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Redundant configuration coordinates and nonholonomic velocity coordinates in analytical mechanics

IFAC-PapersOnLine 2018年第2期51卷 409-414页

作者： Konz, Matthias Rudolph, Joachim Chair of Systems Theory and Control Engineering Saarland University Saarbrücken66123 Germany

Several established concepts of analytical mechanics are reviewed and extended to include redundant configuration coordinates and nonholonomic velocity coordinates. The main motivation for redundant coordinates is that the resulting formulations can be global, whereas minimal coordinates might necessarily be local depending on the topology of the configuration space e.g. for SO(3). The resulting formulations for Lagrange's equations, the Gibbs-Appell equations and the coefficients of the Levi-Civita connection are derived. These are then applied to the example of the free rigid body to derive the well-known Newton-Euler equations. © 2018

关键词： Mechanics Rigid structures Analytical mechanics Energy method First principles Gibbs Appell equations Newton Euler equation Redundant configuration Redundant coordinates Rigid body

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An Algebraic Approach to the Identification of Linear systems with Fractional Derivatives

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IFAC-PapersOnLine 2017年第1期50卷 6214-6219页

作者： Gehring N. Rudolph J. Chair of Automatic Control Technical University of Munich Munich Germany Chair of Systems Theory and Control Engineering Saarland University Saarbrücken Germany

Identification of fractional-order systems is considered from an algebraic point of view. The approach presented allows for a simultaneous estimation of model parameters and fractional (or integer) orders from input and output data. It is exact in that no approximations are required. Using the Laplace transform, algebraic manipulations are performed on the operational representation of the system. The unknown parameters and fractional orders are calculated solely from convolutions of known signals. A generalized Voigt model describing a viscoelastic material and a diffusion-wave equation representing a fractional partial differential equation are used to illustrate the approach. © 2017

关键词： algebraic approaches fractional derivatives fractional-order systems parameter identification system identification

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Flatness-based control of a rigid body carried by multiple heavy ropes

Flatness-based control of a rigid body carried by multiple h...

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89th Annual Meeting on the International Association of Applied Mathematics and Mechanics, GAMM 2018

作者： Irscheid, Abdurrahman Gerbet, Daniel Rudolph, Joachim Chair of Systems Theory and Control Engineering Saarland University Saarbrücken Germany

Flatness-based trajectory planning for the distributed-parameter system consisting of a rigid body carried by multiple heavy ropes is discussed. The suspension points (controlled ends) of the ropes are assumed to be freely movable. The other ends of the ropes are parametrized by a flat output of the nonlinear boundary system at the load that describes the motion of the rigid body. This parametrization is then used to express the solution of the linearized partial differential equations for the heavy ropes under small angle approximations around a vertical equilibrium configuration by the means of operational calculus. It is shown that the system trajectories of the ropes depend on distributed delays and advances of the flat output trajectory at the load-side boundary system. Evaluating the derived parametrization of the heavy ropes at the controllable ends yields the desired open-loop controller by using a planned trajectory for the flat output. This control can be used to realize a desired transition of the load position and orientation in finite time. The introduced method is illustrated for the example of a linear infinite-dimensional model of two heavy ropes carrying a rigid rod. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

关键词： Calculations

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Set-point invariant control design by integrator backstepping

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IFAC Proceedings Volumes 2010年第14期43卷 1163-1168页

作者： Carsten Collon Joachim Rudolph Laboratory of Control Theory TU Dresden Chair of Systems Theory and Control Engineering Saarland University

Invariant feedback design for nonlinear systems in state representation with Lie symmetries is considered. Existing results regarding invariant control design based on (differential) invariants of the admitted symmetry group via exact input-output linearization are extended to the backstepping algorithm for systems in feedback form. Based on invariant errors obtained by normalization an approach for the design of set-point invariant feedback is proposed. Its application is demonstrated using the control of a predator-prey bioreactor as an example.

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Position Observation for Proportional Solenoid Valves by Signal Injection

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IFAC-PapersOnLine 2016年第21期49卷 74-79页

作者： Braun, Tristan Reuter, Johannes Rudolph, Joachim Institute of System Dynamics Konstanz University of Applied Sciences Konstanz78462 Germany Chair of Systems Theory and Control Engineering Saarland University Campus A5 1 Saarbrücken66123 Germany

The method of signal injection is investigated for position estimation of proportional solenoid valves. A simple observer is proposed to estimate a position-dependent parameter, i.e. the eddy current resistance, from which the position is calculated analytically. Therefore, the relationship of position and impedance in the case of sinusoidal excitation is accurately described by consideration of classical electrodynamics. The observer approach is compared with a standard identification method, and evaluated by practical experiments on an off-the-shelf proportional solenoid valve. © 2016

关键词： Solenoid valves Electromagnets Hydraulic actuators Magnetic actuators Magnetic fields Parameter estimation Solenoids Classical electrodynamics Electromagnetic devices Identification method Observers Position dependents Position estimation Proportional solenoid valves Sinusoidal excitations

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On moment relaxations for linear state feedback controller synthesis with non-convex quadratic costs and constraints 63

On moment relaxations for linear state feedback controller s...

