Stability analysis of a continuous implementation of variable structure control

Esfandiari, F.; Khalil, Hassan K.

doi:10.1109/9.76367

Cited by 94 publications

(30 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…However, controller (8) still su!ers from chattering. Boundary-layer can be implemented if the sgn( * ) is substituted for a saturation sat( * ) function in (8), in which case the invariant condition is not satis"ed, however it renders tracking with guaranteed precision, Reference [5]. Note that thanks to the workless forces A, dissipativity arises for a storage function <, and observe that there does not exist, for this parametrization, an additional smooth control input to (8) that can satisfy the invariant condition.…”

Section: Preliminary Resultsmentioning

confidence: 99%

“…However, the controller still switches discontinuously around the vicinity of the boundary-layer and it may su!er from high frequency inside the domain of the boundary-layer and around the ideal sliding surface. Since this approach does not render the Coulomb-friction e!ect, then it yields a quasi-sliding mode instead of a sliding mode with ultimately bounded stability, see References [5,6]. The tracking errors introduced by this method cannot be further eliminated, unless feedback gains and bandwidth are increased, which are not always possible.…”

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

Chattering‐free sliding mode control for a class of nonlinear mechanical systems

Parra-Vega

Hirzinger²

2001

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

SUMMARYSecond-order sliding mode control (2-smc) and dynamic sliding mode control (dsmc) eliminate the disturbing characteristic of chattering in static sliding mode control under the assumption that the derivative of the sliding surface is available or complex inequalities at the acceleration level can be constructed. In this paper, passivity-based adaptive and non-adaptive chattering-free sliding mode controllers are proposed assuming that the upper bound of the norm of the derivative of the sliding surface is available, a weaker and easy to implement assumption in comparison to those of 2-smc and dsmc. The closed-loop system accounts explicitly for the invariance condition without reaching phase, and therefore for a desired transient response with global exponential convergence of tracking errors. Preliminary experiments are presented.

show abstract

Section: Preliminary Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Chattering‐free sliding mode control for a class of nonlinear mechanical systems

Parra-Vega

Hirzinger²

2001

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…Figure 1 shows the estimates for the (18) is discontinuous which may result in chattering. In the simulation, the discontinuous function (19) has been replaced by the saturation function to avoid chattering [5]. It should be noted that in the simulation example, the matrix Ξ(·) is chosen as [0.14 0.1346](1 + 1 u ) due to the term θu in (47), which may result in large gain in the adaptive law (20) when u is very small.…”

Section: An Application Example-bioreactormentioning

confidence: 99%

State and Parameter Estimation for Nonlinear Delay Systems Using Sliding Mode Techniques

Yan

Spurgeon

Edwards

2013

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

Abstract-In this paper, a class of time varying delay nonlinear systems is considered where both parametric uncertainty and structural uncertainty are involved. The uncertain parameters are embedded in the system nonlinearly. The bound on the structural uncertainty takes nonlinear form and is time delayed. A sliding mode observer is proposed to estimate the system state and an adaptive law is proposed to estimate the unknown parameters simultaneously. Using the LyapunovRazuminkhin approach, sufficient conditions are developed such that the error system is uniformly ultimately bounded. A simulation on a bioreactor system shows the effectiveness of the approach.

show abstract

“…The choice of the surface is mostly related to some stabilization problem: The shape of the surface is selected a priori, leading to a set of parameters that are to be computed (adjusted) in order to obtain the desired dynamics (El-Ghezaoui et al, 1983;Esfandiari and Khalil, 1991).…”

Section: Introductionmentioning

confidence: 99%

Piecewise Sliding Mode Decoupling Fault Tolerant Control System

Youssef¹

2010

American Journal of Applied Sciences

View full text Add to dashboard Cite

Problem statement: Proposed method in the present study could deal with fault tolerant control system by using the so called decentralized control theory with decoupling fashion sliding mode control, dealing with subsystems instead of whole system and to the knowledge of the author there is no known computational algorithm for decentralized case, Approach: In this study we present a decoupling strategy based on the selection of sliding surface, which should be in piecewise sliding surface partition to apply the PwLTool which have as purpose in our case to delimit regions where sliding mode occur, after that as Results: We get a simple linearized model selected in those regions which could depict the complex system, Conclusion: With the 3 water tank level system as example we implement this new design scenario and since we are interested in networked control system we believe that this kind of controller implementation will not be affected by network delays.

show abstract

Stability analysis of a continuous implementation of variable structure control

Cited by 94 publications

References 7 publications

Chattering‐free sliding mode control for a class of nonlinear mechanical systems

Chattering‐free sliding mode control for a class of nonlinear mechanical systems

State and Parameter Estimation for Nonlinear Delay Systems Using Sliding Mode Techniques

Piecewise Sliding Mode Decoupling Fault Tolerant Control System

Contact Info

Product

Resources

About