Chattering suppression methods in sliding mode control systems
TL;DR: Analysis of chattering in such systems with unmodeled based on the Lyapunov theory and the describing function method and various approaches to reduce chattering are described including methods based on relay control gain adaptation.
About: This article is published in Annual Reviews in Control.The article was published on 2007-01-01. It has received 535 citations till now. The article focuses on the topics: Sliding mode control & Describing function.
Citations
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TL;DR: The goal is to obtain a robust sliding mode adaptive-gain control law with respect to uncertainties and perturbations without the knowledge of uncertainties/perturbations bound (only the boundness feature is known).
Abstract: This article proposes new methodologies for the design of adaptive sliding mode control. The goal is to obtain a robust sliding mode adaptive-gain control law with respect to uncertainties and perturbations without the knowledge of uncertainties/perturbations bound (only the boundness feature is known). The proposed approaches consist in having a dynamical adaptive control gain that establishes a sliding mode in finite time. Gain dynamics also ensures that there is no overestimation of the gain with respect to the real a priori unknown value of uncertainties. The efficacy of both proposed algorithms is confirmed on a tutorial example and while controlling an electropneumatic actuator.
676 citations
Cites background or methods from "Chattering suppression methods in s..."
...Suppose now that (0)1⁄4 0: Theorem 1 of Lee and Utkin (2007) claims that, if K is large enough with respect to uncertainties/perturbations effects, then sliding mode control (7) with the gain-adaptation algorithm (9) allows keeping trajectories of system (1) on the sliding surface 1⁄4 0....
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...Then, the proof follows the same way as the proof of Theorem 3 based on Lyapunov analysis when j j4 , and on Theorem 1 of Lee and Utkin (2007) when j j ....
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...…of system (1) on (4) is called ‘real sliding mode’ with respect to the sliding variable (x, t). œ 2.2 Discussion of adaptive sliding mode control solutions and motivations Two adaptive sliding mode controllers have been given in Lee and Utkin (2007) and Huang et al. (2008) and are discussed now....
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...The first controller is based on a gain-adaptation law derived from coupling of Lee and Utkin (2007) and Huang et al. (2008) methods, whereas the second one is using an original gain-adaptation law....
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...Given that trajectories of system (1) reach ¼ 0, it means that K is large enough as required by Theorem 1 of Lee and Utkin (2007)....
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TL;DR: In this paper an adaptation methodology is developed for searching the minimum possible value of control based on evaluations of the, so-called, equivalent control by a low-pass filter based on direct measurements of the first-order low- pass filter.
436 citations
TL;DR: A new adaptive sliding-mode control scheme that uses the time-delay estimation (TDE) technique, then applies the scheme to robot manipulators and shows that the tracking errors of the proposed ASMC scheme are guaranteed to be uniformly ultimately bounded (UUB) with arbitrarily small bound.
Abstract: This paper presents a new adaptive sliding-mode control (ASMC) scheme that uses the time-delay estimation (TDE) technique, then applies the scheme to robot manipulators. The proposed ASMC uses a new adaptive law to achieve good tracking performance with small chattering effect. The new adaptive law considers an arbitrarily small vicinity of the sliding manifold, in which the derivatives of the adaptive gains are inversely proportional to the sliding variables. Such an adaptive law provides remarkably fast adaptation and chattering reduction near the sliding manifold. To yield the desirable closed-loop poles and simplify a complicated system model by adapting feedback compensation, the proposed ASMC scheme works together with a pole-placement control (PPC) and a TDE technique. It is shown that the tracking errors of the proposed ASMC scheme are guaranteed to be uniformly ultimately bounded (UUB) with arbitrarily small bound. The practical effectiveness and the fast adaptation of the proposed ASMC are illustrated in simulations and experiments with robot manipulators, and compared with those of an existing ASMC.
366 citations
Cites methods from "Chattering suppression methods in s..."
...These methods include the boundary layer setting [20], [21], low-pass filtering [22], [23], and higher order control [24], [25]....
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TL;DR: The objective is to alter the modulation gains associated with these schemes in such a way that they are as small as possible to mitigate chattering effects, but large enough to ensure that sliding can be maintained in the presence of bounded and derivative bounded uncertainties.
