Designing a terminal optimal control with an integral sliding mode component using a saddle point method approach: a Cartesian 3D-crane application

Solis, Cesar U.; Clempner, Julio B.; Poznyak, Alexander S.

doi:10.1007/s11071-016-2932-9

Cited by 14 publications

(3 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Fridman et al presented an integral sliding mode technique in order to vanish the undesirable dynamics from the beginning. Solis et al suggested a terminal optimal control based on sliding modes applied to a van der Pol oscillator and a 3D crane, for control based on sliding modes and MIMO systems that we found . For stochastic control and methods in other works, Rastrigin proposed a stochastic algorithm to optimize discrete‐time systems, Liu and Krstic suggest a stochastic averaging and stochastic extremum seeking, Stanković and Stipanović presented a discrete‐time extremum seeking applied to autonomous vehicles in a stochastic environment and mobile sensors, and Wang et al made an experimental application of extremum seeking algorithm.…”

Section: Introductionmentioning

confidence: 93%

Extremum seeking by a dynamic plant using mixed integral sliding mode controller with synchronous detection gradient estimation

Solis¹,

Clempner

Poznyak³

2018

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

Summary This paper presents a continuous‐time optimization method for an unknown convex function restricted to a dynamic plant with an available output including a stochastic noise. For solving the problem, we propose an extremum seeking algorithm based on a modified synchronous detection method for computing a stochastic gradient descent approach. In order to reject from the beginning the undesirable uncertainties and perturbations of the dynamic plant, we employ the standard deterministic integral sliding mode control transforming the initial dynamic plant to the static one, and after (in fact, from the beginning of the process), we apply the gradient decedent technique. We consider time‐decreasing parameters for compensating the stochastic dynamics. We prove the stability and the mean‐square convergence of the method. To validate the exposition, we perform a numerical example simulation.

show abstract

Section: Introductionmentioning

confidence: 93%

Extremum seeking by a dynamic plant using mixed integral sliding mode controller with synchronous detection gradient estimation

Solis¹,

Clempner

Poznyak³

2018

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

show abstract

“…Results based on the same methodology are presented by Vazquez et al (2012;. Solis et al (2016) use a control strategy for a Cartesian 3D crane based on a terminal optimal control together with an integral sliding mode component (Chwa, 2017) develops a robust finite-time anti-swing tracking control method for a 3D overhead crane system. A full review of this topic is beyond the scope of this study; however, we suggest the interested reader the survey by Ramli et al (2017).…”

Section: Introductionmentioning

confidence: 99%

A Trajectory Planning Based Controller to Regulate an Uncertain 3D Overhead Crane System

Aguilar-Ibáñez

Suárez-Castañón

2019

International Journal of Applied Mathematics and Computer Science

View full text Add to dashboard Cite

We introduce a control strategy to solve the regulation control problem, from the perspective of trajectory planning, for an uncertain 3D overhead crane. The proposed solution was developed based on an adaptive control approach that takes advantage of the passivity properties found in this kind of systems. We use a trajectory planning approach to preserve the accelerations and velocities inside of realistic ranges, to maintaining the payload movements as close as possible to the origin. To this end, we carefully chose a suitable S-curve based on the Bezier spline, which allows us to efficiently handle the load translation problem, considerably reducing the load oscillations. To perform the convergence analysis, we applied the traditional Lyapunov theory, together with Barbalat’s lemma. We assess the effectiveness of our control strategy with convincing numerical simulations.

show abstract

“…The major factor in such approach is optimization criterion. Minimization of transition regimes duration [18][19][20][21][22][23][24][25] is attended by increasing of dynamical loads. The integral criterion which includes dynamical and energetic functions [9,26,27] allows to increase productivity, reliability and energy effi-ciency.…”

Section: Introductionmentioning

confidence: 99%

Optimization of Bridge Crane Movement Control

Ловейкін

Romasevych

2018

Nauka teh.

View full text Add to dashboard Cite

Transient modes of bridge cranes movement determine their energy, dynamic and electrical performance, as well as productivity and durability of work. An optimal control problem of its movement has been solved while making an analysis of indicators for efficient performance of a bridge crane. Terminal and integral criteria have been selected as optimization criteria. They represent undesirable dynamic properties of the crane. Legendre method has been used to determine the possibility for achieving minimum of the optimization criterion. An analysis of the Euler-Poisson equation, which is a necessary condition for the minimum of the integral criterion, has shown that it is impossible to find a solution for the optimization problem in an analytical form. A method of differential evolution has been used in order to find an approximate solution to the optimization problem. The approximate (suboptimal) solution has been found in the complex domain, which is a limited domain conjunction of dynamic parameters and phase coordinates of the system. Limitation in the domain of the system phase coordinates (a polynomial basis function has been used in the paper) provides the possibility to attain absolute minimums of terminal problem criteria. A simulation of the bridge crane motion has been carried out in order to establish an efficiency for implementation of the suboptimal control. During this process dynamic mechanical characteristics of its electric drive have been taken into account. While carrying out the simulation, a frequency and an amplitude of the electric drive voltage in the crane movement mechanism have been changed (frequency scalar method for speed changing of an asynchronous electric drive has been used). A comparative analysis of the dynamic, kinematic, electrical and energy performance indicators of the bridge crane under suboptimal and S-curved (standard) laws of frequency and voltage variations in the crane electric drive has made it possible to establish an improvement in the efficiency of its operation under suboptimal control.

show abstract

Designing a terminal optimal control with an integral sliding mode component using a saddle point method approach: a Cartesian 3D-crane application

Cited by 14 publications

References 29 publications

Extremum seeking by a dynamic plant using mixed integral sliding mode controller with synchronous detection gradient estimation

Extremum seeking by a dynamic plant using mixed integral sliding mode controller with synchronous detection gradient estimation

A Trajectory Planning Based Controller to Regulate an Uncertain 3D Overhead Crane System

Optimization of Bridge Crane Movement Control

Contact Info

Product

Resources

About