Stabilization of Nonlinear Continuous Systems Based on Discrete Integrator Backstepping

2021 ◽  
Author(s):  
Jean Oscard Domguia Teto ◽  
Jorg Seewig
Keyword(s):  
Continuous Systems ◽  
Integrator Backstepping ◽  
Discrete Integrator

Evaluation of fractional order of the discrete integrator. Part II

2020 ◽  
Vol 23 (2) ◽  
pp. 408-426
Author(s):  
Piotr Ostalczyk ◽  
Marcin Bąkała ◽  
Jacek Nowakowski ◽  
Dominik Sankowski
Keyword(s):  
Fractional Order ◽  
Output Signal ◽  
Linear Time ◽  
Mathematical Problem ◽  
Simple Method ◽  
Linear Time Invariant ◽  
Input And Output ◽  
Order Difference Equation ◽  
Time Invariant ◽  
Discrete Integrator

AbstractThis is a continuation (Part II) of our previous paper [19]. In this paper we present a simple method of the fractional-order value calculation of the fractional-order discrete integration element. We assume that the input and output signals are known. The linear time-invariant fractional-order difference equation is reduced to the polynomial in a variable ν with coefficients depending on the measured input and output signal values. One should solve linear algebraic equation or find roots of a polynomial. This simple mathematical problem complicates when the measured output signal contains a noise. Then, the polynomial roots are unsettled because they are very sensitive to coefficients variability. In the paper we show that the discrete integrator fractional-order is very stiff due to the degree of the polynomial. The minimal number of samples guaranteeing the correct order is evaluated. The investigations are supported by a numerical example.

scholarly journals Hidden Attractors in Discrete Dynamical Systems

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 616
Author(s):  
Marek Berezowski ◽  
Marcin Lawnik
Keyword(s):  
Dynamical Systems ◽  
Chaos Theory ◽  
Scientific Literature ◽  
Discrete Systems ◽  
Discrete Dynamical Systems ◽  
Continuous Systems ◽  
Hidden Attractors ◽  
Negative Effects ◽  
Chemical Reactors ◽  
Points Of View

Research using chaos theory allows for a better understanding of many phenomena modeled by means of dynamical systems. The appearance of chaos in a given process can lead to very negative effects, e.g., in the construction of bridges or in systems based on chemical reactors. This problem is important, especially when in a given dynamic process there are so-called hidden attractors. In the scientific literature, we can find many works that deal with this issue from both the theoretical and practical points of view. The vast majority of these works concern multidimensional continuous systems. Our work shows these attractors in discrete systems. They can occur in Newton’s recursion and in numerical integration.

scholarly journals Generation of Photopolymerized Microparticles Based on PEGDA Using Microfluidic Devices. Part 1. Initial Gelation Time and Mechanical Properties of the Material

Micromachines ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 293
Author(s):  
José M. Acosta-Cuevas ◽  
José González-García ◽  
Mario García-Ramírez ◽  
Víctor H. Pérez-Luna ◽  
Erick Omar Cisneros-López ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Gelation Time ◽  
Mesh Size ◽  
Microfluidic Devices ◽  
Future Generation ◽  
Mechanical Tests ◽  
Continuous Systems ◽  
Polyethylene Glycol Diacrylate ◽  
Glycol Diacrylate ◽  
Close Relationship

Photopolymerized microparticles are made of biocompatible hydrogels like Polyethylene Glycol Diacrylate (PEGDA) by using microfluidic devices are a good option for encapsulation, transport and retention of biological or toxic agents. Due to the different applications of these microparticles, it is important to investigate the formulation and the mechanical properties of the material of which they are made of. Therefore, in the present study, mechanical tests were carried out to determine the swelling, drying, soluble fraction, compression, cross-linking density (Mc) and mesh size (ξ) properties of different hydrogel formulations. Tests provided sufficient data to select the best formulation for the future generation of microparticles using microfluidic devices. The initial gelation times of the hydrogels formulations were estimated for their use in the photopolymerization process inside a microfluidic device. Obtained results showed a close relationship between the amount of PEGDA used in the hydrogel and its mechanical properties as well as its initial gelation time. Consequently, it is of considerable importance to know the mechanical properties of the hydrogels made in this research for their proper manipulation and application. On the other hand, the initial gelation time is crucial in photopolymerizable hydrogels and their use in continuous systems such as microfluidic devices.

scholarly journals Investigating the performance of agricultural wastes and their ashes in removing phenol from leachate in a fixed-bed column

2020 ◽  
Vol 81 (10) ◽  
pp. 2109-2126 ◽  
Author(s):  
Seyed Omid Ahmadinejad ◽  
Seyed Taghi Omid Naeeni ◽  
Zahra Akbari ◽  
Sara Nazif
Keyword(s):  
Activated Carbon ◽  
Large Scale ◽  
Fixed Bed ◽  
Walnut Shell ◽  
Continuous Systems ◽  
Phenol Removal ◽  
Adsorption Method ◽  
Fixed Bed Column ◽  
Saturation Time ◽  
Coconut Shell Activated Carbon

Abstract One of the major pollutants in leachate is phenol. Due to safety and environmental problems, removal of phenol from leachate is essential. Most of the adsorption studies have been conducted in batch systems. Practically, large-scale adsorption is carried out in continuous systems. In this research, the adsorption method has been used for phenol removal from leachate by using walnut shell activated carbon (WSA) and coconut shell activated carbon (CSA) as adsorbents in a fixed-bed column. The effect of adsorbent bed depth, influent phenol concentration and type of adsorbent on adsorption was explored. By increasing the depth of the adsorbent bed in the column, phenol removal efficiency and saturation time increase significantly. Also, by increasing the influent concentration, saturation time of the column decreases. To predict the column performance and describe the breakthrough curve, three kinetic models of Yon-Nelson, Adams-Bohart and Thomas were applied. The results of the experiments indicate that there is a good match between the results of the experiment and the predicted results of the models.

Stability Criteria for Distributed Nonlinear Sampled-Data Systems Defined by Green’s Functions

1974 ◽  
Vol 96 (3) ◽  
pp. 315-321 ◽  
Author(s):  
G. Jumarie
Keyword(s):  
Stability Criterion ◽  
Feedback Gain ◽  
Continuous Systems ◽  
Mean Square ◽  
Data Systems ◽  
Sampled Data ◽  
Input Output ◽  
Output Stability ◽  
Lumped Parameter ◽  
The Mean

Sampled-data, nonlinear, distributed systems, which exhibit a structure similar to that of the standard closed loop with lumped parameter, are investigated from the viewpoint of their input-output stability. These systems are governed by operational equations involving discrete Laplace-Green kernels. Their feedback gains are bounded by upper and lower values which depend explicitly on the time and the distributed parameter. The main result is: an input-output stability theorem is given which applies both in L∞ (O, ∞) and L2 (O, ∞). This criterion, which may be considered as being an extension of the ≪circle criterion≫, involves the mean square value on the bounds of the feedback gain. Stability conditions for continuous systems are derived from this result. In the special case of systems with distributed periodical time-varying feedback gains, a stability criterion is given which applies in Marcinkiewicz space M2 (O, ∞). This result which involves the mean square value of the feedback gain is generally less restrictive than the L2 (O, ∞) stability criterion mentioned above.

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