Design of a global discrete‐time sliding mode control scheme for a class of nonlinear systems with state delays and uncertainties

Sarvi, Amir; Mobayen, Saleh; Fekih, Afef; Mohammadi, Sayed Zia; Asad, Jihad

doi:10.1002/asjc.2639

Cited by 4 publications

(6 citation statements)

References 32 publications

(37 reference statements)

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“…which is derived by substituting (3), ( 9), (15), and ( 24) into (14). G(k) in ( 27) is expressed as…”

Section: Analysis Of the Control Effortmentioning

confidence: 99%

“…The procedure of SMC design mainly involves constructing a sliding surface and organizing the sliding-mode controller (SMCer). Ideally, by using the organized controller in the continuous-time domain, the system states are supposed to be driven and many authors have devoted themselves to the study of DSMC [11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

“…This is because the sampling frequency is finite and the organized controller cannot timely change the control input when the state trajectories cross the sliding surface [10]. Considering the particularity of discrete‐time SMC (DSMC) compared to continuous‐time SMC (CSMC), many authors have devoted themselves to the study of DSMC [11–17].…”

Section: Introductionmentioning

confidence: 99%

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A generalized reaching‐law‐based discrete‐time integral sliding‐mode controller with matched/mismatched disturbance attenuation

Guo

Zhang

Huang

et al. 2023

Asian Journal of Control

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A generalized reaching‐law‐based (RL‐based) discrete‐time integral sliding‐mode controller, which is versatile for either matched or mismatched disturbances, is designed in this paper to obtain high output tracking accuracy and avoid tremendous control efforts. Specifically, a disturbance decomposition‐based discrete‐time integral sliding surface is designed, and a generalized discrete‐time reaching law is established. Different from the existing integral sliding surfaces, the proposed sliding surface synthesizes a disturbance‐related integral term that is defined based on disturbance decomposition; this is crucial to the disturbance attenuation. Moreover, different from the available discrete‐time reaching laws, the proposed reaching law introduces an adaptive exponential term into the control gains, and hence, the conventional RL‐based discrete‐time integral sliding‐mode control (DISMC) and the equivalent‐control‐based (EC‐based) DISMC can be integrated. Rigorous analysis shows that the closed‐loop system is stable, the control effort can be satisfactory, and the steady‐state output tracking accuracy is of order for both matched and mismatched disturbances. The proposed method is proven effective through numerical simulations.

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“…which is derived by substituting (3), ( 9), (15), and ( 24) into (14). G(k) in ( 27) is expressed as…”

Section: Analysis Of the Control Effortmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A generalized reaching‐law‐based discrete‐time integral sliding‐mode controller with matched/mismatched disturbance attenuation

Guo

Zhang

Huang

et al. 2023

Asian Journal of Control

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“…There are a wide variety of robust tracking controllers for robotic applications [19] among which the sliding mode controller has been a well-known technique for uncertain systems [20,21]. Also, fractional controllers (compared to conventional ones) offer better performance, due to more tunable parameters [22,23].…”

Section: Introductionmentioning

confidence: 99%

Fractional‐order sliding mode control for a novel magneto‐electro‐elastic microtube robot

Tofigh,

Shah‐Mohammadi‐Azar,

Rezazadeh

et al. 2023

Asian Journal of Control

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In this paper, a tracking controller based on a non‐integer sliding surface is proposed for a magneto‐electro‐elastic (MEE) fluid‐conveying microtube robot. The smart/adaptive MEE material enables us to control the robot with no need for external sensors and actuators. The micro‐robot lateral motion is modeled by Euler–Bernoulli beam equations. The governing equation of the robot is derived using the constitutive equations of MEE materials and Maxwell's principle followed by Hamilton's variational method. Based on the extracted dynamic model, a novel non‐integer order sliding mode controller is introduced to suppress the microtube vibration and to provide robust path following for the robot tip. This control approach is compatible with the parameter‐varying nature of the robot dynamics. Theoretical analyses, based on Lyapunov theory, are also conducted to verify the stability of the closed‐loop system. Comparative simulations are finally performed to show the efficiency of the proposed system in comparison with the conventional micro tubes made of smart materials and with an integer order sliding mode controller (SMC). The results demonstrate that the proposed robot properly meets the performance requirements in terms of vibration suppression and trajectory tracking, even in the presence of disturbances.

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“…One advantage of this method is that the global sliding surface ensures robust performance without the need for a reaching phase, thus establishing sliding around the surface right from the beginning and reducing the control effort. Furthermore, for a class of linear discrete‐time dynamic systems with time delays, parameter uncertainties, and external disturbances, a discrete‐time sliding mode controller was developed and a lumped disturbance function was used to estimate the unknown parameters and time‐delayed terms at the same time 42 . One of the important advantage is that the proposed sliding function can remove the reaching phase.…”

Section: Introductionmentioning

confidence: 99%

The use of adaptive multiple models for predefined exponential stability of control systems of uncertain discrete‐time nonlinear objects

Zhang,

Wang,

Wang

2023

Adaptive Control & Signal

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SummaryIn this work, an adaptive multiple model pre‐assigned exponential convergence control scheme based on the time varying exponential function is demonstrated for a class of discrete‐time nonlinear systems. For coping with the noncausality problem from previous adaptive backstepping design method of nonlinear discrete‐time systems, a first‐order recursive filter is used in controller design procedures and the n‐step prediction model is not needed, thereby reducing the computational burden effectively. The time varying function is employed to force all states variables to convergence to zero with a pre‐defined rate which does not rely on the initial conditions of systems. In addition, the multiple model set is constructed to address unknown parameters problem and further the second level adaptive algorithm of unknown parameters is developed. A characteristic feature of the second‐level multi‐model adaptation algorithm is that it dynamically adapts to time changes in the identified model (it uses identification information better than the switching multiple model control). In a unified framework of second level adaption, a first‐order recursive filter and backstepping technique, a pre‐assigned exponential convergence controller is presented. Finally, the results about discrete‐time pre‐assigned exponential convergence method are compared with other methods using two case studies.

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Design of a global discrete‐time sliding mode control scheme for a class of nonlinear systems with state delays and uncertainties

Cited by 4 publications

References 32 publications

A generalized reaching‐law‐based discrete‐time integral sliding‐mode controller with matched/mismatched disturbance attenuation

A generalized reaching‐law‐based discrete‐time integral sliding‐mode controller with matched/mismatched disturbance attenuation

Fractional‐order sliding mode control for a novel magneto‐electro‐elastic microtube robot

The use of adaptive multiple models for predefined exponential stability of control systems of uncertain discrete‐time nonlinear objects

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