arXiv subjects

M. Reza J. Harandi

Publications and source records attributed to M. Reza J. Harandi.

10 recordsLinked to original sources

arXiv2026

Matched Disturbance Rejection for Port-Hamiltonian Systems with Coupled Dynamics

This paper investigates the rejection of matched disturbances generated by coupled port-Hamiltonian (PH) dynamics in previously stabilized PH systems. The disturbance dynamics are incorporated into a unified PH representation, allowing the disturbance to affect the plant through both the matched input channel and an interconnection structure. Unlike existing results that typically impose restrictive structures on the disturbance dynamics, the proposed framework accommodates a more general class of coupled PH disturbances, including nonzero interconnection and damping terms. A baseline disturbance rejection scheme is first established for known disturbance storage parameters. The framework is then extended to the case of an unknown symmetric storage matrix through online parameter estimation. Two control designs are developed under different structural conditions, with the latter relaxing the dimensional restriction imposed by the first design. The proposed methods guarantee asymptotic convergence of the plant state to the desired equilibrium, while preserving a port-Hamiltonian representation of the closed-loop dynamics under the corresponding conditions. The results generalize existing disturbance rejection approaches and broaden their applicability to coupled PH disturbance models.

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arXiv2026

Reduction of Velocity-Dependent Terms in Total Energy Shaping Approach

Total energy shaping through interconnection and damping assignment passivity-based control (IDA-PBC) provides a powerful and systematic framework for stabilizing underactuated mechanical systems. Despite its theoretical appeal, incorporating actuator limitations into total energy shaping remains a largely open problem, with only limited results reported in the existing literature. In practice, the closed-loop behavior of energy-shaping controllers is strongly affected by the kinetic energy shaping terms. In this paper, a simultaneous IDA-PBC (SIDA-PBC) framework is employed to systematically attenuate the kinetic energy shaping terms by exploiting generalized forces, without altering the matching partial differential equations (PDEs). The free component of the generalized forces is derived analytically via an $\ell_\infty$-norm optimization formulation. Although a reduction in kinetic energy shaping terms does not necessarily guarantee a decrease in the overall control effort, the proposed approach effectively suppresses kinetic energy shaping components and achieves a reduced control magnitude whenever such a reduction is structurally feasible. Unlike existing approaches based on gyroscopic terms, which require multiple actuators, the proposed method is applicable to mechanical systems with a single actuator. Simulation and experimental results are provided to validate the effectiveness of the proposed approach.

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arXiv2026

Robust Energy Shaping Control of an Underactuated Inverted Pendulum

Although the stabilization of underactuated systems remains a challenging problem, the total energy shaping approach provides a general framework for addressing this objective. However, the practical implementation of this method is hindered by the need to analytically solve a set of partial differential equations (PDEs), which constitutes a major obstacle. In this paper, a rotary inverted pendulum system is considered, and an interconnection and damping assignment passivity-based control (IDA-PBC) scheme is developed by deriving concise analytical solutions to the kinetic and potential energy PDEs. Furthermore, a novel robust term is incorporated into the control law to compensate for a specific class of disturbances that has not been addressed within the existing IDA-PBC literature. The effectiveness of the proposed method is validated through numerical simulations, demonstrating satisfactory control performance.

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arXiv2024

Stabilization of a Quadrotor via Energy Shaping

Stabilization of a quadrotor without a controller based on cascade structure is a challenging problem. Besides, due to the dynamics and the number of underactuation, an energy shaping controller has not been designed in 3D for a quadrotor. This paper presents a novel solution to the potential energy shaping problem for a quadrotor utilizing the Interconnection and Damping Assignment Passivity Based Control (IDA-PBC) approach. For the first time, we extend the solution of PDEs from the 2D case to the full 3D scenario. This advancement seems to be a significant step forward for stabilization of underactuated aerial vehicles without a cascade controller. The results are verified via simulation on a typical quadrotor.

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arXiv2022

On the Controllers Based on Time Delay Estimation for Robotic Manipulators

Assurance of asymptotic trajectory tracking in robotic manipulators with a smooth control law in the presence of unmodeled dynamics or external disturbance is a challenging problem. Recently, it is asserted that it is achieved via a rigorous proof by designing a traditional model-free controller together with time delay estimation (TDE) such that neither dynamical parameters nor conservative assumptions on external disturbance are required. The purpose of this note is to show that this claim is not true and the stability proof of the method is incorrect. Finally, some modified versions of this controller with rigorous proof is presented for robotic manipulators.

