Analysis of Feed-Forward Control Design Approaches for Flexible Multibody Systems

Seifried, Robert; Held, Alexander; Fabian, Dietmann

doi:10.1299/jsdd.5.429

Cited by 8 publications

(16 citation statements)

References 13 publications

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“…Similar linearly combined outputs are also often used in end-effector tracking of flexible manipulators, see e.g. De Luca (1998); Seifried et al (2011). For this rotational arm the servo-constraint is given by…”

Section: Illustrative Example 2: Rotational Manipulator Armmentioning

confidence: 98%

“…Analysis of 124 R. Seifried and W. Blajer: Analysis of servo-constraint problems for underactuated multibody systems such systems are given e.g. in Seifried (2012b) and Seifried et al (2011), respectively.…”

Section: Illustrative Example 2: Rotational Manipulator Armmentioning

confidence: 99%

“…(25) for the orthogonal realization. Examples are the feedforward control design of flexible manipulators, see Seifried et al (2011). With this approach bounded trajectories q u ,q u of the internal dynamics (Eq.…”

Section: Systems With Unstable Internal Dynamicsmentioning

confidence: 99%

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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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Section: Illustrative Example 2: Rotational Manipulator Armmentioning

confidence: 98%

Section: Illustrative Example 2: Rotational Manipulator Armmentioning

confidence: 99%

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Analysis of servo-constraint problems for underactuated multibody systems

Seifried

Blajer

2013

Mech. Sci.

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“…This paper addresses the inverse dynamics of non-minimum phase underactuated multibody systems, which represent an important class of practical applications. For example, nonminimum phase behavior can occur when joint actuators are used to control the end effector of a flexible manipulator [23] or a manipulator with passive joints [20]. The inverse dynamics of a non-minimum phase system is known to be non-causal, which means that the control forces and torques should start before the beginning of the trajectory (pre-actuation phase) and continue after the end-point is reached (post-actuation phase).…”

Section: Introductionmentioning

confidence: 99%

Inverse dynamics of serial and parallel underactuated multibody systems using a DAE optimal control approach

2013

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The inverse dynamics analysis of underactuated multibody systems aims at determining the control inputs in order to track a prescribed trajectory. This paper studies the inverse dynamics of non-minimum phase underactuated multibody systems with serial and parallel planar topology, e.g. for end-effector control of flexible manipulators or manipulators with passive joints. Unlike for minimum phase systems, the inverse dynamics of non-minimum phase systems cannot be solved by adding trajectory constraints (servo-constraints) to the equations of motion and applying a forward time integration. Indeed, the inverse dynamics of a non-minimum phase system is known to be non-causal, which means that the control forces and torques should start before the beginning of the trajectory (pre-actuation phase) and continue after the end-point is reached (post-actuation phase). The existing stable inversion method proposed for general nonlinear non-minimum phase systems requires to derive explicitly the equations of the internal dynamics and to solve a boundary value problem. This paper proposes an alternative solution strategy which is based on an optimal control approach using a direct transcription method. The method is illustrated for the inverse dynamics of an underactuated serial manipulator with rigid links and four degrees-of-freedom and an underactuated parallel machine. An important advantage of the proposed approach is that it can be applied directly to the standard equations of motion of multibody systems either in ODE or in DAE form. Therefore, it is easier to implement this method in a general purpose simulation software.

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“…Thereby, for a given system output y the inverse model provides the control input for exact output reproduction. For flexible manipulators it is often possible to define a simplified linearly combined system output y = q r + Γ Γ Γq e to approximate the end-effector position bŷ r ef (y) ≈ r ef (q r , q e ), see [1]. It can be shown that flexible manipulators in end-effector trajectory tracking in many cases have vector relative degree {2, · · · , 2}, while often the internal dynamics is unbounded, i.e.…”

mentioning

confidence: 99%

End‐Effector Trajectory Tracking of Serial Flexible Manipulators

Seifried

Wörner

Gorius

2012

Proc Appl Math and Mech

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Light weight manipulator design results in low energy consumption and allow often high working speeds. However, due to the increased system flexibility undesired vibrations occur. Thus, in the control design these flexibilities must be taken into account. In order to obtain a good performance in end-effector trajectory tracking an efficient feedforward control is used, which is then supplemented by additional feedback control to account for small disturbances and uncertainties. Flexible Model and Control DesignIn this contribution a control design based on model inversion is presented and applied to a serial manipulator with two flexible arms, see Fig. 1. The two flexible arms are connected by two rotational joints described by the rigid generalized coordinates q r ∈ IR 2 . In direction of these coordinates motor torques act, which form the control input u = [T 1 , T 2 ]. The elastic deformation of the arms is described using the floating frame of reference approach, where the elastic deformation field is described by a global Ritz approach as Φ Φ Φq e . Thereby, the matrix Φ Φ Φ contains the shape functions and q e ∈ IR f e are the elastic generalized coordinates. In this research eigenmodes are used as shape functions. Then, the equations of motion follows as,with mass matrix M, Coriolis-, gyroscopic and centrifugal forces k, applied forces g, structural stiffness K and damping D. For end-effector trajectory tracking a control design based on an inverse model is used. Thereby, for a given system output y the inverse model provides the control input for exact output reproduction. For flexible manipulators it is often possible to define a simplified linearly combined system output y = q r + Γ Γ Γq e to approximate the end-effector position bŷ r ef (y) ≈ r ef (q r , q e ), see [1]. It can be shown that flexible manipulators in end-effector trajectory tracking in many cases have vector relative degree {2, · · · , 2}, while often the internal dynamics is unbounded, i.e. the system is non-minimum phase. For the linear output y the nonlinear input-output normal can be obtained fully symbolically using a diffeomorphic coordinate transformation. From this, the inverse model can be derived consisting of an algebraic part for the desired system outputand internal dynamics driven by the desired output trajectory y d ,

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Analysis of Feed-Forward Control Design Approaches for Flexible Multibody Systems

Cited by 8 publications

References 13 publications

Analysis of servo-constraint problems for underactuated multibody systems

Analysis of servo-constraint problems for underactuated multibody systems

Inverse dynamics of serial and parallel underactuated multibody systems using a DAE optimal control approach

End‐Effector Trajectory Tracking of Serial Flexible Manipulators

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