Discontinuous H ∞ control of underactuated mechanical systems with friction and backlash

Rascón, Raúl; Álvarez, Joaquín; Aguilar, Luis T.

doi:10.1007/s12555-014-0498-1

Cited by 8 publications

(8 citation statements)

References 22 publications

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“…A previous work involving an integral/exponential gain law to absorb matched perturbations is that by Zhu and Khayati (2015). In contrast to the H ∞ controller used by Rascón et al (2016), in this work the authors proposed a sliding mode controller which includes an H ∞ control stage in the sliding surface; this controller is capable of handling matched and unmatched perturbations. The former could be eliminated if they are bounded, and the latter are mitigated through the H ∞ control stage.…”

Section: 2mentioning

confidence: 99%

“…In order to appreciate the performance of the sliding mode H ∞ controller, a comparison is made against an H ∞ control scheme presented by Rascón et al (2016); also, a nonvanishing perturbation was considered as in (48). The gains of the H ∞ controller were set as in the work of Rascón et al (2016) the velocities of the system were estimated using a filter implemented therein. The results can be seen in Figs.…”

Section: 1mentioning

confidence: 99%

“…Recently, Rascón et al (2016) considered the implementation and control design of a class of Lagrangian systems, particularly underactuated mechanical systems with friction and backlash; the control methodology used for this purpose was H ∞ , while an experimental comparison was carried out using the proposed controller and a PI algorithm.…”

mentioning

confidence: 99%

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Regulation control of an underactuated mechanical system with discontinuous friction and backlash

Rascón

Almeida

Hernández-Balbuena

2017

International Journal of Applied Mathematics and Computer Science

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In this work, the problem of position regulation control is addressed for a 2DOF underactuated mechanical system with friction and backlash. For this purpose, a method combining sliding mode and H∞ control is developed. We prove that the application of the method to the nonlinear model considered results in an asymptotically stable equilibria set. Moreover, it is possible to achieve a sufficiently small and bounded steady-state position error even in the presence of disturbances by employing the proposed technique. That is, the developed controller is able to account not only for unmatched external perturbations and model discrepancies of the test rig considered, but also for matched bounded perturbations. The control methodology is presented from both the theoretical and experimental angles to demonstrate the good performance of the proposed controller.

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Section: 2mentioning

confidence: 99%

Section: 1mentioning

confidence: 99%

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Regulation control of an underactuated mechanical system with discontinuous friction and backlash

Rascón

Almeida

Hernández-Balbuena

2017

International Journal of Applied Mathematics and Computer Science

Self Cite

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“…Two works that address the control problem of the underactuated systems with backlash are [15,16]. In [15], an ∞ control for tracking of a class of nonsmooth systems that include dry friction and backlash is proposed.…”

Section: Introductionmentioning

confidence: 99%

“…However, it cannot be applied to solve the regulation problem because a necessary condition is that the derivative of the reference signal must be different from zero for almost all times. In [16], a controller based on ∞ control to solve the regulation problem on a 2DOF underactuated massspring-damper system with backlash and dry friction is proposed. In this case, they get satisfactory results but the strategy cannot be applied to tracking control in direct way.…”

Section: Introductionmentioning

confidence: 99%

Robust Output Control of an Uncertain Underactuated 2DOF Mass-Spring-Damper System with Backlash Based on Active Disturbance Rejection Control Structure

Mora

Almeida

Rascon

et al. 2018

Mathematical Problems in Engineering

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We propose a strategy to solve the tracking and regulation problem for a 2DOF underactuated mass-spring-damper system with backlash on the underactuated joint, parametric uncertainties, and partial measurement of the state vector. The design of the controller is divided into two stages; in the first stage, it is assumed that the full state vector and all perturbations in the system are available. The model is divided into one actuated subsystem and one underactuated subsystem. The position of the actuated mass is defined as the control input of the underactuated subsystem, which is designed as an ideal controller that solves the tracking and regulation control problems for the underactuated mass. Finally, the control input of the actuated subsystem is designed to solve the tracking problem considering as a reference signal the control signal of the underactuated subsystem. The second stage solves the problem of the implementation of the previously designed ideal controller using the active disturbances rejection control structure (ADRC). Here state observers estimate the nonmeasured state variables and, at the same time, estimate perturbations and auxiliary signals for their compensation. The performance of the closed-loop system is illustrated by numerical simulations and experimental results.

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Sensor Less Fuzzy Logic Tracking Control for a Servo System with Friction and Backlash

Duarte

Aguilar

Castillo

2016

Studies in Computational Intelligence

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Discontinuous H ∞ control of underactuated mechanical systems with friction and backlash

Cited by 8 publications

References 22 publications

Regulation control of an underactuated mechanical system with discontinuous friction and backlash

Regulation control of an underactuated mechanical system with discontinuous friction and backlash

Robust Output Control of an Uncertain Underactuated 2DOF Mass-Spring-Damper System with Backlash Based on Active Disturbance Rejection Control Structure

Sensor Less Fuzzy Logic Tracking Control for a Servo System with Friction and Backlash

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