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arXiv2022

Solution of matching equations of IDA-PBC by Pfaffian differential equations

Finding the general solution of partial differential equations (PDEs) is essential for controller design in newly developed methods. Interconnection and damping assignment passivity based control (IDA-PBC) is one of such methods in which the solution to corresponding PDEs which are called matching equations, is needed to apply it in practice. In this paper, these matching equations are transformed to corresponding Pfaffian differential equations. Furthermore, it is shown that upon satisfaction of the integrability condition, the solution to the corresponding third-order Pfaffian differential equation may be obtained quite easily. The method is applied to the PDEs of IDA-PBC in some benchmark systems such as Magnetic levitation system, Pendubot, and underactuated cable driven robot to verify its applicability.

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arXiv2021

Reformulation of Matching Equation in Potential Energy Shaping

Stabilization of an underactuated mechanical system may be accomplished by energy shaping. Interconnection and damping assignment passivity-based control is an approach based on total energy shaping by assigning desired kinetic and potential energy to the system. This method requires solving a partial differential equation (PDE) related to he potential energy shaping of the system. In this short paper, we focus on the reformulation of this PDE to be solved easier. For this purpose, under a certain condition that depends on the physical parameters and the controller gains, it is possible to merely solve the homogeneous part of potential energy PDE. Furthermore, it is shown that the condition may be reduced into a linear matrix inequality form. The results are applied to a number of benchmark systems.

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arXiv2021

On the Matching Equations of Kinetic Energy Shaping in IDA-PBC

Interconnection and damping assignment passivity-based control scheme has been used to stabilize many physical systems such as underactuated mechanical systems through total energy shaping. In this method, some partial differential equations (PDEs) arisen by kinetic and potential energy shaping, shall be solved analytically. Finding a suitable desired inertia matrix as the solution of nonlinear PDEs related to kinetic energy shaping is a challenging problem. In this paper, a systematic approach to solve this matching equation for systems with one degree of underactuation is proposed. A special structure for desired inertia matrix is proposed to simplify the solution of the corresponding PDE. It is shown that the proposed method is more general than that of some reported methods in the literature. In order to derive a suitable desired inertia matrix, a necessary condition is also derived. The proposed method is applied to three examples, including VTOL aircraft, pendubot and 2D SpiderCrane system.

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arXiv2021

Bounded Inputs Total Energy Shaping for Mechanical Systems

Designing control systems with bounded input is a practical consideration since realizable physical systems are limited by the saturation of actuators. The actuators' saturation degrades the performance of the control system, and in extreme cases, the stability of the closed-loop system may be lost. However, actuator saturation is typically neglected in the design of control systems, with compensation being made in the form of over-designing the actuator or by post-analyzing the resulting system to ensure acceptable performance. The bounded input control of fully actuated systems has been investigated in multiple studies, but it is not generalized for under actuated mechanical systems. This article proposes a systematic framework for finding the upper bound of control effort in underactuated systems, based on interconnection and the damping assignment passivity based control (IDA-PBC) approach. The proposed method also offers design variables for the control law to be tuned, considering the actuator's limit. The major difficulty in finding the control input upper bounds is the velocity dependent kinetic energy related terms. Thus, the upper bound of velocity is computed using a suitable Lyapunov candidate as a function of closed-loop system parameters. The validity and application of the proposed method are investigated in detail through two benchmark systems.

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arXiv2020

Adaptive motion control of parallel robots with kinematic and dynamic uncertainties

One of the most challenging issues in adaptive control of robot manipulators with kinematic uncertainties is requirement of the inverse of Jacobian matrix in regressor form. This requirement is inevitable in the case of the control of parallel robots, whose dynamic equations are written directly in the task space. In this paper, an adaptive controller is designed for parallel robots based on representation of Jacobian matrix in regressor form, such that asymptotic trajectory tracking is ensured. The main idea is separation of determinant and adjugate of Jacobian matrix and then organize new regressor forms. Simulation and experimental results on a 2--DOF R\underline{P}R and 3--DOF redundant cable driven robot, verify promising performance of the proposed methods.

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