Sliding Modes, Differential Flatness and Integral Reconstructors

The standard ISO 10328 specifies the procedure for structural tests on lower limb prosthetic devices, as a method for quality control. Having the standard as reference, a machine is designed and implemented to follow the test routine, which if succeeded, shows the quality concept for the devices tested. Furthermore, it is shown the controller design process, which manage the application of a sinusoid force with specified amplitude, frequency and offset, in order to realize the dynamic test, by means of a double effect cylinder and proportional valves for pressure and flow.The dynamic model was calculated through a parametric identification technique in a pre-stabilized closed loop. Later, a hybrid control strategy was set using the differential flatness concept and a sliding modes controller, so that both identified model and real system could be properly controlled.

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Design and control of multiphase interleaved boost converters-based on differential flatness theory for PEM fuel cell multi-stack applications

International Journal of Electrical Power & Energy Systems ◽

10.1016/j.ijepes.2020.106346 ◽

2021 ◽

Vol 124 ◽

pp. 106346

Author(s):

Phatiphat Thounthong ◽

Pongsiri Mungporn ◽

Damien Guilbert ◽

Noureddine Takorabet ◽

Serge Pierfederici ◽

...

Keyword(s):

Fuel Cell ◽

Pem Fuel Cell ◽

Differential Flatness ◽

Differential Flatness Theory ◽

Boost Converters ◽

And Control

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Three-phase phase-locked loop algorithms based on sliding modes

IEEE Transactions on Power Electronics ◽

10.1109/tpel.2021.3064674 ◽

2021 ◽

pp. 1-1

Author(s):

Arnau Doria-Cerezo ◽

Victor Repecho ◽

Domingo Biel

Keyword(s):

Phase Locked Loop ◽

Sliding Modes ◽

Three Phase ◽

Phase Phase

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On complexity reduction of the discrete-event subsystem of Flat Hybrid Automata for control design

at - Automatisierungstechnik ◽

10.1515/auto-2020-0061 ◽

2020 ◽

Vol 68 (7) ◽

pp. 529-540

Author(s):

Tobias Kleinert ◽

Frederik Zahn ◽

Veit Hagenmeyer

Keyword(s):

Heuristic Algorithm ◽

Adjacency Matrix ◽

Discrete Event ◽

Control Design ◽

Differential Flatness ◽

Hybrid Automata ◽

Connected Automaton ◽

Strongly Connected ◽

Design Perspective ◽

Technical Systems

AbstractThe class of hybrid systems describes most technical systems in great detail. However, the respective models and their behavior tend to be very complex. Recently, a new subclass of hybrid automata has been introduced, the Flat Hybrid Automata (FHA) that relies on the concepts of differential flatness for the continuous parts, and strongly connected automaton graphs for the discrete event part, in order to deal with the complexity from a design perspective. Therefore, we introduce in the present paper an approach to reduce the automaton graph of an FHA in a systematic way by removing edges from the adjacency matrix. The main contribution of the paper is twofold: Firstly, based on practical considerations we develop a heuristic algorithm to reduce the automaton graph. Secondly, we present possible ways to include knowledge about the system in the reduction.

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Sliding modes solution for the ℋ/sub 2/ singular problem

Proceedings of 35th IEEE Conference on Decision and Control ◽

10.1109/cdc.1996.574305 ◽

2002 ◽

Cited By ~ 2

Author(s):

R.H.C. Takahashi ◽

P.L.D. Peres

Keyword(s):

Singular Problem ◽

Sliding Modes

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NonlinearL2-Gain Analysis of Hybrid Systems in the Presence of Sliding Modes and Impacts

Mathematical Problems in Engineering ◽

10.1155/2016/9074096 ◽

2016 ◽

Vol 2016 ◽

pp. 1-10 ◽

Cited By ~ 5

Author(s):

T. Osuna ◽

O. E. Montano ◽

Y. Orlov

Keyword(s):

Sliding Mode ◽

Numerical Study ◽

Sufficient Conditions ◽

Disturbance Attenuation ◽

Sliding Modes ◽

Time Dynamics ◽

Attenuation Level ◽

Disturbance Factor ◽

Disturbance Attenuation Level ◽

The Impact

TheL2-gain analysis is extended towards hybrid mechanical systems, operating under unilateral constraints and admitting both sliding modes and collision phenomena. Sufficient conditions for such a system to be internally asymptotically stable and to possessL2-gain less than ana priorigiven disturbance attenuation level are derived in terms of two independent inequalities which are imposed on continuous-time dynamics and on discrete disturbance factor that occurs at the collision time instants. The former inequality may be viewed as the Hamilton-Jacobi inequality for discontinuous vector fields, and it is separately specified beyond and along sliding modes, which occur in the system between collisions. Thus interpreted, the former inequality should impose the desired integral input-to-state stability (iISS) property on the Filippov dynamics between collisions whereas the latter inequality is invoked to ensure that the impact dynamics (when the state trajectory hits the unilateral constraint) are input-to-state stable (ISS). These inequalities, being coupled together, form the constructive procedure, effectiveness of which is supported by the numerical study made for an impacting double integrator, driven by a sliding mode controller. Desired disturbance attenuation level is shown to satisfactorily be achieved under external disturbances during the collision-free phase and in the presence of uncertainties in the transition phase.

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