Control of Dynamic Objects in the Conditions of Uncertainty in the Point Sliding Mode

2019 ◽  
Vol 20 (12) ◽  
pp. 714-722
Author(s):  
G. A. Rustamov ◽  
M. B. Namazov ◽  
A. Y. Gasimov ◽  
R. G. Rustamov
Keyword(s):  
Finite Number ◽  
Sliding Mode ◽  
Practical Importance ◽  
Practical Significance ◽  
Switching Frequency ◽  
Time Interval ◽  
Initial State ◽  
Classical Formulation ◽  
Sliding Motion ◽  
Switching Line

There is development of the well-known sliding mode, which in the classical formulation didn’t find the development to be applied to control systems discussed. Alternatively, there is method of organizing one of the uniformity of the sliding mode called the "point sliding mode" proposed. The distinctive feature of this mode is that here the control gaps occur at time-equal points of the switching line (hyperplane) which allows the origin of coordinates for a finite number of switches. The possibility of changing the time interval between these points makes it possible to obtain various modes: a finite mode, in which a given point is reached from any initial state in one switch, and in this mode the switch line is "isochronous"; point sliding mode in which a given point is reached in a finite number of switchings; limit mode, when the length of time intervals tend to zero, and the switching frequency to infinity. Considering this feature the concept of "degree of slip" is introduced. It is shown that in the case of forced movement in the SPS, a sliding motion is observed, which does not allow for ensuring invariance with respect to external disturbances. There are two ways to eliminate the forced component of the movement offered. One of the advantages of using a point sliding mode is that, in order to improve performance, it is not necessary to use a boundary layer, which is realized by entering various logical conditions into the control algorithm. The practical significance of a point sliding mode lies in the fact that, with a small switching frequency, it is possible to maintain the quality indices of an undefined object within an acceptable interval. The studies were conducted for onedimensional second-order linear systems (SISO). Results can be generalized for higher order multidimensional systems. Solution of model problems on MATLAB / Simulink allows us to make a number of positive conclusions that are of great practical importance in terms of expanding the area of use of skipping modes, especially in relation to the management of undefined objects.

scholarly journals Zero-Width Quasi-Sliding Mode Band in the Presence of Non-Matched Uncertainties

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3011
Author(s):  
Paweł Latosiński ◽  
Andrzej Bartoszewicz
Keyword(s):  
Sliding Mode Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
Control Strategies ◽  
Relative Degree ◽  
Band Width ◽  
Representative Point ◽  
Mode Control ◽  
Sliding Motion ◽  
Selection Of

Sliding mode control strategies are well known for ensuring robustness of the system with respect to disturbance and model uncertainties. For continuous-time plants, they achieve this property by confining the system state to a particular hyperplane in the state space. Contrary to this, discrete-time sliding mode control (DSMC) strategies only drive the system representative point to a certain vicinity of that hyperplane. In established literature on DSMC, the width of this vicinity has always been strictly greater than zero in the presence of uncertainties. Thus, ideal sliding motion was considered impossible for discrete-time systems. In this paper, a new approach to DSMC design is presented with the aim of driving the system representative point exactly onto the sliding hyperplane even in the presence of uncertainties. As a result, the quasi-sliding mode band width is effectively reduced to zero and ideal discrete-time sliding motion is ensured. This is achieved with the proper selection of the sliding hyperplane, using the unique properties of relative degree two sliding variables. It is further demonstrated that, even in cases where selection of a relative degree two sliding variable is impossible, one can use the proposed technique to significantly reduce the quasi-sliding mode band width.

scholarly journals Reaching Law Based Sliding Mode Control of Sampled Time Systems

Energies ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1882
Author(s):  
Piotr Leśniewski ◽  
Andrzej Bartoszewicz
Keyword(s):  
Sliding Mode Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
Rate Of Change ◽  
Reaching Law ◽  
Mode Control ◽  
Sliding Motion ◽  
Control Precision ◽  
Continuous Time Systems ◽  
Time Systems

In this paper, discrete time reaching law-based sliding mode control of continuous time systems is considered. In sliding mode control methods, usually the assumption of bounded absolute values of disturbances is used. However in many cases, the rate of change of the disturbance is also bounded. In the presented approach, this knowledge is used to improve the control precision and reduce the undesirable chattering. Another advantage of the proposed method is that the disturbance does not have to satisfy the matching conditions. In the paper two new reaching laws are analyzed, one of them ensures the switching quasi-sliding motion and the other the non-switching motion. For both of them, the robustness is assessed by calculating the quasi-sliding mode band width, as well as the greatest possible state error values. Specifically, the state errors are not considered only at the sampling instants, as is usual for discrete time systems, but the bounds on the continuous values “between” the sampling instants are also derived. Then, the proposed approaches are compared and analyzed with respect to energy expenditure of the control signal.

