as an additional spatial dimension. In particular, WFS problems are analysed using discrete methods. It is shown that a fully finite element-based scheme is very natural and effective method for the solution of such problems. Distributed WFS in the context of two-dimensional problems is outlined and incorporation of any geometric or material non-linearities is shown to be straightforward. This has significant implications for problems in geophysics or biological media, where material inhomogeneities are quite prevalent. Numerical results are presented for several problems referring to media with material inhomogeneities and predefined absorption profiles. The method can be extended to three-dimensional problems involving anisotropic media properties in a relatively straightforward manner

Jarcho-Levin syndrome

This article does not have an abstract

Future evolution due to backreaction in a Universe with multiple inhomogeneous domains

We formulate a model of spacetime with inhomogeneous matter distribution in multiple domains. In the context of the backreaction framework using Buchert's averaging procedure, we evaluate the effect of backreaction due to the inhomogeneities on the late time global evolution of the Universe. Examining the future evolution of this universe, we find that it can transit from the presently accelerating phase to undergo future deceleration. The future deceleration is governed by our model parameters. We constrain the model parameters using observational analysis of the Union 2.1 supernova Ia data employing the Markov Chain Monte Carlo method.Comment: 12 pages, 7 figure

Analyzing the 21-cm signal brightness temperature in the Universe with inhomogeneities

We explore the 21-cm signal in our Universe containing inhomogeneous matter distribution at considerably large scales. Employing Buchert's averaging procedure in the context of a model of spacetime with multiple inhomogeneous domains, we evaluate the effect of our model parameters on the observable 21-cm signal brightness temperature. Our model parameters are constrained through the Markov Chain Monte Carlo method using the Union 2.1 supernova Ia observational data. We find that a significant dip in the brightness temperature compared to the $\Lambda$CDM prediction could arise as an effect of the inhomogeneities present in the Universe.Comment: 17 pages, 7 figure

Optimum Weight Selection Based LQR Formulation for the Design of Fractional Order PIλDμ Controllers to Handle a Class of Fractional Order Systems

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.A weighted summation of Integral of Time Multiplied Absolute Error (ITAE) and Integral of Squared Controller Output (ISCO) minimization based time domain optimal tuning of fractional-order (FO) PID or PI{\lambda}D{\mu} controller is proposed in this paper with a Linear Quadratic Regulator (LQR) based technique that minimizes the change in trajectories of the state variables and the control signal. A class of fractional order systems having single non-integer order element which show highly sluggish and oscillatory open loop responses have been tuned with an LQR based FOPID controller. The proposed controller design methodology is compared with the existing time domain optimal tuning techniques with respect to change in the trajectory of state variables, tracking performance for change in set-point, magnitude of control signal and also the capability of load disturbance suppression. A real coded genetic algorithm (GA) has been used for the optimal choice of weighting matrices while designing the quadratic regulator by minimizing the time domain integral performance index. Credible simulation studies have been presented to justify the proposition