Cascade Synthesis of Differentiators with Piecewise Linear Correction Signals

Kokunko, Yu. G.; Krasnova, Svetlana A.; Utkin, Victor A.

doi:10.1134/s000511792107002x

Cited by 11 publications

(3 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As noted in the introduction, dynamic differentiators of one type or another can be used to solve the first two problems [ 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 ]. Let us briefly outline the principles of their construction.…”

Section: Problem Definitionmentioning

confidence: 99%

“…Here, the order of the sliding mode must be at least one greater than the order of the estimated derivative. An alternative method is to approximate the sign function by a linear function with saturation [ 11 , 14 , 15 , 16 ]. Such observer-differentiators combine the advantages of linear observers with high-gains and sliding mode observers, but are free from their drawbacks.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic Smoothing, Filtering and Differentiation of Signals Defining the Path of the UAV

Antipov

Kokunko

Krasnova

et al. 2022

Sensors

View full text Add to dashboard Cite

On the example of a control system for an unmanned aerial vehicle, we consider the problems of filtering, smoothing and restoring derivatives of reference action signals. These signals determine the desired spatial path of the plant at the first approximation. As a rule, researchers have considered these problems separately and have used different methods to solve each of them. The paper aims to develop a unified approach that provides a comprehensive solution to mentioned problems. We propose a dynamic admissible path generator. It is constructed as a copy of the canonical control plant model with smooth and bounded sigmoid corrective actions. For the deterministic case, a synthesis procedure has been developed, which ensures that the output variables of the generator track a non-smooth reference signal. Moreover, it considers the constraints on the velocity and acceleration of the plant. As a result, the generator variables produce a naturally smoothed spatial curve and its derivatives, which are realizable reference actions for the plant. The construction of the generator does not require exact knowledge of the plant parameters. Its dynamic order is less than that of the standard differentiators. We confirm the effectiveness of the approach by the results of numerical simulation.

show abstract

Section: Problem Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic Smoothing, Filtering and Differentiation of Signals Defining the Path of the UAV

Antipov

Kokunko

Krasnova

et al. 2022

Sensors

View full text Add to dashboard Cite

show abstract

“…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%

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

2021

View full text Add to dashboard Cite

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.

show abstract