Nonlinear Active Cancellation of the Parametric Resonance in a Magnetically Levitated Body

2004 ◽  
Vol 126 (3) ◽  
pp. 433-442 ◽  
Author(s):  
Hiroshi Yabuno ◽  
Ryo Kanda ◽  
Walter Lacarbonara ◽  
Nobuharu Aoshima
Keyword(s):  
Parametric Resonance ◽  
Degrees Of Freedom ◽  
Control Method ◽  
Inertial Force ◽  
Phase Lock Loop ◽  
Vibration Absorber ◽  
Control Input ◽  
Main System ◽  
Magnetically Levitated ◽  
Active Control Strategy

An active control strategy for the stabilization of parametric resonance in a magnetically levitated body is proposed. The characteristic feature of the strategy is the exploitation of the nonlinear effect of the inertial force associated with the motion of a pendulum-type vibration absorber driven by an appropriate control torque. As a distinguished feature, the proposed control method does not rely on the effective autoparametric energy transfer between the main system and the absorber. Because the main system is not linearly coupled with the absorber, the drawback inherent in the increase of the system degrees of freedom (i.e., the increase of the linear vibrational mode for the main system due to the attachment of the absorber) is overcome. The effective frequency and amplitude of the pure-tone control input—the torque driving the vibration absorber—are designed so that the nonlinear action of the pendulum on the main system counteracts the effect of the resonant parametric excitation. The effectiveness of the theoretically proposed control method is experimentally validated using an apparatus that comprises a phase-lock loop system.

Design and Realtime Implementation of an Adaptive Variation Absorber for Uncertain Mechanical Systems Subjected to Unknown Disturbances

2004 ◽  
Vol 10 (1) ◽  
pp. 55-84
Author(s):  
Raffi Derkhorenian ◽  
Nader Jalili ◽  
D M Dawson
Keyword(s):  
Degrees Of Freedom ◽  
Controller Design ◽  
Linear Time ◽  
Vibration Absorber ◽  
Primary System ◽  
Control Input ◽  
Adaptation Algorithm ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output

In this paper we describe the design and implementation of a nonlinear adaptive disturbance rejection approach for single-input-single-output linear-time-invariant uncertain systems subject to sinusoidal disturbances with unknown amplitude and frequency. This is an extension of our earlier study to a more complicated plant, a two-degrees-of-freedom (2DOF) system representing a vibration absorber setting. The controller design is based on a single Lyapunov function incorporating both the error states and the update laws and, hence, global stability and improved transient performance are readily achieved. Utilizing only the system output, a virtual control input is used in place of non-measurable and unknown signals. The performance of the adaptation algorithm is demonstrated through real-time simulations, both for regulation and tracking, on a 2DOF system representing an active vibration absorber setup. It is shown that when the primary system is subjected to an unknown sinusoidal disturbance, the proposed controller in the absorber subsection completely suppresses the primary system vibration in the presence of unknown disturbance.

State Dependent Riccati Equation (SDRE) Control Method Applied in Cancellation of a Parametric Resonance in a Magnetically Levitated Body

2011 ◽  
Author(s):  
Fa´bio Roberto Chavarette ◽  
Jose´ Manoel Balthazar ◽  
Ce´lia Aparecida dos Reis ◽  
Nelson Jose´ Peruzzi
Keyword(s):  
Riccati Equation ◽  
Control Method ◽  
Equations Of Motion ◽  
Control Design ◽  
Inertial Force ◽  
The Body ◽  
State Dependent ◽  
Oscillatory Movement ◽  
Magnetically Levitated ◽  
Static Equilibrium State

Here, a simplified dynamical model of a magnetically levitated body is considered. The origin of an inertial Cartesian reference frame is set at the pivot point of the pendulum on the levitated body in its static equilibrium state (ie, the gap between the magnet on the base and the magnet on the body, in this state). The governing equations of motion has been derived and the characteristic feature of the strategy is the exploitation of the nonlinear effect of the inertial force associated, with the motion of a pendulum-type vibration absorber driven, by an appropriate control torque [4]. In the present paper, we analyzed the nonlinear dynamics of problem, discussed the energy transfer between the main system and the pendulum in time, and developed State Dependent Riccati Equation (SDRE) control design to reducing the unstable oscillatory movement of the magnetically levitated body to a stable fixed point. The simulations results showed the effectiveness of the (SDRE) control design.

Chattering-free sliding modes in robotic manipulators control

Robotica ◽  
1996 ◽  
Vol 14 (1) ◽  
pp. 17-29 ◽  
Author(s):  
Asif Šabanović ◽  
Karel Jezernik ◽  
Kenzo Wada
Keyword(s):  
Degrees Of Freedom ◽  
Control Method ◽  
Sliding Mode ◽  
Impedance Control ◽  
Robotic Manipulators ◽  
Explicit Calculation ◽  
Control Input ◽  
Mathematical Form ◽  
Sliding Modes ◽  
Variable Structure Systems

