An intrinsic PID controller for mechanical systems on Lie groups

Maithripala, D. H. S.; Berg, Jordan M.

doi:10.1016/j.automatica.2015.01.005

Cited by 53 publications

(72 citation statements)

References 23 publications

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“…The Riemann metric on the tangent space can be used to describe the kinetic energy of the mechanical system. And a smooth Morse function related to the configuration q ∈ G can be found to describe the potential energy [3]. Generalized forces are all defined in the cotangent space, which is the dual space of the tangent space.…”

Section: Mechanical Systems On Lie Groupmentioning

confidence: 99%

“…Many conventional works in nonlinear control theory have been developed in flat space framework with local coordinates [3]. However, those control methods cannot be applied to the system represented by Lie group directly.…”

Section: Introductionmentioning

confidence: 99%

“…Maithripala designed an intrinsic Luenberger observer on Lie group with intrinsic information and provide a coordinate-free tracking controller for mechanical systems on Lie group [7][8][9]. He also introduced an intrinsic geometric PID method with covariant differentiation for left-invariant or right-invariant system [3,10]. Bullo et al used a smooth Morse function as the configuration error function which induced the configuration error in a nature coordinate on Lie group.…”

Section: Introductionmentioning

confidence: 99%

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Intrinsic Optimal Control for Mechanical Systems on Lie Group

Liu

Tang

Guo

2017

Advances in Mathematical Physics

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The intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal problem in the geometric viewpoint, a simplified nominal system on Lie group with an extra feedback loop is presented. With geodesic distance and Riemann metric on Lie group integrated into the cost function, a dynamic programming approach is employed and an analytical solution of the optimal problem on Lie group is obtained via the HamiltonJacobi-Bellman equation. For a special case on SO(3), the intrinsic optimal control method is used for a quadrotor rotation control problem and simulation results are provided to show the control performance.

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Section: Mechanical Systems On Lie Groupmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Intrinsic Optimal Control for Mechanical Systems on Lie Group

Liu

Tang

Guo

2017

Advances in Mathematical Physics

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“…8,9 The PID control is widely applied to mechanical and electrical control systems, which shows great control performance. 10,11 However, due to the inherent nonlinearities existing in the control system as mentioned above, it is difficult for the linear PID control strategy to achieve excellent control behaviors, and consequently the unsuitable PID controller may significantly limit its dynamic performances. Facing this dilemma, a more robust and efficient control method should be further explored for the gun control system.…”

Section: Introductionmentioning

confidence: 99%

Extended state observer–based fractional order proportional–integral–derivative controller for a novel electro-hydraulic servo system with iso-actuation balancing and positioning

Gao

Hou

Deng³

et al. 2015

Advances in Mechanical Engineering

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Aiming at balancing and positioning of a new electro-hydraulic servo system with iso-actuation configuration, an extended state observer-based fractional order proportional-integral-derivative controller is proposed in this study. To meet the lightweight requirements of heavy barrel weapons with large diameters, an electro-hydraulic servo system with a three-chamber hydraulic cylinder is especially designed. In the electro-hydraulic servo system, the balance chamber of the hydraulic cylinder is used to realize active balancing of the unbalanced forces, while the driving chambers consisting of the upper and lower chambers are adopted for barrel positioning and dynamic compensation of external disturbances. Compared with conventional proportional-integral-derivative controllers, the fractional order proportional-integralderivative possesses another two adjustable parameters by expanding integer order to arbitrary order calculus, resulting in more flexibility and stronger robustness of the control system. To better compensate for strong external disturbances and system nonlinearities, the extended state observer strategy is further introduced to the fractional order proportional-integral-derivative control system. Numerical simulation and bench test indicate that the extended state observer-based fractional order proportional-integral-derivative significantly outperforms proportional-integral-derivative and fractional order proportional-integral-derivative control systems with better control accuracy and higher system robustness, well demonstrating the feasibility and effectiveness of the proposed extended state observer-based fractional order proportional-integral-derivative control strategy. KeywordsElectro-hydraulic servo system, iso-actuation balancing and positioning, fractional order proportional-integral-derivative, extended state observer Date

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“…Recently, in [5,4] and [8], a canonical definition of integral control has been given for systems evolving on Lie groups, to which the above examples belong. It consists in integrating the input command, instead of the output.…”

Section: Introductionmentioning

confidence: 99%

Integral control on nonlinear spaces: two extensions**This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The first author’s visit to Ghent University has been supported by a CSC scholarship, initiated by the China Scholarship Council. The authors want to thank prof.R.Sepulchre for suggesting the pendulum example.

2016

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This paper applies the recently developed framework for integral control on nonlinear spaces to two non-standard cases. First, we show that the property of perfect target stabilization in presence of actuation bias holds also if this bias is state dependent. This might not be surprising, but for practical purposes it provides an easy way to robustly cancel nonlinear dynamics of the uncontrolled plant. We specifically illustrate this for robust stabilization of a pendulum at arbitrary angle, a problem posed as non-trivial by some colleagues. Second, as previous work has been restricted to systems with as many control inputs as configuration dimensions, we here provide results for integral control of a non-holonomic system. More precisely, we design robust steering control of a rigid body under velocity bias.

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An intrinsic PID controller for mechanical systems on Lie groups

Cited by 53 publications

References 23 publications

Intrinsic Optimal Control for Mechanical Systems on Lie Group

Intrinsic Optimal Control for Mechanical Systems on Lie Group

Extended state observer–based fractional order proportional–integral–derivative controller for a novel electro-hydraulic servo system with iso-actuation balancing and positioning

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