A Direct Discrete-time IDA-PBC Design Method for a Class of Underactuated Hamiltonian Systems

Goren-Sumer, Leyla; Yalçın, Yaprak

doi:10.3182/20110828-6-it-1002.01187

Cited by 14 publications

(25 citation statements)

References 20 publications

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“…(27) were successfully used utilizing the 3 proposed discrete gradients, where the explicit models are given by Eq. (19) with (21) or (23) and (26) in [14][15][16][17][18], and, specifically, [17] presents results of a real application of an overhead crane system. The simulation results demonstrate that the proposed discrete-time models satisfactorily represent the continuous time dynamics of the considered class of systems and they are convenient to use for engineering application purposes.…”

Section: Discussionmentioning

confidence: 99%

“…It might be noted that the discrete time models proposed here were used in the sampled-data control of port-Hamiltonian systems in the sense of passivity-based control and disturbance attenuation in [14][15][16][17][18], respectively. It should be emphasized that [17] reported a real application where the proposed model was easily and successfully utilized.…”

Section: Introductionmentioning

confidence: 99%

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Discrete-time modeling of Hamiltonian systems

Yalçın¹,

Goren-Sumer²,

Kurtulan³

2015

Turk J Elec Eng & Comp Sci

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Abstract:The problem of discrete-time modeling of the lumped-parameter Hamiltonian systems is considered for engineering applications. Hence, a novel gradient-based method is presented, exploiting the discrete gradient concept and the forward Euler discretization under the assumption of the continuous Hamiltonian model is known. It is proven that the proposed discrete-time model structure defines a symplectic difference system and has the energy-conserving property under some conditions. In order to provide alternate discrete-time models, 3 different discrete-gradient definitions are given. The proposed models are convenient for the design of sampled-data controllers. All of the models are considered for several well-known Hamiltonian systems and the simulation results are demonstrated comparatively.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Discrete-time modeling of Hamiltonian systems

Yalçın¹,

Goren-Sumer²,

Kurtulan³

2015

Turk J Elec Eng & Comp Sci

Self Cite

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“…If (4), (5) are satisfied ∀(q, p) ∈ R 2n , control (3) in closed-loop with (1) achieves stability of the equilibrium (q, p) = (q * , 0), and if ∇ q V d (q * ) = 0 and ∇ 2 q V d (q * ) > 0, the equilibrium is a strict minimum of V d . Finally, asymptotic stability is concluded if the output y = G T ∇ p H d is detectable.…”

Section: Overview Of Ida-pbcmentioning

confidence: 99%

“…3 Although these approaches have proved effective for a wide range of applications 4 including discrete-time systems, 5 most studies have been focusing on ideal systems free from uncertainties and disturbances. The most notable results include the method of Controlled Lagrangians (CLs) based on the Euler-Lagrange formulation 1,2 and the Interconnection-and-damping-assignment Passivity-based control (IDA-PBC) for port-controlled Hamiltonian systems.…”

Section: Introductionmentioning

confidence: 99%

“…The most notable results include the method of Controlled Lagrangians (CLs) based on the Euler-Lagrange formulation 1,2 and the Interconnection-and-damping-assignment Passivity-based control (IDA-PBC) for port-controlled Hamiltonian systems. 3 Although these approaches have proved effective for a wide range of applications 4 including discrete-time systems, 5 most studies have been focusing on ideal systems free from uncertainties and disturbances. 6 However, the practical importance of disturbances in real systems has recently been attracting increasing interest within the research community.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive IDA‐PBC for underactuated mechanical systems with constant disturbances

Franco

2018

Adaptive Control & Signal

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This work investigates the control of nonlinear underactuated mechanical systems with matched and unmatched constant disturbances. To this end, a new control strategy is proposed, which builds upon the interconnection-anddamping-assignment passivity-based control, augmenting it with an additional term for the purpose of disturbance compensation. In particular, the disturbances are estimated adaptively and then accounted for in the control law employing a new matching condition of algebraic nature. Stability conditions are discussed, and for comparison purposes, an alternative controller based on partial feedback linearization is presented. The effectiveness of the proposed approach is demonstrated with numerical simulations for three motivating examples: the inertia wheel pendulum, the disk-on-disk system, and the pendulum-on-cart system. KEYWORDS adaptive control, matched and unmatched disturbances, nonlinear control, underactuated mechanical systems Int J Adapt Control Signal Process. 2019;33:1-15.wileyonlinelibrary.com/journal/acs

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Robust Disturbance Attenuation in Hamiltonian Systems Via Direct Digital Control

Yalçın¹,

Goren-Sumer²,

Kurtulan³

2014

Asian Journal of Control

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The discrete‐time robust disturbance attenuation problem for the n‐degrees of freedom (dof) mechanical systems with uncertain energy function is considered in this paper. First, it is shown in the continuous time‐setting that the robust control problem of n‐dof mechanical systems can be reduced to a disturbance attenuation problem when a specific type of control rule is used. Afterwards, the robust disturbance attenuation problem is formulised as a special disturbance attenuation problem. Then, the discrete‐time counterpart of this problem characterised by means of L2 gain is given. Finally, a solution of the problem via direct‐discrete‐time design is presented as a sufficient condition. The proposed discrete‐time design utilizes discrete gradient of the energy function of considered system. Therefore, a new method is also proposed using the quadratic approximation lemma to construct discrete gradients for general energy functions. The proposed direct‐discrete‐time design method is used to solve the robust disturbance attenuation problem for the double pendulum system. Simulation results are given for the discrete gradient obtained with the method presented in this paper. Note that the solution presented here for the robust disturbance attenuation problem give an explicit algebraic condition on the design parameter, whereas solution of the same problem requires solving a Hamilton–Jacobi–Isaacs partial differential inequality in general nonlinear systems.

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A Direct Discrete-time IDA-PBC Design Method for a Class of Underactuated Hamiltonian Systems

Cited by 14 publications

References 20 publications

Discrete-time modeling of Hamiltonian systems

Discrete-time modeling of Hamiltonian systems

Adaptive IDA‐PBC for underactuated mechanical systems with constant disturbances

Robust Disturbance Attenuation in Hamiltonian Systems Via Direct Digital Control

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