SummaryIn this paper sliding mode motion design is considered for nonlinear plants which are linear with respect to control input. The dynamics of the robotic manipulators is treated with and without those of the actuators. When the dynamics of the actuators is included a design of the sliding modes for the systems with discontinuous control is performed. If actuators' dynamics is negelected the control is assumed to be continuous quantity. By combining the variable structure systems and Lyapunov designs a new algorithm is developed which has all the good properties of the sliding mode systems while avoiding unnecessary discontinuity of the control thus eliminating chattering. Neither the explicit calculation of the equivalent control, nor high gain inside the boundary layer are used. The parameters of the control depend on the plant's gain matrix, and the gradients of the sliding mode manifold. This control method is then applied to develop a unified control strategy for the motion control systems including the path tracking control, the impedance control and the force control of a robotic manipulator. It is shown that all these tasks can be formulated in the same mathematical form in which selected so-called sliding mode functions must track their references. In this way the systems state is forced to remain on the selected manifold in the state space after reaching it. The solution is interpreted in both the Joint space and the Work space for n -degrees of freedom robotic manipulators.

scholarly journals A 4-DOF Upper Limb Exoskeleton for Physical Assistance: Design, Modeling, Control and Performance Evaluation

2021 ◽  
Vol 11 (13) ◽  
pp. 5865
Author(s):  
Muhammad Ahsan Gull ◽  
Mikkel Thoegersen ◽  
Stefan Hein Bengtson ◽  
Mostafa Mohammadi ◽  
Lotte N. S. Andreasen Struijk ◽  
...  
Keyword(s):  
Upper Limb ◽  
Tracking Control ◽  
Degrees Of Freedom ◽  
Control Method ◽  
Mechanical Design ◽  
Trajectory Tracking Control ◽  
Upper Limb Exoskeleton ◽  
And Performance ◽  
Physically Disabled People ◽  
Human Upper Limb

Wheelchair mounted upper limb exoskeletons offer an alternative way to support disabled individuals in their activities of daily living (ADL). Key challenges in exoskeleton technology include innovative mechanical design and implementation of a control method that can assure a safe and comfortable interaction between the human upper limb and exoskeleton. In this article, we present a mechanical design of a four degrees of freedom (DOF) wheelchair mounted upper limb exoskeleton. The design takes advantage of non-backdrivable mechanism that can hold the output position without energy consumption and provide assistance to the completely paralyzed users. Moreover, a PD-based trajectory tracking control is implemented to enhance the performance of human exoskeleton system for two different tasks. Preliminary results are provided to show the effectiveness and reliability of using the proposed design for physically disabled people.

scholarly journals Torque Ripple Suppression of PMSM Based on Robust Two Degrees-of-Freedom Resonant Controller

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 1015
Author(s):  
Mingfei Huang ◽  
Yongting Deng ◽  
Hongwen Li ◽  
Jing Liu ◽  
Meng Shao ◽  
...  
Keyword(s):  
Control Strategy ◽  
Measurement Errors ◽  
Degrees Of Freedom ◽  
Control Method ◽  
Torque Ripple ◽  
Current Loop ◽  
Two Degrees Of Freedom ◽  
Robust Stability Analysis ◽  
Resonant Controller ◽  
Testing Environments

This paper concentrates on a robust resonant control strategy of a permanent magnet synchronous motor (PMSM) for electric drivers with model uncertainties and external disturbances to improve the control performance of the current loop. Firstly, to reduce the torque ripple of PMSM, the resonant controller with fractional order (FO) calculus is introduced. Then, a robust two degrees-of-freedom (Robust-TDOF) control strategy was designed based on the modified resonant controller. Finally, by combining the two control methods, this study proposes an enhanced Robust-TDOF regulation method, named as the robust two degrees-of-freedom resonant controller (Robust-TDOFR), to guarantee the robustness of model uncertainty and to further improve the performance with minimized periodic torque ripples. Meanwhile, a tuning method was constructed followed by stability and robust stability analysis. Furthermore, the proposed Robust-TDOFR control method was applied in the current loop of a PMSM to suppress the periodic current harmonics caused by non-ideal factors of inverter and current measurement errors. Finally, simulations and experiments were performed to validate our control strategy. The simulation and experimental results showed that the THDs (total harmonic distortion) of phase current decreased to a level of 0.69% and 5.79% in the two testing environments.

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.

Parametric Resonance of a Two Degrees-of-Freedom System Induced by Bounded Noise

2009 ◽  
Vol 76 (4) ◽  
Author(s):  
Jinyu Zhu ◽  
W.-C. Xie ◽  
Ronald M. C. So ◽  
X. Q. Wang
Keyword(s):  
Lyapunov Exponents ◽  
Parametric Resonance ◽  
Degrees Of Freedom ◽  
Singular Perturbation Method ◽  
Bounded Noise ◽  
Two Degrees Of Freedom ◽  
Moment Lyapunov Exponent ◽  
The Moment ◽  
Combined Resonance ◽  
Moment Lyapunov Exponents

The dynamic stability of a two degrees-of-freedom system under bounded noise excitation with a narrowband characteristic is studied through the determination of moment Lyapunov exponents. The partial differential eigenvalue problem governing the moment Lyapunov exponent is established. For weak noise excitations, a singular perturbation method is employed to obtain second-order expansions of the moment Lyapunov exponents and Lyapunov exponents, which are shown to be in good agreement with those obtained using Monte Carlo simulation. The different cases when the system is in subharmonic resonance, combination additive resonance, and combined resonance in the absence of noise, respectively, are considered. The effects of noise and frequency detuning on the parametric resonance are investigated.

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