scholarly journals The Complex Adaptive Delta-Modulator in Sliding Mode Theory

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 814
Author(s):  
Dhafer Almakhles
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Sliding Mode ◽  
Stability Conditions ◽  
Mode Theory ◽  
Dynamical Behaviors ◽  
Complex Adaptive ◽  
The Stability ◽  
Parameter Values

In this paper, we consider the stability and various dynamical behaviors of both discrete-time delta modulator (Δ-M) and adaptive Δ-M. The stability constraints and conditions of Δ-M and adaptive Δ-M are derived following the theory of quasi-sliding mode. Furthermore, the periodic behaviors are explored for both the systems with steady-state inputs and certain parameter values. The results derived in this paper are validated using simulated examples which confirms the derived stability conditions and the existence of periodicity.

Discrete-time Inversion Model Control of a Double-damper System with Uncertain Parameters

2017 ◽  
Vol 6 (3) ◽  
pp. 168
Author(s):  
Marwa Hannachi ◽  
Ikbel Bencheikh Ahmed ◽  
Dhaou Soudani
Keyword(s):  
Discrete Time ◽  
Algebraic Approach ◽  
Building Blocks ◽  
Internal Model Control ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Time Inversion ◽  
Time Model ◽  
Model Control ◽  
The Stability

<span>This paper addresses the control at discrete time of physical complex systems multi-inputs multi-outputs with variables parameters. Classified among the robust control laws the Internal Model Control (IMC) is adopted in this work to ensure the desired performances adjacent to the complexities of the system. However, the application of this control strategy requires that these different building blocks be open loop stable, which invites us, on the one hand, to apply the algebraic approach of Kharitinov for delimiting the summits stability domain’s system. On the other case, the Linear Matrix Inequalities (LMI) approach is applied to determine the corrector’s stability conditions obtained by a specific inversion of the chosen model. It is in this sense that we contribute by this work to execute the command by inversion the discrete-time model in order to ensure the stability and to maintain the performances the stability conditions of required for the double damper system with variable parameters.</span>

scholarly journals On the Stability of Digital Position Control with Viscous Damping and Coulomb Friction

2017 ◽  
Vol 61 (4) ◽  
pp. 266 ◽  
Author(s):  
Csaba Budai ◽  
László Kovács L.
Keyword(s):  
Discrete Time ◽  
Dry Friction ◽  
Coulomb Friction ◽  
Control Parameter ◽  
Position Control ◽  
Viscous Damping ◽  
Sampled Data ◽  
Stable Domain ◽  
The Stability ◽  
Parameter Values

In this paper, we investigate the combined effect of viscous damping and Coulomb friction on sampled-data mechanical systems. In these systems, instability can occur due the sampling of the applied discrete-time controller which is compensated by the two different physical dissipation effects. In order to investigate the interplay between these, we focus on how the stable domain of operation is extended by the dry friction compared to viscous damping. We also show that dry friction causes concave envelope vibrations in this extended region. The analytical results, presented in the form of stability charts, are verified by a detailed set of simulations at different representative control parameter values.

Robust Control of Permanent Magnet Synchronous Motor: Synergetic Approach

2020 ◽  
Vol 21 (8) ◽  
pp. 480-488
Author(s):  
A. A. Kuz’menko
Keyword(s):  
Robust Control ◽  
Sliding Mode Control ◽  
Permanent Magnet ◽  
Sliding Mode ◽  
System Stability ◽  
Stability Conditions ◽  
Rotor Speed ◽  
Control Laws ◽  
Mode Control ◽  
The Stability

