Continuous terminal sliding-mode controller

Kamal, Shyam; Moreno, Jaime A.; Chalanga, Asif; Bandyopadhyay, B.; Fridman, Leonid

doi:10.1016/j.automatica.2016.02.001

Cited by 166 publications

(130 citation statements)

References 20 publications

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“… Let the vector of states Σ with virtual state

normalΓ = f + \int_{t_{0}}^{t} U_{d} d τ

, then the extended system can be written as

σ^{false(r false)} = U_{c} + normalΓ, \overset{Γ}{true} \in false[- normalΔ, normalΔ false] + U_{d},

where a Lipschitz perturbation

false| \overset{f}{true} false| \leq normalΔ

is assumed. Some examples of these controllers are the Super‐Twisting, Higher‐Order Super‐Twisting, Continuous‐Terminal, Discontinuous Integral, and Continuous Twisting, where the gains of the algorithm are usually selected from Δ. The inclusion and the controller are homogeneous of degree q = −1 with the dilation

{\overset{d}{true}}_{κ} : (() t, σ, \dot{σ}, …, σ^{(r)}) \to (() κ t, κ^{m_{1}} σ, κ^{m_{2}} \dot{σ}, …, κ^{m_{r}} σ^{(r)}),

where m 1 = r + 1, m 2 = r , …, m r = 1 are the homogeneity weights and κ > 0. The ( r + 1)‐CSMC enforce the ( r + 1)th‐order sliding‐mode in a finite‐time, ie, there exist a time t r such that

\forall t \geq t_{r} : σ false(t false) = \overset{σ}{true} false(t false) = ⋯ = σ^{false(r false)} false(t false) = 0 .

Note that, in ( r + 1)‐CSMC, the vector field is tangent to e...…”

Section: Preliminariesmentioning

confidence: 99%

“…Let the vector of states Σ with virtual state

normalΓ = f + \int_{t_{0}}^{t} U_{d} d τ

, then the extended system can be written as

σ^{false(r false)} = U_{c} + normalΓ, \overset{Γ}{true} \in false[- normalΔ, normalΔ false] + U_{d},

where a Lipschitz perturbation

false| \overset{f}{true} false| \leq normalΔ

Section: Preliminariesmentioning

confidence: 99%

“…For systems of relative degree two, the most popular DSMC are Twisting, Terminal, and Suboptimal . Recently, CSMC for systems of relative degree two the Discontinuous Integral, Continuous Terminal, and Continuous Twisting algorithms were developed. Higher‐Order Sliding‐Mode Controllers (HOSMC) drive the output of the system and its ( r − 1) successive time derivatives to zero in finite‐time by means of discontinuous control, for example, Quasi‐continuous and Nested algorithms (see also the recent works of Ding et al and Cruz‐Zavala and Moreno).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

When is it reasonable to implement the discontinuous sliding‐mode controllers instead of the continuous ones? Frequency domain criteria

Pérez‐Ventura

Fridman

2018

Intl J Robust & Nonlinear

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Summary Professor Utkin proposed an example showing that the amplitude of chattering caused by the presence of parasitic dynamics (stable actuators) in some systems governed by the First‐Order Sliding‐Mode Controller is lower than that produced by the Super‐Twisting Algorithm. This example served to motivate this paper reconsidering the problem of comparison of chattering in systems with stable actuators, and driven by Discontinuous Sliding‐Mode Controllers (DSMCs) and Continuous Sliding‐Mode Controllers (CSMCs). Comparison of chattering produced by DSMC and CSMC taking into account their amplitudes, frequencies, and average power (AP) needed to maintain the system into real‐sliding modes, allowing to conclude the following: (i) for systems with slow actuators, the amplitude of oscillations and AP produced by DSMC be smaller than those caused by CSMC; (ii) for bounded disturbances with fixed Lipschitz constant, there exist sufficiently fast actuators for which the amplitude of oscillations and AP produced by CSMC be smaller than those caused by DSMC.

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“… Let the vector of states Σ with virtual state

normalΓ = f + \int_{t_{0}}^{t} U_{d} d τ

, then the extended system can be written as

σ^{false(r false)} = U_{c} + normalΓ, \overset{Γ}{true} \in false[- normalΔ, normalΔ false] + U_{d},

where a Lipschitz perturbation

false| \overset{f}{true} false| \leq normalΔ

{\overset{d}{true}}_{κ} : (() t, σ, \dot{σ}, …, σ^{(r)}) \to (() κ t, κ^{m_{1}} σ, κ^{m_{2}} \dot{σ}, …, κ^{m_{r}} σ^{(r)}),

\forall t \geq t_{r} : σ false(t false) = \overset{σ}{true} false(t false) = ⋯ = σ^{false(r false)} false(t false) = 0 .

