Analysis of Chattering in Systems With Second-Order Sliding Modes

Boiko, Igor; Fridman, Leonid; Pisano, Alessandro; Usai, Elio

doi:10.1109/tac.2007.908319

Cited by 321 publications

(200 citation statements)

References 33 publications

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“…Thus, this research line will be explored in next activities. Other interesting directions for next research entail the use of more sophisticated controllers rather than the standard relay, in particular the "generalized" relay arising within the context of the so-called "high-order" sliding mode control theory (see [8,6,7,18]). …”

Section: Shaping Of the Self Excited Oscillation Via Lead/lag Compensmentioning

confidence: 99%

Analysis and shaping of the self-sustained oscillations in relay controlled fractional-order systems

Caponetto

Maione

Pisano

et al. 2013

fcaa

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This work deals with Single-Input-Single-Output (SISO) fractional order systems with a discontinuous relay control element in the feedback loop. Stable self-sustained oscillations often occur in the closed loop relay system, and this work takes advantage of Describing Function (DF) analysis and of another more accurate approach, called Locus of a Perturbed Relay System (LPRS) method, for analyzing in the frequency domain the characteristics of the limit cycle oscillations. The use of fractional lead compensator is also suggested for the purpose of shaping the characteristics of the limit cycle. The proposed analysis and design procedures will be supported by thoroughly discussed simulation examples.MSC 2010 : Primary 34A08; Secondary 34C25, 93C80, 34A36

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Section: Shaping Of the Self Excited Oscillation Via Lead/lag Compensmentioning

confidence: 99%

Analysis and shaping of the self-sustained oscillations in relay controlled fractional-order systems

Caponetto

Maione

Pisano

et al. 2013

fcaa

Self Cite

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“…After a transient phase, called "reaching phase", during which the insensitiveness of the system with respect to the uncertain terms is not guaranteed, the so-called "sliding phase" starts and the controlled system proves to be robust versus a specific class of uncertainties, the so-called "matched uncertainties", i.e., uncertain terms which act on the same channel of the control variable. The main drawback of SMC is the so-called chattering phenomenon, i.e., oscillations of the controlled variable due to the discontinuity of the control input [Boiko et al, 2007;Levant, 2010]. The most effective solution to alleviate this phenomenon is the generation of higher order sliding modes (HOSM), which are able to reduce the chattering effect while maintaining good stability properties [Bartolini et al, 1998[Bartolini et al, , 2000Levant, 2003;Dinuzzo and Ferrara, 2009;Ferrara et al, 2014b].…”

Section: Introductionmentioning

confidence: 99%

Hierarchical Model Predictive/Sliding Mode Control of Nonlinear Constrained Uncertain Systems

2015

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Abstract-This paper presents an overview of some hierarchical control schemes composed by a high level Model Predictive Control (MPC) and a low level Sliding Mode Control (SMC). The latter is realized by using the so-called Integral Sliding Mode (ISM) control approach and is meant to reject the matched disturbances affecting the plant, thus providing a system with reduced uncertainty for the MPC design. Both continuous and discrete-time solutions are discussed in the paper. Moreover, assuming the presence of a network in the control loop, a networked version of the control scheme is presented. It is a model-based event-triggered MPC/ISM control scheme aimed at minimizing the packets transmission. The input-to-state (practical) stability properties of the proposed approaches are also addressed in the paper.

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“…The absence of a computationally tractable dynamic model for these robots also prevents the study of interaction of external forces and the impact of collisions on these continuum structures. This impedes the study and ultimate usage of continuum robots in various practical applications like grasping and manipulation, where impulsive dynamics [4][5][6][7][8][9][10] are important factors. Although continuum robotics is an interesting subclass of robotics with promising applications for the future, from the current state of the literature, this field is still in its stages of inception.…”

Section: Introductionmentioning

confidence: 99%

Design New Intelligent PID like Fuzzy Backstepping Controller

Khajeh¹,

Piltan²,

Rashidian³

et al. 2014

IJMECS

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Abstract-The minimum rule base Proportional Integral Derivative (PID) Fuzzy backstepping Controller is presented in this research. The popularity of PID Fuzzy backstepping controller can be attributed to their robust performance in a wide range of operating conditions and partly to their functional simplicity. The process of setting of PID Fuzzy backstepping controller can be determined as an optimization task. Over the years, use of intelligent strategies for tuning of these controllers has been growing. PID methodology has three inputs and if any input is described with seven linguistic values, and any rule has three conditions we will need 7 × 7 × 7 = 343 rules. It is too much work to write 343 rules. In this research the PID-like fuzzy controller can be constructed as a parallel structure of a PD-like fuzzy controller and a PI-like controller to have the minimum rule base. However backstepping controller is work based on cancelling decoupling and nonlinear terms of dynamic parameters of each link, this controller is work based on manipulator dynamic model and this technique is highly sensitive to the knowledge of all parameters of nonlinear robot manipulator"s dynamic equation. This research is used to reduce or eliminate the backstepping controller problem based on minimum rule base fuzzy logic theory to control of flexible robot manipulator system and testing of the quality of process control in the simulation environment of MATLAB/SIMULINK Simulator.Index Terms-PID like fuzzy control, backstepping controller, PD like fuzzy control, PI like control, flexible robot manipulator.

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Analysis of Chattering in Systems With Second-Order Sliding Modes

Cited by 321 publications

References 33 publications

Analysis and shaping of the self-sustained oscillations in relay controlled fractional-order systems

Analysis and shaping of the self-sustained oscillations in relay controlled fractional-order systems

Hierarchical Model Predictive/Sliding Mode Control of Nonlinear Constrained Uncertain Systems

Design New Intelligent PID like Fuzzy Backstepping Controller

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