Permanent magnet synchronous motors (PMSM) are widely used in practice due to its high-energy efficiency, compactness, reliability and high regulation performance. When controlling a PMSM rotor speed, the main control principle is the principle of cascade control with PI-regulators, which includes an external control loop for speed and two internal loops for stator currents along the (d, q)-axes. There are attempts to eliminate the disadvantages of this principle using for the control laws synthesis of modern methods of nonlinear control such methods as linearization feedback, backstepping, predictive control, sliding mode control, methods of robust and adaptive control, fuzzy and neural network control, a combination of these methods etc. However, in most cases, the use of these methods are intended to by means of an appropriate method to synthesize a static or dynamic set points for the standard PI-controllers of rotor speed and currents. In this paper we propose to consider two approaches of synergetic control theory (SCT) to construct a robust control law of PMSM: a sliding mode control laws design by the SCT method with subsequent invariant manifolds aggregation and the principle of integral adaptation (PIA). These approaches implement vector control and are not guided by the standard structure of the principle of cascade regulation of PMSM. The proposed approaches simplify the stability analysis of the closed-loop system: stability conditions consist of stability conditions of functional equations of SCT and the stability conditions for finish decomposed system, which the dimension is substantially less than the dimension of the original system. From the results of the comparisons of synthesized the PMSM robust control laws, we can say that more preferable laws synthesized in accordance with the PIA. The theoretical positions of this paper are illustrated by the results of modeling, which are showing the fulfillment of the control tasks: the achievement of targets, robustness to the change of the PMSM load moment.

Synchronization of Fractional-Order Chaotic Systems with Uncertain Parameters

2010 ◽  
Vol 171-172 ◽  
pp. 723-727
Author(s):  
Hong Zhang ◽  
Qiu Mei Pu
Keyword(s):  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
System Stability ◽  
Order System ◽  
Uncertain Parameters ◽  
Mode Theory ◽  
Simulation Results ◽  
The Stability

For the synchronization of fractional-order chaotic systems with uncertain parameters, a controller based on sliding mode theory is presented. Based on the stability theory of fractional-order system, stability of the proposed method is analyzed. The theory is successfully applied to synchronize fractional Newton-Leipnik chaotic systems with uncertain parameters. The simulation results show the effectiveness of the proposed controller.

scholarly journals Discrete-time sliding mode observer for the state estimation of a manoeuvring target

2019 ◽  
Vol 233 (7) ◽  
pp. 847-854
Author(s):  
K Harikumar ◽  
Titas Bera ◽  
Rajarshi Bardhan ◽  
Suresh Sundaram
Keyword(s):  
Boundary Layer ◽  
Discrete Time ◽  
Sliding Mode ◽  
Estimation Error ◽  
Sliding Mode Observer ◽  
Unknown Parameters ◽  
First Order ◽  
Error Dynamics ◽  
And Performance ◽  
The Stability

This article addresses the problem of estimating the position, velocity, and acceleration of a manoeuvring target from noisy position measurements. A discrete-time sliding mode observer is designed to handle unmeasured disturbance input and measurement noise. A first-order linear dynamics is considered for target acceleration. The acceleration input command and the pole of the first-order acceleration dynamics are considered to be unknown parameters with known upper bounds. A finite non-zero boundary layer is employed to reduce the chattering phenomenon typically associated with sliding mode observers. Analysis of estimation error dynamics is presented for the case where the discrete-time sliding mode observer is operating outside the boundary layer and also within the boundary layer. An algorithm is developed for obtaining the observer gain vector that guarantees the stability of the error dynamics. Numerical simulations and experimental results are presented to validate the stability and performance of the proposed observer.

MODELING AND NONLINEAR DYNAMICAL ANALYSIS OF THE ĆUK CONVERTER UNDER FREE-RUNNING CURRENT-PROGRAMMED CONTROL

2008 ◽  
Vol 18 (10) ◽  
pp. 3093-3099 ◽  
Author(s):  
YI-BO ZHAO ◽  
DU-QU WEI ◽  
XIAO-SHU LUO
Keyword(s):  
Sliding Mode ◽  
Variable Structure ◽  
Dynamical Analysis ◽  
Nonlinear Dynamical ◽  
Cuk Converter ◽  
Dynamical Behaviors ◽  
Free Running ◽  
Nonlinear Dynamical Analysis ◽  
Sliding Mode Variable Structure ◽  
The Stability

In this paper, a sliding-mode variable structure model is proposed for studying the nonlinear dynamical behaviors of the free-running current-programmed Ćuk converter. Conditions for the occurrence of various bifurcations are derived analytically, along with simulation results that illustrate the theoretical findings. This paper provides useful information for the stability design of Ćuk converters under free-running current-programmed control and illustrates the application of the nonlinear analysis method to a specific type of plant.

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