Integral IDA-PBC and PID-like control for port-controlled Hamiltonian systems

Ryalat, Mutaz; Laila, Dina Shona; Torbati, Mohamed Moshrefi

doi:10.1109/acc.2015.7172178

Cited by 25 publications

(43 citation statements)

References 21 publications

(61 reference statements)

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“…To prove the first claim, we observe that q * is a strict minimum of V ′ d due to (16), (17). To prove the first claim, we observe that q * is a strict minimum of V ′ d due to (16), (17).…”

Section: Theorem 1 Consider System (6) Under Assumptions 1 To 3 In Cmentioning

confidence: 85%

“…In this sense, (15) can be interpreted as an additional matching condition of algebraic nature, which is therefore always solvable and relates the disturbance estimatẽto Λ(q) by means of the coupling term M d M −1 . (18), where Λ(q) is defined according to (15), (16), (17) and̃is estimated according to (10). Then, q * is a strict minimum of V ′ d , all trajectories q(t), p(t) are bounded and the equilibrium (q, p) = (q * , 0) is asymptotically stable for some parameters , k v > 0.…”

Section: Resultsmentioning

confidence: 99%

“…If, in addition, G ⟂ is constant, then (15), (16), (17) admit a constant solution Λ(q) = Λ(q * ) = −∇ q V d (q * ), and consequently, (17) reduces to the strict-minimum condition for the disturbance-free system: ∇ 2 q V d (q * ) > 0. If system (6) has a constant inertia matrix M, the kinetic-energy PDE (4) is trivially satisfied with J 2 = 0 and a constant M d .…”

Section: Theorem 1 Consider System (6) Under Assumptions 1 To 3 In Cmentioning

confidence: 99%

“…Evaluating (7) and replacing the disturbances with their estimates, the open-loop unstable equilibrium of (33) is q * = (q * 1 , q * 2 ) with q * 1 = sin −1 (̃1∕a 3 ). 17,18 Conversely, no condition is imposed on the matched disturbancẽ2 and q * 2 can be freely chosen. It must be highlighted that this is not dependent on the specific IDA-PBC design but is common to (3) and to the integral IDA-PBC designs.…”

Section: Inertia Wheel Pendulummentioning

confidence: 99%

“…Important results in this sense include the investigation of linear viscous friction within CL. Initial results in this respect were presented in the works of Teo et al 16 and Ryalat et al,17 where integral control was overlaid to IDA-PBC in order to compensate constant matched disturbances (ie, only affecting the actuated joints). 12 Besides IDA-PBC, a sliding-mode-control formulation was proposed in the work of Martinez et al 13 for underactuated mechanical systems with Coulomb friction of known amplitude.…”

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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Section: Theorem 1 Consider System (6) Under Assumptions 1 To 3 In Cmentioning

confidence: 85%

Section: Resultsmentioning

confidence: 99%

Section: Theorem 1 Consider System (6) Under Assumptions 1 To 3 In Cmentioning

confidence: 99%

Section: Inertia Wheel Pendulummentioning

confidence: 99%

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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Robust IDA-PBC for underactuated mechanical systems subject to matched disturbances

Donaire

Romero

Ortega

et al. 2016

Int. J. Robust. Nonlinear Control

110

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The problem of robustification of interconnection and damping assignment passivity-based control for underactuated mechanical system vis-à-vis matched, constant, and unknown disturbances is addressed in the paper. This is achieved adding an outer-loop controller to the interconnection and damping assignment passivity-based control. Three designs are proposed, with the first one being a simple nonlinear PI, while the second and the third ones are nonlinear PIDs. While all controllers ensure stability of the desired equilibrium in spite of the presence of the disturbances, the inclusion of the derivative term allows us to inject further damping enlarging the class of systems for which asymptotic stability is ensured. Numerical simulations of the Acrobot system and experimental results on the disk-on-disk system illustrate the performance of the proposed controller.

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Robust dynamic state feedback for underactuated systems with linearly parameterized disturbances

Franco

Baena

Astolfi

2020

Intl J Robust & Nonlinear

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This article investigates the control problem for underactuated port-controlled Hamiltonian systems with multiple linearly parameterized additive disturbances including matched, unmatched, constant, and state-dependent components. The notion of algebraic solution of the matching equations is employed to design an extension of the interconnection and damping assignment passivity-based control methodology that does not rely on the solution of partial differential equations. The result is a dynamic state-feedback that includes a disturbance compensation term, where the unknown parameters are estimated adaptively. A simplified implementation of the proposed approach for underactuated mechanical systems is detailed. The effectiveness of the controller is demonstrated with numerical simulations for the magnetic-levitated-ball system and for the ball-on-beam system. K E Y W O R D Sadaptive control, disturbance rejection, mechanical systems, passivity-based control, underactuated systems 1 This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. 4112wileyonlinelibrary.com/journal/rnc Int J Robust Nonlinear Control. 2020;30:4112-4128.FRANCO et al. 4113A further aspect of energy shaping control that has been attracting increasing attention is robustness to disturbances, which are common to most practical application. Notable results in this area include the study of viscous friction within the controlled Lagrangians formulation, 12,13 and of continuous and smooth physical dissipation within the IDA-PBC framework, 14,15 while friction according to the Dahl model affecting the actuated part of the state was considered in Reference 16. Stability and robustness of disturbed PCH systems with dissipation were investigated in Reference 17. The robust energy shaping control of fully actuated mechanical systems with disturbances was presented in Reference 18, while disturbance attenuation for discrete-time systems was studied in Reference 19. More recently, integral IDA-PBC designs that rely on the classical solution of the PDE were proposed in References 20-22 for a class of underactuated mechanical systems with constant matched disturbances (ie, those affecting the actuated part of the state), and in Reference 23 for bounded matched disturbances. The result in Reference 21 was extended to unmatched constant disturbances in Reference 24, which, however, is only applicable to mechanical systems with constant inertia matrix. The case of nonconstant inertia matrix and variable but bounded disturbances was considered in Reference 25. In addition, the adaptive compensation of constant disturbances within energy shaping control was attempted in References 26,27: while the former still requires solving the PDE, the latter is confined to a limited class of mechanical systems. Besides energy shaping, a sliding mode control for a class of underactuated systems with dry friction was presented in Ref...

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Integral IDA-PBC and PID-like control for port-controlled Hamiltonian systems

Cited by 25 publications

References 21 publications

Adaptive IDA‐PBC for underactuated mechanical systems with constant disturbances

Adaptive IDA‐PBC for underactuated mechanical systems with constant disturbances

Robust IDA-PBC for underactuated mechanical systems subject to matched disturbances

Robust dynamic state feedback for underactuated systems with linearly parameterized disturbances

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