Block approach to analysis and design of the invariant nonlinear tracking systems

Krasnova, Svetlana A.; Utkin, Victor A.; Utkin, Anton V.

doi:10.1134/s0005117917120025

Cited by 48 publications

(23 citation statements)

References 15 publications

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“…Another approach is to represent the model of the control plant in the canonical or block input-output form, with the differentiation of external signals. In the process of obtaining this form, mixed variables are generated, which are the functions of state variables with additive external influences and their derivatives [19,20]. For system (1) under the assumption of differentiability of external disturbances η 1,2 (t), the canonical system in mixed variables has the form .…”

Section: Block Synthesis Of Linear Local Feedbacks In System With Unmatched Disturbancesmentioning

confidence: 99%

“…It consists of elementary blocks, in each of which the dimension of the controlled variables is equal to the rank of the matrix before the fictitious controls, which are the variables of the next block. For the general case of a controllable minimum-phase nonlinear system of the n-th order with affine external influences η, the block form is the following [20]:…”

Section: Block Synthesis Of Linear Local Feedbacks In System With Unmatched Disturbancesmentioning

confidence: 99%

“…In the third case (19), the lower bounds of the parameter's selection of the piecewise linear control have the form (20) and k 3 > 1/∆ 3 , ∆ 3 > 0. In both the second and third cases, the convergence of the variable to some neighborhood of zero is ensured…”

Section: Block Synthesis Of Linear Local Feedbacks In System With Unmatched Disturbancesmentioning

confidence: 99%

“…The bounded control in the form of a saturation function is not smooth. On the one hand, it is not an obstacle when these functions are used in corrective actions of observers of the state of systems with disturbances [20,29]. However, on the other hand, it narrows the possibilities of its application as fictitious controls in practical problems.…”

Section: Block Synthesis Of Linear Local Feedbacks In System With Unmatched Disturbancesmentioning

confidence: 99%

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Methods of Ensuring Invariance with Respect to External Disturbances: Overview and New Advances

2021

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In this paper, we carry out a demonstration and comparative analysis of known methods of the synthesis of various control laws ensuring the invariance of the output (controlled) variable with respect to external disturbances under various assumptions about their type and channels of acting on the control plant. Methods of the synthesis are presented on the example of a third-order nonlinear system with single input and single output (SISO-systems), dynamic feedback synthesis is presented at a descriptive level and the focus is on procedures of static feedback synthesis. For the systems in which the matching conditions are not satisfied, it is concluded that it is expedient to introduce smooth and bounded nonlinear local feedbacks. Within the framework of the block control principle, we developed an iterative procedure of synthesis of S-shaped sigmoid feedbacks for such systems. Nonlinear local feedbacks ensure stabilization of the output variable with the given accuracy and settling time as in a system with traditionally used linear local feedbacks with high gains. However, in contrast to it, sigmoid functions do not lead to a large overshoot of state variables and control actions.

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Section: Block Synthesis Of Linear Local Feedbacks In System With Unmatched Disturbancesmentioning

confidence: 99%

Section: Block Synthesis Of Linear Local Feedbacks In System With Unmatched Disturbancesmentioning

confidence: 99%

Section: Block Synthesis Of Linear Local Feedbacks In System With Unmatched Disturbancesmentioning

confidence: 99%

Section: Block Synthesis Of Linear Local Feedbacks In System With Unmatched Disturbancesmentioning

confidence: 99%

See 2 more Smart Citations

Methods of Ensuring Invariance with Respect to External Disturbances: Overview and New Advances

2021

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“…It is essential that in these approaches, the results are expressed in terms of matrix elements rather than their eigenvalues. Possibilities for extending this approach are available by using the block approach [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Robust Stabilization via Super-Stable Systems Techniques

et al. 2021

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In this paper, we propose a direct method for the synthesis of robust systems operating under parametric uncertainty of the control plant model. The developed robust control procedures are based on the assumption that the structural properties of the nominal system are conservated over the entire range of parameter changes. The invariant-to-parametric-uncertainties transformation of the initial model to a regular form makes it possible to use the concept of super-stable systems for the synthesis of a stabilizing feedback. It is essential that the synthesis of super-stable systems is carried out not on the basis of assigning eigenvalues to the matrix of the close-loop system, but in terms of its elements. The proposed approach is applicable to a wide class of linear systems with parametric uncertainties and provides a given degree of stability.

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A Comparison of Two Algorithms for Control over a Three-Link Robot-Manipulator under the Conditions of a Description Uncertainty

Paraev

Kolesnikova

Tsvetnitskaya

2023

Cyber-Physical Systems and Control II

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Block approach to analysis and design of the invariant nonlinear tracking systems

Cited by 48 publications

References 15 publications

Methods of Ensuring Invariance with Respect to External Disturbances: Overview and New Advances

Methods of Ensuring Invariance with Respect to External Disturbances: Overview and New Advances

Robust Stabilization via Super-Stable Systems Techniques

A Comparison of Two Algorithms for Control over a Three-Link Robot-Manipulator under the Conditions of a Description Uncertainty

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