Design of decentralised sliding surfaces for a class of large-scale systems with mismatched perturbations

Variable structure control with sliding mode can provide good control performance and excellent robustness. Unfortunately, the chattering phenomenon investigated due to discontinuous switching gain restricting their applications. In this paper, a chattering free improved variable structure control (IVSC) for a class of mismatched uncertain interconnected systems with an unknown time-varying delay is proposed. A sliding function is first established to eliminate the reaching phase in traditional variable structure control (TVSC). Next, a new reduced-order sliding mode estimator (ROSME) without time-varying delay is constructed to estimate all unmeasurable state variables of plants. Then, based on the Moore-Penrose inverse approach, a decentralized single-phase robustness sliding mode controller (DSPRSMC) is synthesized, which is independent of time delays. A DSPRSMC solves a complex interconnection problem with an unknown time-varying delay term and drives the system’s trajectories onto a switching surface from the initial time instance. Particularly, by applying the well-known Barbalat’s lemma, the chattering phenomenon in control input is alleviated. Moreover, a sufficient condition is established by using an appropriate Lyapunov theory and linear matrix inequality (LMI) method such that a sliding mode dynamics is asymptotically stable from the beginning time. Finally, a developed method is validated by numerical example with computer simulations.

show abstract

“…Remark 1. The mathematical model of the system (Equation 1) is extended from the published studies [15,19,40].…”

Section: A1mentioning

confidence: 99%

Chattering-Free Single-Phase Robustness Sliding Mode Controller for Mismatched Uncertain Interconnected Systems with Unknown Time-Varying Delays

Nguyen

Duong

et al. 2020

Energies

View full text Add to dashboard Cite

show abstract

“…However, asymptotic stability is generally difficult to achieve for systems with mismatched perturbations when applying the traditional SMC technique, since the mismatched perturbations cannot be effectively suppressed unless specific sliding surface is designed. Thus, some researchers designed novel sliding surface functions for mismatched perturbed systems instead of using traditional ones so that not only asymptotic stability is achieved but also the (prior) knowledge of the upper bound of the perturbations is not required (Chang and Cheng 2007a;Wen and Cheng 2008;Cheng, Wen, and Lee 2009). However, it is found that designing a specific and novel sliding surface function is generally not an easy job.…”

Section: Introductionmentioning

confidence: 95%

“…Recently, Chang and Cheng (2007a, b), Wen and Cheng (2008), Cheng et al (2009) designed adaptive sliding mode controllers for solving regulation or tracking problems without requiring the upper bounds of matched or mismatched perturbations. However, all these control schemes can only handle systems with n 2m (n is the dimension of the system, m is the number of inputs).…”

Section: Introductionmentioning

confidence: 99%

Block backstepping control of multi-input nonlinear systems with mismatched perturbations for asymptotic stability

Chang

Cheng

2010

International Journal of Control

Self Cite

View full text Add to dashboard Cite

“…SMC is capable of providing robustness and invariance to matched external disturbances and model uncertainties [1], [2]. If a sliding mode controller is properly designed, asymptotic stability for systems with mismatched perturbations still can be obtained [3]- [6]. However, it is observed that designing novel sliding surface functions to achieve asymptotic stability for mismatched perturbed systems are in general not easy and quite complicated.…”

Section: Introductionmentioning

confidence: 99%

Design of adaptive block backstepping controllers for semi-strict feedback nonlinear systems with perturbation estimation

Cheng

Chien

Huang

2013

2013 European Control Conference (ECC)

Self Cite

View full text Add to dashboard Cite

Based on the Lyapunov stability theorem, a design methodology of adaptive block backstepping control with perturbation estimation scheme is proposed in this paper for a class of multi-input systems with perturbations to solve regulation problems. First of all, the virtual input controllers are designed from the first block to the .m 1/t h block. Then the proposed robust controller and the perturbation estimator are designed in accordance with the last block. Adaptive mechanisms are employed in each of the virtual input as well as the robust controller so that they may automatically adapt the least upper bounds of perturbations or perturbation estimation errors which may not fulfill the strict-feedback form. Furthermore, the proposed control scheme is able to achieve asymptotic stability. A numerical example is also given for demonstrating the feasibility of the proposed control scheme.

show abstract

Design of decentralised sliding surfaces for a class of large-scale systems with mismatched perturbations

Cited by 9 publications

References 29 publications

Chattering-Free Single-Phase Robustness Sliding Mode Controller for Mismatched Uncertain Interconnected Systems with Unknown Time-Varying Delays

Chattering-Free Single-Phase Robustness Sliding Mode Controller for Mismatched Uncertain Interconnected Systems with Unknown Time-Varying Delays

Block backstepping control of multi-input nonlinear systems with mismatched perturbations for asymptotic stability

Design of adaptive block backstepping controllers for semi-strict feedback nonlinear systems with perturbation estimation

Contact Info

Product

Resources

About