Speed Observation and Position Feedback Stabilization of Partially Linearizable Mechanical Systems

Venkatraman, Aneesh; Ortega, Roméo; Sarras, Ioannis; Schaft, A.J. van der

doi:10.1109/tac.2010.2042010

Cited by 84 publications

(91 citation statements)

References 23 publications

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“…Unfortunately, the right hand side of (31) does not depend on q a and, consequently, cannot be a positive definite function of the full state. At this point we invoke Assumption A6 and replace (24) in (28) to get…”

Section: Construction Of the Lyapunov Functionmentioning

confidence: 99%

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Global Stabilisation of Underactuated Mechanical Systems via PID Passivity-Based Control

et al. 2017

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In this note we identify a class of underactuated mechanical systems whose desired constant equilibrium position can be globally stabilised with the ubiquitous PID controller. The class is characterised via some easily verifiable conditions on the systems inertia matrix and potential energy function, which are satisfied by many benchmark examples. The design proceeds in two main steps, first, the definition of two new passive outputs whose weighted sum defines the signal around which the PID is added. Second, the observation that it is possible to construct a Lyapunov function for the desired equilibrium via a suitable choice of the aforementioned weights and the PID gains and initial conditions. The results reported here follow the same research line as [7] and [20]-bridging the gap between the Hamiltonian and the Lagrangian formulations used, correspondingly, in these papers. Two additional improvements to our previous works are the removal of a non-robust cancellation of a potential energy term and the establishment of equilibrium attractivity under weaker assumptions.

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Section: Construction Of the Lyapunov Functionmentioning

confidence: 99%

“…The prize that is paid for this relaxation is that there is no guarantee that trajectories remain bounded. However, there are cases where boundedness of trajectories can be established invoking other (non Lyapunov-based) considerations-see, for instance, the proof of Proposition 9 in [24].…”

Section: Propositionmentioning

confidence: 99%

Global Stabilisation of Underactuated Mechanical Systems via PID Passivity-Based Control

et al. 2017

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“…the system is only affected by the potential field [38]. In [11] and [37], some necessary and sufficient conditions (such as, Riemannian curvature, constant inertia matrix, skew-symmetry, and zero Christoffel symbols) on the inertia matrix M have been given, which need to be verified for the existence of such transformation. Although these methods simplify the control problem, the application is limited to the class of systems that admits quasi-linearization.…”

Section: Simplifying the Pdes Via Change Of Coordinatesmentioning

confidence: 99%

“…In some cases, a non-separable UMS model can be transformed into a separable one via partial feedback linearization [31] or a change of coordinates [22,37].…”

Section: Separable Umssmentioning

confidence: 99%

A simplified IDA-PBC design for underactuated mechanical systems with applications

Ryalat

Laila

2016

European Journal of Control

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Please check your proof carefully and mark all corrections at the appropriate place in the proof (e.g., by using on-screen annotation in the PDF file) or compile them in a separate list. Note: if you opt to annotate the file with software other than Adobe Reader then please also highlight the appropriate place in the PDF file. To ensure fast publication of your paper please return your corrections within 48 hours.For correction or revision of any artwork, please consult http://www.elsevier.com/artworkinstructions.Any queries or remarks that have arisen during the processing of your manuscript are listed below and highlighted by flags in the proof. Click on the Q link to go to the location in the proof.Your article is registered as a regular item and is being processed for inclusion in a regular issue of the journal. If this is NOT correct and your article belongs to a Special Issue/Collection please contact p.atterbury@elsevier.com immediately prior to returning your corrections. Location in articleQuery / Remark: click on the Q link to go Please insert your reply or correction at the corresponding line in the proof Q1Please confirm that given names and surnames have been identified correctly and are presented in the desired order. Q2Corresponding author has not been indicated in the author group. Kindly provide the corresponding author's footnote. Q3Please provide the city of publication for Refs. [10,12,15].Thank you for your assistance. We develop a method to simplify the partial differential equations (PDEs) associated to the potential energy for interconnection and damping assignment passivity based control (IDA-PBC) of a class of underactuated mechanical systems (UMSs). Solving the PDEs, also called the matching equations, is the main difficulty in the construction and application of the IDA-PBC. We propose a simplification to the potential energy PDEs through a particular parametrization of the closed-loop inertia matrix that appears as a coupling term with the inverse of the original inertia matrix. The parametrization accounts for kinetic energy shaping, which is then used to simplify the potential energy PDEs and their solution that is used for the potential energy shaping. This energy shaping procedure results in a closed-loop UMS with a modified energy function. This approach avoids the cancellation of nonlinearities, and extends the application of this method to a larger class of systems, including separable and non-separable portcontrolled Hamiltonian (PCH) systems. Applications to the inertia wheel pendulum and the rotary inverted pendulum are presented, and some realistic simulations are presented which validate the proposed control design method and prove that global stabilization of these systems can be achieved. Experimental validation of the proposed method is demonstrated using a laboratory set-up of the rotary pendulum. The robustness of the closed-loop system with respect to external disturbances is also experimentally verified.

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“…There has been active research on quasilinearization [2,5,7,8], but the results were obtained by the zero curvature condition or by some complicated PDE conditions, producing restrictive outcomes. Then, very strong results were finally obtained in [4] where easily verifiable quasilinearizability conditions were derived.…”

Section: Introductionmentioning

confidence: 99%

A Sufficient Condition for the Feedback Quasilinearization of Control Mechanical Systems

Chang¹,

Song²,

Kim³

2016

Journal of Electrical Engineering and Technology

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Speed Observation and Position Feedback Stabilization of Partially Linearizable Mechanical Systems

Cited by 84 publications

References 23 publications

Global Stabilisation of Underactuated Mechanical Systems via PID Passivity-Based Control

Global Stabilisation of Underactuated Mechanical Systems via PID Passivity-Based Control

A simplified IDA-PBC design for underactuated mechanical systems with applications

A Sufficient Condition for the Feedback Quasilinearization of Control Mechanical Systems

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