An implicit discretization-based adaptive reaching law for discrete-time sliding mode control systems

In conventional reaching law approaches, the disturbance suppression is achieved at the cost of high-frequency chattering or increasing the complexity of algorithm such as adding a high-order disturbance compensator. This paper presents the design and analysis of a novel implicit discretization-based adaptive reaching law for discrete-time sliding mode control systems. First, the implicit Euler technique is introduced into the design of discrete reaching laws, and it is proved to be able to eliminate numerical chattering completely. By using a self-adaptive power term, the newly designed reaching law can obtain an arbitrarily small boundary layer of sliding surface, and at the different phases of sliding mode motion, the adaptive power parameter can automatically regulate its value to guarantee globally fast convergence without destroying the accuracy of sliding variable. Then, based on a predefined trajectory of sliding variable, the discrete-time sliding mode control law is developed to realize high control accuracy without additional design. Compared with previous methods, the main contribution of proposed reaching law lies in that it can acquire high-precision sliding mode motion and simultaneously eliminate numerical chattering in spite of complex uncertainties only by adjusting the adaptive power parameter. Finally, a simulation example on the piezomotor-driven linear stage is provided to verify the theoretical results.

Estimation of Global Solar Radiation on Horizontal Surfaces using Temperature-Based Model in Ilorin, Nigeria

In this study, the Solar Irradiation received was estimated in Illorin, Kwara, Nigeria, using the maximum and minimum temperature measured by an Arduino-based solar power parameter measuring system. The Extraterrestrial, Global and Diffuse Solar Radiation were estimated monthly using the Hargreaves and Samani model. This model also required the daily temperature, clearness index, and extraterrestrial solar irradiation in its use alongside the maximum and minimum temperatures. In using this model, we resolved the graphs of the three types of Solar Irradiation over ten days. For the selected days, the estimated extraterrestrial solar irradiation varies from 10.41kWh/m2 to 10.47 kWh/m2, while the mean extraterrestrial solar irradiation is 10.44 kWh/m2. The estimated global solar irradiation varies from 4.42 kWh/m2 to 5.677kWh/m2, while the estimated mean global solar irradiation is 5.19kWh/m2 per day. The estimated diffuse solar irradiation varies from 3.46kWh/m2 to 5.48kWh/m2, while the mean diffuse solar irradiation is per day is 4.61kWh/m2.

Peculiarities in computation of mode parameters and qualitative indices of ring joining surface lapping in flanges of manufacturing equipment

Peculiarities in the computation of cutting modes and power parameter choice during flange ring surface lapping on flat-bed smooth finish machines for joining pipeline equipment to pipes or manufacturing equipment are shown. There are defined qualitative indices of surfaces worked in above-mentioned parts requiring a high degree of sealing.

Improving representation of zero flows in probabilistic hydrological modelling of ephemeral catchments

<p>Ephemeral catchments, where streamflow is frequently zero or negligible, are common across the world yet difficult to model reliably. This paper evaluates probabilistic approaches for modelling streamflow in ephemeral catchments, with a focus on the description of predictive uncertainty using residual error models.</p><p>We compare an explicit treatment of zero flows using a censoring approach versus a simpler pragmatic approach where the lower streamflow bound of zero is applied in prediction only. Following a theoretical exposition, empirical comparisons are reported using a daily rainfall-runoff model (GR4J), four residual error schemes (based on log, log-sinh and Box-Cox (BC) transformations with power parameter L = 0.2 and 0.5), 74 Australian catchments with diverse hydroclimatology, and five performance metrics, including reliability, precision, bias and proportion of zero flow days.</p><p>The explicit approach is most beneficial in "mid-ephemeral" catchments (5-50% zero flows) where it offers substantial improvements over the pragmatic approach. The BC0.2 and BC0.5 transformations are Pareto optimal: BC0.2 achieves better characterisation of predictive uncertainty, whereas BC0.5 attains lower volumetric bias. In "low-ephemeral" catchments (<5% zero flows) the pragmatic approach is sufficient, whereas in "high-ephemeral" catchments (>50% zero flows) both approaches incur limitations and further method development is warranted. The findings provide guidance on improving probabilistic streamflow predictions in ephemeral catchments.</p>

Use of Power Transform Mixing Ratios as Hydrometeor Control Variables for Direct Assimilation of Radar Reflectivity in GSI En3DVar and Tests with Five Convective Storms Cases

When directly assimilating radar data within a variational framework using hydrometeor mixing ratios (q) as control variables (CVq), the gradient of the cost function becomes extremely large when background mixing ratio is close to zero. This significantly slows down minimization convergence and makes the assimilation of radial velocity and other observations ineffective because of the dominance of reflectivity observation term in the cost function gradient. Using logarithmic hydrometeor mixing ratios as control variables (CVlogq) can alleviate the problem but the high nonlinearity of logarithmic transformation can introduce spurious analysis increments into mixing ratios.In this study, power transform of hydrometeors is proposed to form new control variables (CVpq) where the nonlinearity of transformation can be adjusted by tuning exponent or power parameter p. The performance of assimilating radar data using CVpq is compared with those using CVq and CVlogq for the analyses and forecasts of five convective storm cases from spring of 2017. Results show that CVpq with p = 0.4 (CVpq0.4) gives the best reflectivity forecasts in terms of root mean square error and equitable threat score. Furthermore, CVpq0.4 has faster convergence of cost function minimization than CVq and produces less spurious analysis increment than CVlogq. Compared to CVq and CVlogq, CVpq0.4 have better skills of 0-3h composite reflectivity forecasts, and the updraft helicity tracks for the 16 May 2017 Texas and Oklahoma tornado outbreak case are more consistent with observations when using CVpq0.4.

Box-Cox Gamma-G Family of Distributions: Theory and Applications

This paper is devoted to a new class of distributions called the Box-Cox gamma-G family. It is a natural generalization of the useful Ristić–Balakrishnan-G family of distributions, containing a wide variety of power gamma-G distributions, including the odd gamma-G distributions. The key tool for this generalization is the use of the Box-Cox transformation involving a tuning power parameter. Diverse mathematical properties of interest are derived. Then a specific member with three parameters based on the half-Cauchy distribution is studied and considered as a statistical model. The method of maximum likelihood is used to estimate the related parameters, along with a simulation study illustrating the theoretical convergence of the estimators. Finally, two different real datasets are analyzed to show the fitting power of the new model compared to other appropriate models.