Control of Fractional-Order Systems Using Chatter-Free Sliding Mode Approach

2014 ◽  
Vol 9 (3) ◽  
Author(s):  
Mohammad Pourmahmood Aghababa
Keyword(s):  
Fractional Derivative ◽  
Sliding Mode ◽  
Variable Structure ◽  
Stability And Convergence ◽  
Control Input ◽  
Fractional Systems ◽  
Sliding Motion ◽  
Efficient Performance ◽  
Sliding Manifold ◽  
Chattering Free

The problem of stabilization of nonlinear fractional systems in spite of system uncertainties is investigated in this paper. First, a proper fractional derivative type sliding manifold with desired stability and convergence properties is designed. Then, the fractional stability theory is adopted to derive a robust sliding control law to force the system trajectories to attain the proposed sliding manifold and remain on it evermore. The existence of the sliding motion is mathematically proven. Furthermore, the sign function in the control input, which is responsible to the being of harmful chattering, is transferred into the fractional derivative of the control input. Therefore, the resulted control input becomes smooth and free of the chattering. Some numerical simulations are presented to illustrate the efficient performance of the proposed chattering-free fractional variable structure controller.

Time scale dependence of wind speed patterns - implications for wind power site assessment

2021 ◽  
Author(s):  
Cristian Suteanu
Keyword(s):  
Wind Speed ◽  
Wind Power ◽  
Practical Importance ◽  
Sampling Rate ◽  
Fluctuation Analysis ◽  
Time Interval ◽  
Time Averaging ◽  
Time Intervals ◽  
Site Assessment ◽  
Wind Pattern

<p>Characterizing properties of wind speed variability and their dependence on the temporal scale is important: from sub-second intervals (for the design and monitoring of wind turbines) to longer time scales – months, years (for the evaluation of the wind power potential). Wind speed data are usually reported as averages over time intervals of various length (minutes, days, months, etc). The research project presented in this paper addressed the following questions: What aspects of the wind pattern are changed, in what ways and to what extent, in the process of producing time-averaged values? What precautions should be considered when time-averaged values are used in the assessment of wind variability? What are the conditions to be fulfilled for a meaningful comparison of wind pattern characteristics obtained in distinct studies? Our research started from wind speed records sampled at 0.14 second intervals, which were averaged over increasingly longer time intervals. Variability evaluation was based on statistical moments, L-moments, and detrended fluctuation analysis. We present the change suffered by characteristics of temporal variability as a function of sampling rate and the averaging time interval. In particular, the height dependence of wind speed variability, which is of theoretical and practical importance, is shown to be progressively erased when averaging intervals are increased. The paper makes recommendations regarding the interpretation of wind pattern characteristics obtained at different sites as a function of sampling rate and time-averaging intervals.</p>

scholarly journals Switching Frequency Regulation in Sliding Mode Control by a Hysteresis Band Controller

2017 ◽  
Vol 32 (2) ◽  
pp. 1557-1569 ◽  
Author(s):  
Victor Repecho ◽  
Domingo Biel ◽  
Josep M. Olm ◽  
Enric Fossas Colet
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Frequency Regulation ◽  
Switching Frequency ◽  
Mode Control

scholarly journals A Novel Filter Extracted Equivalent Control Based Fixed Frequency Sliding Mode Approach for Power Electronic Converters

Energies ◽  
2019 ◽  
Vol 12 (5) ◽  
pp. 853 ◽  
Author(s):  
Abdul Yasin ◽  
Muhammad Ashraf ◽  
Aamer Bhatti
Keyword(s):  
Boundary Layer ◽  
Pulse Width ◽  
Pulse Width Modulation ◽  
Sliding Mode ◽  
Discontinuous Function ◽  
Switching Frequency ◽  
Power Electronic ◽  
Power Electronic Converters ◽  
Fixed Frequency ◽  
Equivalent Control

