Stabilization of Internal Dynamics of Underactuated Systems by Periodic Servo-Constraints

2017 ◽  
Vol 17 (05) ◽  
pp. 1740004 ◽  
Author(s):  
László Bencsik ◽  
László L. Kovács ◽  
Ambrus Zelei
Keyword(s):  
Stability Analysis ◽  
Dynamic Behavior ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Underactuated Mechanical Systems ◽  
Algorithmic Approach ◽  
Servo Constraints ◽  
And Control ◽  
Dependent Coordinates

The model-based motion control of underactuated, multiple degree-of-freedom, complex multibody systems is in focus. Underactuated mechanical systems possess less number of independent control inputs than degrees-of-freedom. The main difficulty in their control is caused by the dynamics of the uncontrolled part of the system. The complexity of multibody systems makes the dynamical and control formulation difficult. The direct application of traditional control techniques available in the literature can lead to unstable dynamic behavior in many cases. In order to avoid instability, these general methods are usually adapted for specific problems in an intuitive way. Here, we present a direct, more algorithmic approach, and propose the use of periodic servo-constraints to overcome stability problems and enhance the dynamic behavior. An exact, stability analysis-based method is also proposed for tuning the control parameters. A stability analysis procedure is developed which is directly applicable for investigating the dynamics of mechanical systems described by dependent coordinates and mathematically formulated as a set of algebraic differential equations.

scholarly journals Analysis of servo-constraint problems for underactuated multibody systems

2013 ◽  
Vol 4 (1) ◽  
pp. 113-129 ◽  
Author(s):  
R. Seifried ◽  
W. Blajer
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Feedforward Control ◽  
Underactuated Mechanical Systems ◽  
Trajectory Tracking Control ◽  
Model Inversion ◽  
Flat Systems ◽  
First Results ◽  
Servo Constraints ◽  
Constraint Approach

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.

scholarly journals MATLAB-based Tools for Modelling and Control of Underactuated Mechanical Systems

2020 ◽  
Vol 6 (3) ◽  
Author(s):  
Slávka Jadlovská ◽  
Lukáš Koska ◽  
Matej Kentoš
Keyword(s):  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Underactuated Systems ◽  
Underactuated Mechanical Systems ◽  
Software Support ◽  
Nonlinear Mechanical ◽  
Inertia Wheel Pendulum ◽  
Nonlinear Mechanical Systems ◽  
And Control ◽  
Insight Into

Underactuated systems, defined as nonlinear mechanical systems with fewer control inputs than degrees of freedom, appear in a broad range of applications including robotics, aerospace, marine and locomotive systems. Studying the complex low-order nonlinear dynamics of appropriate benchmark underactuated systems often enables us to gain insight into the principles of modelling and control of advanced, higher-order underactuated systems. Such benchmarks include the Acrobot, Pendubot and the reaction (inertia) wheel pendulum. The aim of this paper is to introduce novel MATLAB-based tools which were developed to provide complex software support for modelling and control of these three benchmark systems. The presented tools include a Simulink block library, a set of demo simulation schemes and several innovative functions for mathematical and simulation model generation.

scholarly journals Observer-based robust integral of the sign of the error control of class I of underactuated mechanical systems: Theory and real-time experiments

2021 ◽  
pp. 014233122110313
Author(s):  
Afef Hfaiedh ◽  
Ahmed Chemori ◽  
Afef Abdelkrim
Keyword(s):  
Real Time ◽  
Error Control ◽  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Mechanical Systems ◽  
Class I ◽  
Control Input ◽  
Underactuated Mechanical Systems ◽  
Control Scheme ◽  
And Performance

In this paper, the control problem of a class I of underactuated mechanical systems (UMSs) is addressed. The considered class includes nonlinear UMSs with two degrees of freedom and one control input. Firstly, we propose the design of a robust integral of the sign of the error (RISE) control law, adequate for this special class. Based on a change of coordinates, the dynamics is transformed into a strict-feedback (SF) form. A Lyapunov-based technique is then employed to prove the asymptotic stability of the resulting closed-loop system. Numerical simulation results show the robustness and performance of the original RISE toward parametric uncertainties and disturbance rejection. A comparative study with a conventional sliding mode control reveals a significant robustness improvement with the proposed original RISE controller. However, in real-time experiments, the amplification of the measurement noise is a major problem. It has an impact on the behaviour of the motor and reduces the performance of the system. To deal with this issue, we propose to estimate the velocity using the robust Levant differentiator instead of the numerical derivative. Real-time experiments were performed on the testbed of the inertia wheel inverted pendulum to demonstrate the relevance of the proposed observer-based RISE control scheme. The obtained real-time experimental results and the obtained evaluation indices show clearly a better performance of the proposed observer-based RISE approach compared to the sliding mode and the original RISE controllers.

scholarly journals Dynamics and control of a class of underactuated mechanical systems

1999 ◽  
Vol 44 (9) ◽  
pp. 1663-1671 ◽  
Author(s):  
M. Reyhanoglu ◽  
A. van der Schaft ◽  
N.H. Mcclamroch ◽  
I. Kolmanovsky
Keyword(s):  
Mechanical Systems ◽  
Underactuated Mechanical Systems ◽  
Dynamics And Control ◽  
And Control

scholarly journals Vibration Protection of Mechanical Systems Consisting of Solid And Deformable Bodies

2018 ◽  
Vol 3 (9) ◽  
pp. 18
Author(s):  
Ismail Ibrahimovich Safarov ◽  
Teshaev Muhsin Khudoyberdiyevich
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Numerical Results ◽  
Constructive Method ◽  
Vibration Protection ◽  
Deformable Bodies ◽  
Reaction Forces ◽  
Active Vibration ◽  
Servo Constraints

In this  paper active vibration protection of mechanical systems consisting of solid and deformable bodies is considered. To actively control the oscillations of dissipative mechanical systems, a constructive method is used to determine the structure of the reaction forces of servo constraints. As an example, we consider the system with a finite number of degrees of freedom. Numerical results for various harmonic are also given.

scholarly journals The Modeling of Redundantly Actuated Mechanical Systems

2019 ◽  
Vol 11 (6) ◽  
Author(s):  
Yaojun Wang ◽  
Bruno Belzile ◽  
Jorge Angeles ◽  
Qinchuan Li
Keyword(s):  
Degrees Of Freedom ◽  
Screw Theory ◽  
Mechanical Systems ◽  
Coefficient Matrix ◽  
Dynamics Modeling ◽  
Norm Minimization ◽  
Redundantly Actuated ◽  
The Right ◽  
And Control

Abstract Dynamics modeling is essential in the design and control of mechanical systems, the focus of the paper being redundantly actuated systems, which bring about special challenges. The authors resort to the natural orthogonal complement (NOC), based on an adaptation of screw theory, to derive the dynamics model. Benefiting from the elimination of the constraint wrenches, the NOC offers a simple, systematic alternative to the modeling of redundantly actuated mechanical systems. The optimum actuator-torque distribution is determined via Euclidean-norm minimization; then, by relying on the QR-decomposition, an efficient and robust method is produced to compute explicitly the right Moore–Penrose generalized inverse of the coefficient matrix. The methodology is illustrated via a case study involving a redundantly actuated parallel-kinematics machine with three degrees of freedom and four actuators.

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