Energy-based Hamiltonian approach in H∞ controller design for n-degree of freedom mechanical systems

Karimi, M.; Binazadeh, Tahereh

doi:10.1080/21642583.2019.1649216

Cited by 3 publications

(4 citation statements)

References 29 publications

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“…Consider the following dynamical equations, which represent the motion equations of n-degree-offreedom mechanical systems: 29,35,36…”

Section: Problem Statementmentioning

confidence: 99%

“…28 Generally, this technique uses properties of the internal structure of the actual system in designing controllers and gives a relatively simpler controller with better performance. 29 To the best knowledge of the authors, this is the first paper that robustly studies this issue based on the PCH model of multi-input mechanical systems. For this purpose, designing control law is done in two steps.…”

Section: Introductionmentioning

confidence: 99%

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Robust Stable Limit Cycle Generation in Multi-Input Mechanical Systems

Binazadeh

Karimi

2021

Robotica

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SUMMARY This paper proposes a robust controller for the generation of stable limit cycles in multi-input mechanical systems subjected to model uncertainties. The proposed idea is based on Port-Controlled Hamiltonian (PCH) model and energy-based control by considering the Hamiltonian function as the Lyapunov function. For this purpose, first, a nominal controller is designed by shaping the energy function of the system according to the structure of the desired limit cycle. Then, an additional robustifying control term is designed based on the integral sliding mode method with the selection of an appropriate sliding surface. Finally, computer simulations for two practical case studies are provided to confirm the effectiveness of the proposed controller in the generation of stable limit cycles in the presence of uncertainties.

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“…Consider the following dynamical equations, which represent the motion equations of n-degree-offreedom mechanical systems: 29,35,36…”

Section: Problem Statementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Stable Limit Cycle Generation in Multi-Input Mechanical Systems

Binazadeh

Karimi

2021

Robotica

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“…There is a wide literature about energy-based analysis and design, energy-based analysis and control design and analysis and control of Port-Hamiltonian systems(see for instance (Meigooni & Mollaioli, 2021), (Guerrero et al, 2019) and (Karimi & Binazadeh, 2019), respectively). The present work focus on BG analysis and control design, due to BG allows to analyze the structure of the system, obtain symbolic equations and analyze the energy interactions.…”

Section: Introductionmentioning

confidence: 99%

Passivity analysis and control of nonlinear systems modelled by bond graphs

Galindo

Ngwompo

2022

International Journal of Control

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Recent results on the passivity analysis and control of physical systems, based on the balance of dissipated and internally generated energy, are generalized to nonlinear systems represented by bond graphs. For linear systems, the internally generated energy associated with modulated sources can be coupled with the dissipative field, so that if external energy sources are excluded, then the system is passive (or dissipative) if the resulting composite multiport field is passive. Such a result for linear systems was previously conveniently expressed in terms of a characteristic matrix being positive semi-definite. Parasitic elements of previous works are no longer required, which allows working on the original bond graph of lower dimension than the augmented bond graph and for no-linear systems avoid inverting the dissipative non-linear constitutive relations. For nonlinear systems, passivity is now considered through the explicit difference between the dissipated and the internally generated energy. If this energy difference is positive the system is passive. For control systems, the current work proposes that the controller is designed to have a structure similar to the plant (linear or nonlinear) and its parameters are chosen to assure that in closed-loop the difference between the dissipated and the internally generated energy is positive. In particular, the control parameters can be chosen to assign a desired dissipated energy or to cancel by feedback the internally generated energy and to add damping, therefore achieving sufficient condition for the passivity of the closed-loop system.

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“…Studies of underactuated systems have attracted the attention of many researchers since the 1990s because of their wide application field such as robotics industries. [1][2][3] In underactuated systems, there is less number of control inputs than the degrees of freedom of the system. 4 Therefore, they are economical in weight and cost with respect to other systems; however, due to their complex nonlinear dynamics and nonholonomic behavior, conventional control methods may not be applied to these systems directly.…”

Section: Introductionmentioning

confidence: 99%

A Robust Approach to Stabilization of 2-DOF Underactuated Mechanical Systems

Aminsafaee¹,

Shafiei²

2020

Robotica

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SUMMARY This paper studies the stabilization problem for a class of underactuated systems in the presence of unknown disturbances. Due to less number of control inputs with respect to the degrees of freedom of the system, closed-loop asymptotic stability is a challenging issue in this field. In this paper, anti-swing controllers are designed for nominal and disturbed systems. In the case of the nominal system, the proposed two-loop controller is a combination of collocated partial feedback linearization and hierarchical sliding mode control (HSMC) theories. Then, due to the importance of robustness in control of physical systems, the proposed controller is developed for underactuated mechanical systems in the presence of additive disturbances. One of the main advantages of the proposed design method is that it does not need any switching algorithm. Finally, to illustrate the performance of the proposed controllers, they are applied to two underactuated mechanical systems: a pendubot and a Furuta pendulum. In addition, the practicality of the proposed approach is also verified experimentally using a quadrotor stand.

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Energy-based Hamiltonian approach in H_∞ controller design for n-degree of freedom mechanical systems

Cited by 3 publications

References 29 publications

Robust Stable Limit Cycle Generation in Multi-Input Mechanical Systems

Robust Stable Limit Cycle Generation in Multi-Input Mechanical Systems

Passivity analysis and control of nonlinear systems modelled by bond graphs

A Robust Approach to Stabilization of 2-DOF Underactuated Mechanical Systems

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