The key issue in the implementation of the Sliding Mode Control (SMC) in analogue circuits and power electronic converters is its variable switching frequency. The drifting frequency causes electromagnetic compatibility issues and also adversely affect the efficiency of the converter, because the proper size of the inductor and the capacitor depends upon the switching frequency. Pulse Width Modulation based SMC (PWM-SMC) offers the solution, however, it uses either boundary layer approach or employs pulse width modulation of the ideal equivalent control signal. The first technique compromises the performance within the boundary layer, while the latter may not possess properties like robustness and order reduction due to the absence of the discontinuous function. In this research, a novel approach to fix the switching frequency in SMC is proposed, that employs a low pass filter to extract the equivalent control from the discontinuous function, such that the performance and robustness remains intact. To benchmark the experimental observations, a comparison with existing double integral type PWM-SMC is also presented. The results confirm that an improvement of 20% in the rise time and 25.3% in the settling time is obtained. The voltage sag during step change in load is reduced to 42.86%, indicating the increase in the robustness. The experiments prove the hypothesis that a discontinuous function based fixed frequency SMC performs better in terms of disturbances rejection as compared to its counterpart based solely on ideal equivalent control.

scholarly journals Probability distributions of COVID-19 tweet posted trends use a nonhomogeneous Poisson process

2020 ◽  
Vol 1 (4) ◽  
pp. 229-238
Author(s):  
Devi Munandar ◽  
Sudradjat Supian ◽  
Subiyanto Subiyanto
Keyword(s):  
Social Media ◽  
Poisson Process ◽  
Exponential Distribution ◽  
Probability Distributions ◽  
Nonhomogeneous Poisson Process ◽  
Time Interval ◽  
Initial State ◽  
Time Intervals ◽  
Time Parameters ◽  
Parameter Values

The influence of social media in disseminating information, especially during the COVID-19 pandemic, can be observed with time interval, so that the probability of number of tweets discussed by netizens on social media can be observed. The nonhomogeneous Poisson process (NHPP) is a Poisson process dependent on time parameters and the exponential distribution having unequal parameter values and, independently of each other. The probability of no occurrence an event in the initial state is one and the probability of an event in initial state is zero. Using of non-homogeneous Poisson in this paper aims to predict and count the number of tweet posts with the keyword coronavirus, COVID-19 with set time intervals every day. Posting of tweets from one time each day to the next do not affect each other and the number of tweets is not the same. The dataset used in this study is crawling of COVID-19 tweets three times a day with duration of 20 minutes each crawled for 13 days or 39 time intervals. The result of this study obtained predictions and calculated for the probability of the number of tweets for the tendency of netizens to post on the situation of the COVID-19 pandemic.

Theoretical study of Zeno and anti-Zeno effects on photodissociation dynamics: A model approach

2016 ◽  
Vol 15 (08) ◽  
pp. 1650070 ◽  
Author(s):  
Bikram Nath ◽  
Chandan Kumar Mondal
Keyword(s):  
Repeated Measurements ◽  
Time Interval ◽  
Mathematical Tool ◽  
Population Transfer ◽  
Vibrational States ◽  
Initial State ◽  
Zeno Effect ◽  
Dissociation Dynamics ◽  
Vibrational Population

Zeno and anti-Zeno effects in the evolution of the multi-photonic dissociation dynamics of the diatomic molecule HBr[Formula: see text] owing to repeated measurements demand if the system in the initial state have been studied. The effects have been calculated numerically for the case of vibrational population transfer and dissociation dynamics of HBr[Formula: see text] taking it as a model. We use time-dependent Fourier grid Hamiltonian (TDFGH) method as a mathematical tool in presence of intense radiation field as perturbation. The effects have been explored through a probable mechanism of population transfer from the ground vibrational state to the different upper vibrational states which ultimately go to the dissociation continuum. The results show significant differences in the mechanism of population transfer and the significant role of time interval of measurement ([Formula: see text] in Zeno and anti-Zeno effects. In case of survival probability of ground vibrational states, there is Zeno effect when the frequency of the laser to which the molecule is submitted is near the vibrational [Formula: see text] to [Formula: see text] resonance, while there is anti-Zeno effect if it is far from this resonance.

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