Multivariable Output-Feedback Sliding Mode Control

Hsu, Liu; Cunha, José Paulo V. S.; Costa, Ramon R.; Lizarralde, Fernando

doi:10.1007/3-540-45666-x_12

Cited by 41 publications

(61 citation statements)

References 58 publications

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“…This is less restrictive than the assumption of positive definiteness of KpSp required in previous works that assume not necessarily small uncertainties of the HFG. The extension of the proposed controller for systems of arbitrary relative degree is a current research topic [15]. …”

Section: Discussionmentioning

confidence: 99%

“…It is verified in practical applications such as helicopter control [9], furnace control [10] and, fault tolerant control of a trailer chain [14]. The case det(CpBp) = 0 is fairly more complex as can be seen in some preliminary works [8], [15]. Assumption (A3) can be weakened to require only the knowledge of an upper bound on ν, as in [13], which, however, would increase the order of the filters and the number of parameters.…”

Section: Problem Statementmentioning

confidence: 99%

“…Let {Ac, Bc, Co} be a nonminimal realization of WM (s) with state vector XM . Then, the state error (Xe := X − XM ) and the output error satisfy [15] …”

Section: Control Parameterizationmentioning

confidence: 99%

“…The Hurwitz condition on the matrix −K appears to be the least restrictive condition on the plant high frequency gain matrix, since it is a necessary and sufficient condition for the existence of sliding mode in unit vector control systems, according to [22,Theorem 1], [15].…”

Section: Remarkmentioning

confidence: 99%

“…Then, one can conclude that: (a) r(t) is bounded by r(t) ≤ [r(0) + cR] exp(−λ1t) , ∀t ≥ 0 , where c > 0 is an appropriate constant and λ1 < min(λ, γ); (b) if δ > 0 then ∃ts < +∞ such that r(t) ≡ 0 , ∀t ≥ ts. Proof: The proof presented in [15,Lemma 3] is based on the Comparison Theorem [12,Theorem 7].…”

Section: Appendixmentioning

confidence: 99%

See 4 more Smart Citations

Output-feedback model-reference sliding mode control of uncertain multivariable systems

Cunha

Hsu²,

Costa³

et al. 2003

IEEE Trans. Automat. Contr.

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Abstract-This paper considers the robust output tracking problem using a model-reference sliding mode controller for linear multivariable systems of relative degree one. It is shown that the closed loop system is globally exponentially stable and the performance is insensitive to bounded input disturbances and parameter uncertainties. The strategy is based on output-feedback unit vector control to generate sliding mode. The only required a priori information about the plant high frequency gain matrix Kp is the knowledge of a matrix Sp such that −KpSp is Hurwitz which relaxes the positive definiteness requirement usually needed by other methods.

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Section: Discussionmentioning

confidence: 99%

Section: Problem Statementmentioning

confidence: 99%

“…Let {Ac, Bc, Co} be a nonminimal realization of WM (s) with state vector XM . Then, the state error (Xe := X − XM ) and the output error satisfy [15] …”

Section: Control Parameterizationmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: Appendixmentioning

confidence: 99%

See 3 more Smart Citations

Output-feedback model-reference sliding mode control of uncertain multivariable systems

Cunha

Hsu²,

Costa³

et al. 2003

IEEE Trans. Automat. Contr.

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Control of uncertain nonlinear systems with arbitrary relative degree and unknown control direction using sliding modes

Oliveira

Peixoto

Nunes

et al. 2007

Adaptive Control & Signal

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The control of uncertain nonlinear systems by output feedback is addressed. A model-reference tracking sliding mode controller is designed for uncertain plants with arbitrary relative degree. Nonlinearities of a given class are incorporated as state dependent and possibly unmatched disturbances of a linear plant. Such class encompasses nonlinear systems which are triangular in the unmeasured states. In contrast with previous works, exact tracking is achieved by means of a switching strategy based on a locally exact differentiator, and a monitoring function is used to cope with the lack of knowledge of the control direction. Global or semi-global stability properties of the closed-loop system are proved.

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Multivariable extension of global finite‐time HOSM based differentiator for output‐feedback unit vector and smooth binary control

Oliveira

Rodrigues

Battistel

2019

Asian Journal of Control

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In this paper, we propose a unit vector control law by output feedback to solve the problem of global exact output tracking for a class of multivariable uncertain plants with nonlinear disturbances. In order to face the nonuniform arbitrary relative degree obstacle, we extend our earlier estimation scheme based on global finite-time differentiators using dynamic gains to a multivariable architecture. A diagonally stable condition over the system high-frequency gain (HFG) matrix has to be assumed. Preserving the simplicity of its mono variable framework, variable gain super-twisting algorithm (STA) is employed to obtain the robust and exact multivariable differentiator. Moreover, state-norm observers for the unmeasured state variables are constructed to upper bound the disturbances as well as to update the differentiator gains, being both state dependent. Uniform global exponential stability and ultimate exact tracking are proved. As an alternative to chattering alleviation, we appeal to the Emelyanov's concept of binary control in order to obtain a continuous control signal replacing the unit vector function in the controller by a high-gain gradient adaptive law with parameter projection. As shown in the existing literature for mono variable systems, the proposed multiparameter binary-adaptive formulation tends to the unit vector control as the adaptation gain increases to infinity, also smoothing the transition from adaptive to sliding mode control. A numerical example is portrayed to illustrate the potentialities of the developed multivariable techniques.

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Multivariable Output-Feedback Sliding Mode Control

Cited by 41 publications

References 58 publications

Output-feedback model-reference sliding mode control of uncertain multivariable systems

Output-feedback model-reference sliding mode control of uncertain multivariable systems

Control of uncertain nonlinear systems with arbitrary relative degree and unknown control direction using sliding modes

Multivariable extension of global finite‐time HOSM based differentiator for output‐feedback unit vector and smooth binary control

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