Dynamics and control of mechanical systems in partly specified motion

Blajer, Wojciech

doi:10.1016/s0016-0032(96)00091-9

Cited by 45 publications

(51 citation statements)

References 19 publications

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“…The m = dim(y) motion specifications are treated hereafter as servo-constraints [3][4][5] on the system, called also program, control or active constraints [6][7][8][9] as opposed to the classical contact (or passive) constraints in terms of hard surfaces, rigid joints/links, slipless rolling contacts, etc. Using the relationship y = (q) and the output specificationỹ(t), the m servo-constraint equations, respectively, at the position, velocity and acceleration levels are:…”

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confidence: 99%

Servo-constraint realization for underactuated mechanical systems

2015

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The paper deals with underactuated mechanical systems, featured by less control inputs m than degrees of freedom f , m < f , subject to m servo-constraints (specified in time outputs) on the system. The arising servo-constraint problem (inverse dynamics analysis) is discussed with an emphasis on the way the servo-constraints are realized, varying from orthogonal to tangential, and a geometrical illustration of the different realization types is provided. Depending on the way the servo-constraints are realized, the governing equations are formulated either as ordinary differential equations (ODEs) or differential-algebraic equations (DAEs), and some computational issues for the ODEs and DAEs are discussed. The existence or non-existence of an explicit solution to the governing equations is further discussed, related to so-called differentially flat problems (without internal dynamics) and non-flat problems (with internal dynamics). It is shown that in case of non-flat problems with orthogonal realization of servo-constraints, stability of the internal dynamics must be assured. Simple case studies are reported to illustrate the proposed formulations and methodologies.

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Servo-constraint realization for underactuated mechanical systems

2015

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“…As mentioned already in the introduction, the computation of the inverse dynamics of a discrete mechanical system given by a specification of a trajectory is a highly challenging problem [7,8]. The reason is the high-index structure of the resulting DAEs.…”

Section: Solving High-index Daesmentioning

confidence: 99%

“…5.4]. A well-known approach based on a projection of the dynamics was introduced in [8]; see also [6]. For this, we have to compute time-dependent projection matrices in order to split the dynamics of the underactuated system into constrained and unconstrained parts.…”

Section: Solving High-index Daesmentioning

confidence: 99%

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Simulation of multibody systems with servo constraints through optimal control

Altmann

Heiland

2016

Multibody Syst Dyn

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We consider mechanical systems where the dynamics are partially constrained to prescribed trajectories. An example for such a system is a building crane with a load and the requirement that the load moves on a certain path.Enforcing this condition directly in form of a servo constraint leads to differentialalgebraic equations (DAEs) of arbitrarily high index. Typically, the model equations are of index 5, which already poses high regularity conditions. If we relax the servo constraints and consider the system from an optimal control point of view, the strong regularity conditions vanish, and the solution can be obtained by standard techniques.By means of the well-known n-car example and an overhead crane, the theoretical and expected numerical difficulties of the direct DAE and the alternative modeling approach are illustrated. We show how the formulation of the problem in an optimal control context works and address the solvability of the optimal control system. We discuss that the problematic DAE behavior is still inherent in the optimal control system and show how its evidences depend on the regularization parameters of the optimization.

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“…It should be mentioned, that differentially flat systems with higher index exist. Such an example is the n-mass-spring chain as analyzed in Blajer (1997b).…”

Section: Summary and Comparison Of Casesmentioning

confidence: 99%

Analysis of servo-constraint problems for underactuated multibody systems

Seifried

Blajer

2013

Mech. Sci.

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Abstract. Underactuated multibody systems have fewer control inputs than degrees of freedom. In trajectory tracking control of such systems an accurate and efficient feedforward control is often necessary. For multibody systems feedforward control by model inversion can be designed using servo-constraints. So far servo-constraints have been mostly applied to differentially flat underactuated mechanical systems. Differentially flat systems can be inverted purely by algebraic manipulations and using a finite number of differentiations of the desired output trajectory. However, such algebraic solutions are often hard to find and therefore the servo-constraint approach provides an efficient and practical solution method. Recently first results on servo-constraint problems of non-flat underactuated multibody systems have been reported. Hereby additional dynamics arise, so-called internal dynamics, yielding a dynamical system as inverse model. In this paper the servo-constraint problem is analyzed for both, differentially flat and non-flat systems. Different arising important phenomena are demonstrated using two illustrative examples. Also strategies for the numerical solution of servo-constraint problems are discussed.

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Dynamics and control of mechanical systems in partly specified motion

Cited by 45 publications

References 19 publications

Servo-constraint realization for underactuated mechanical systems

Servo-constraint realization for underactuated mechanical systems

Simulation of multibody systems with servo constraints through optimal control

Analysis of servo-constraint problems for underactuated multibody systems

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