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63rd IEEE Conference on Decision and control, CDC 2024

作者： Gramlich, Dennis Gao, Sheng Zhang, Hao Scherer, Carsten W. Ebenbauer, Christian Rwth Aachen University Chair of Intelligent Control Systems Aachen52074 Germany Tongji University College of Electronic and Information Engineering Department of Control Science and Engineering Shanghai200092 China University of Stuttgart Chair of Mathematical Systems Theory Stuttgart70569 Germany

ISBN: (纸本)9798350316339

We present a simple and effective way to account for non-convex costs and constraints in state feedback synthesis, and an interpretation for the variables in which state feedback synthesis is typically convex. We achieve this by deriving the controller design using moment matrices of state and input. It turns out that this approach allows the consideration of non-convex constraints by relaxing them as constraints on the expected value of quadratic functions, and that the variables in which state feedback synthesis is typically convexified can be identified with blocks of these moment matrices. The employed relaxation can lead to constraint violation along sample paths. © 2024 IEEE.

关键词： State feedback

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Quadrotor tracking control based on a moving frame

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IFAC Proceedings Volumes 2013年第23期46卷 80-85页

作者： M. Konz J. Rudolph Chair of Systems Theory and Control Engineering Saarland University 66123 Saarbrücken Germany

A model for a quadrotor helicopter, its flatness-based parameterization, and its control are investigated. The model is transformed by expressing the configuration in terms of a reference trajectory and the deviation from the latter. A flat output for the error system is introduced. A dynamic and a quasi-static feedback for asymptotic stabilization of reference trajectories are derived. The approach avoids introducing artificial singularities and provides the possibility for tracking “acrobatic” trajectories. A simulation result with the quadrotor flying a loop is shown.

关键词： quadrotor flatness tracking control attitude parameterization singularities

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Gauss’s principle and tracking control of underactuated mechanical systems

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IFAC-PapersOnLine 2021年第19期54卷 365-370页

作者： Matthias Konz Joachim Rudolph Chair of Systems Theory and Control Engineering Saarland University 66123 Saarbrücken Germany

Gauss’s principle of least constraint is used to derive equations of motion. The principle is then used to motivate a template for the closed loop of the (tracking) controlled system. The control law arises from minimization of the distance between the controlled model and the template in the sense of least constraint. The control template is derived and analysed for the example of a free rigid body. This leads to quite natural formulations of its controlled inertia, damping and stiffness. This template is then used to compute a controller for a quadcopter, an underactuated system. A simulation result for an aerobatic maneuver demonstrates quite good performance of the proposed controller even though there is no formal proof of stability.

关键词： mechanics first-principles energy methods tracking control rigid body quadcopter

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A Novel Observer Approach for Self Sensing of Single-Coil Digital Valves

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IFAC-PapersOnLine 2017年第1期50卷 782-787页

作者： Braun T. Reuter J. Rudolph J. Institute of System Dynamics Konstanz University of Applied Sciences Konstanz 78462 Germany Chair of Systems Theory and Control Engineering Saarland University Campus A5 1 Saarbrücken 66123 Germany

Observer-based self sensing for digital (on–off) single-coil solenoid valves is investigated. Self sensing refers to the case where merely the driving signals used to energize the actuator (voltage and coil current) are available to obtain estimates of both the position and velocity. A novel observer approach for estimating the position and velocity from the driving signals is presented, where the dynamics of the mechanical subsystem can be neglected in the model. Both the effect of eddy currents and saturation effects are taken into account in the observer model. Practical experimental results are shown and the new method is compared with a full-order sliding mode observer. © 2017

关键词： Observer design Self sensing actuators Singular perturbation analysis

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Equations of motion with redundant coordinates for mechanical systems on manifolds

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IFAC-PapersOnLine 2015年第1期48卷 681-682页

作者： M. Konz J. Rudolph Chair of Systems Theory and Control Engineering Saarland University 66123 Saarbrücken Germany

The Lagrange formalism for deriving equations of motion for lumped mechanical systems is reviewed. When dealing with a con_guration space that is not isomorphic to Rn, the choice of generalized coordinates is local and may result in awkward expressions. It is shown how redundant coordinates can lead to more convenient global expressions.

关键词： energy methods Lagrange equations redundant coordinates embedding

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