Note that, in ( r + 1)‐CSMC, the vector field is tangent to e...…”

Section: Preliminariesmentioning

confidence: 99%

“…Let the vector of states Σ with virtual state

normalΓ = f + \int_{t_{0}}^{t} U_{d} d τ

, then the extended system can be written as

σ^{false(r false)} = U_{c} + normalΓ, \overset{Γ}{true} \in false[- normalΔ, normalΔ false] + U_{d},

where a Lipschitz perturbation

false| \overset{f}{true} false| \leq normalΔ

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

When is it reasonable to implement the discontinuous sliding‐mode controllers instead of the continuous ones? Frequency domain criteria

Pérez‐Ventura

Fridman

2018

Intl J Robust & Nonlinear

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show abstract

“…In this paper one considers an uncertain chain of integrators. Finite time stabilization of an uncertain chain of integrators systems is also known as higher order sliding mode ( Levant (1993), Levant (2003), Levant (2005), Kamal et al (2016), Chalanga et al (2016), Kamal et al (2013)). Finite time stabilization of an uncertain chain of integrators is already reported in Laghrouche et al (2007), Chalanga et al (2015), Edwards and Shtessel (2014), Taleb et al (2015).…”

Section: Introductionmentioning

confidence: 99%

Finite Time Stabilization of An Uncertain Chain of Integrators by Integral Sliding Mode Approach

Chalanga

Plestan

2017

IFAC-PapersOnLine

Self Cite

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In this paper, finite time stabilization of an uncertain chain of integrators is studied. The controller proposed in the paper, under some conditions guarantees the convergence of all the states at time exactly t F and that chosen in advance. The controller is designed based on the integral sliding mode approach, which is the combination of two controls: a nominal control which is designed to obtain desired performances for the disturbance free system and a super-twisting control is designed for the disturbance compensation. The proposed controller also adjusts the chattering because of continuous control. Finally this paper presents the finite time stability proof of super-twisting algorithm by using continuously differentiable Lyapunov function. Thanks to academic example, effectiveness by the proposed method is presented with simulation results. Through the simulations performance of the proposed method is compare with an existing method.

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“…Since the sliding mode control (SMC) method was firstly proposed, it has attracted a lot of researchers worldwide [7,8] due to its robustness to parameter perturbations and external Y. Wang, M. Sun, S. Du, and Z. Chen linear observer is simple and there is only one tunable parameter, it has demonstrated its effectiveness when applied to control diverse nonlinear systems [17][18][19][20][21]. In addition, a binary distillation column can be controlled by using a linear proportional-integral observer in [22].…”

Section: Introductionmentioning

confidence: 99%

Comparative investigations of nonlinear and linear observers for a highly manoeuvrable target in sliding mode guidance

Wang¹,

Sun²,

Du³

et al. 2017

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. Target manoeuvre is one of the key factors affecting guidance accuracy. To intercept highly maneuverable targets, a second-order sliding-mode guidance law, which is based on the super-twisting algorithm, is designed without depending on any information about the target motion. In the designed guidance system, the target estimator plays an essential role. Besides the existing higher-order sliding-mode observer (HOSMO), a first-order linear observer (FOLO) is also proposed to estimate the target manoeuvre, and this is the major contribution of this paper. The closed-loop guidance system can be guaranteed to be uniformly ultimately bounded (UUB) in the presence of the FOLO. The comparative simulations are carried out to investigate the overall performance resulting from these two categories of observers. The results show that the guidance law with the proposed linear observer can achieve better comprehensive criteria for the amplitude of normalised acceleration and elevator deflection requirements. The reasons for the different levels of performance of these two observer-based methods are thoroughly investigated.Key words: guidance law, second-order sliding mode, super-twisting algorithm, linear observer, target manoeuvre. matched disturbances. However, the chattering phenomenon is the major obstacle for the implementation of SMC in practice, and a number of methods have been proposed to reduce the chattering. Levant first proposed the higher-order sliding mode (HOSM) control method to attenuate the chattering [9][10][11][12]. The second-order sliding mode control is the most widely used HOSM method in which the super-twisting algorithm is utilised to attenuate the differentiable disturbance and ensure the finite-time stability [13,14]. To intercept highly manoeuvrable targets, the second-order sliding mode methods were utilised in [13] and [14], based on the nonlinear observers, which are used to check the uncertainty caused by target manoeuvres. However, in many simulations, it is readily observed that the guidance commands (acceleration) generated by the proposed guidance laws of [13] and [14] exhibit the properties of oscillation with a large amplitude. Comparing the fundamental guidance component with the observer component, the latter contributes to this phenomenon much more. Hence, an effective estimation approach is urgently needed to deal with highly manoeuvrable targets.Han proposed a novel philosophy, namely the active disturbance rejection control (ADRC) algorithm [15,16], which has attracted wide attention in the past decade. The core of ADRC is an extended state observer (ESO) that can accurately observe the total disturbance. Han originally presented the ESO in a nonlinear form [15], which is too complicated to tune, and is difficult to be implemented. In [16], a linear ESO (LESO) was proposed in terms of frequency bandwidth, which provides a useful design approach in practical applications. Although this

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Continuous terminal sliding-mode controller

Cited by 166 publications

References 20 publications

When is it reasonable to implement the discontinuous sliding‐mode controllers instead of the continuous ones? Frequency domain criteria

When is it reasonable to implement the discontinuous sliding‐mode controllers instead of the continuous ones? Frequency domain criteria

Finite Time Stabilization of An Uncertain Chain of Integrators by Integral Sliding Mode Approach

Comparative investigations of nonlinear and linear observers for a highly manoeuvrable target in sliding mode guidance

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