279 citations
Additional excerpts
...This paper follows the approach of Utkin & Poznyak (2013a) and Lee & Utkin (2007) in the sense that the adaption scheme relies on the availability, in real time, of the equivalent control signal, and exploits this information in the adaptive scheme....
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TL;DR: In this paper, a sliding-mode-control-based guidance law is proposed to intercept stationary, constant-velocity, and maneuvering targets at a desired impact angle, which is defined in terms of a desired line-of-sight angle, by selecting the missile's lateral acceleration to enforce terminal sliding mode on a switching surface designed using nonlinear engagement dynamics.
Abstract: In this paper, sliding-mode-control-based guidance laws to intercept stationary, constant-velocity, and maneuvering targets at a desired impact angle are proposed. The desired impact angle, which is defined in terms of a desired line-of-sight angle, is achieved in finite time by selecting the missile's lateral acceleration to enforce terminal sliding mode on a switching surface designed using nonlinear engagement dynamics. The conditions for capturability are also presented. In addition, by considering a three-degree-of-freedom linear-interceptor dynamic model and by following the procedure used to design a dynamic sliding-mode controller, the interceptor autopilot is designed as a simple static controller to track the lateral acceleration generated by the guidance law. Numerical simulation results are presented to validate the proposed guidance laws and the autopilot design for different initial engagement geometries and impact angles.
275 citations
Cites background from "Chattering suppression methods in s..."
...This procedure might result in a limit-cyle behavior of the state s, which is known as chattering [22]....
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References
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TL;DR: In this article, the authors proposed arbitrary-order robust exact differentiators with finite-time convergence, which can be used to keep accurate a given constraint and feature theoretically-infinite-frequency switching.
Abstract: Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be 1 and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptot...
2,954 citations
Book•
01 Jan 1999
TL;DR: Sliding mode control (SMC) is gaining increasing importance as a universal design tool for the robust control of linear and nonlinear systems as mentioned in this paper, and is particularly useful for electro-mechanical systems because of its discontinuous structure.
Abstract: Sliding Mode Control (SMC) is gaining increasing importance as a universal design tool for the robust control of linear and nonlinear systems. The strengths of sliding mode controllers result from the ease and flexibility of the methodology for their design and implementation. They provide inherent order reduction, direct incorporation of robustness against system uncertainties and disturbances, and an implicit stability proof. They also allow for the design of high performance control systems at low costs. SMC is particularly useful for electro-mechanical systems because of its discontinuous structure. In fact, since the hardware of many electro-mechanical systems (such as electric motors) prescribes discontinuous inputs, SMC has become the natural choice for direct implementation. The book is intended primarily for engineers and establishes an interdisciplinary bridge between control science, electrical and mechanical engineering.
2,593 citations
Book•
01 Jan 1978
TL;DR: An electric dynamically operated storage element comprises two energy stores and circuitry is provided for applying periodically repeating phase clock pulses simultaneously to the energy stores through the charging circuits.
Abstract: An electric dynamically operated storage element comprises two energy stores. Each store has a charging circuit including a rectifying element and a discharging circuit including a controlled respectively variable resistance connected in series with the rectifying element. Also, circuitry is provided for applying periodically repeating phase clock pulses simultaneously to the energy stores through the charging circuits.
1,802 citations
TL;DR: The content of main theorems is presented in a tutorial form aimed at a broad audience of engineers and applied mathematicians interested in control, estimation and optimization of dynamic systems.
892 citations
TL;DR: For sliding-mode control systems with fast actuators, sufficient conditions for the exponential decreasing of the amplitude of chattering and unlimited growth of frequency are found.
Abstract: For sliding-mode control systems with fast actuators, sufficient conditions for the exponential decreasing of the amplitude of chattering and unlimited growth of frequency are found. The connection between the stability of actuators and the stability of the plant on the one hand and the stability of the sliding-mode system as the whole on the other hand is investigated. The algorithm for correction of sliding-mode equations is suggested for taking into account the presence of fast actuators.
163 citations