Evaluation of Linearization Methods for Control of the Pendubot

Parulski, Paweł; Bartkowiak, Patryk; Pazderski, Dariusz

doi:10.3390/app11167615

Cited by 7 publications

(3 citation statements)

References 17 publications

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“…The ideas developed in this sub-chapter are based on several papers which deal with a class of underactuated mechanical systems (Aminsafaee and Shafiei, 2020;Hoang et al, 2020;Lee et al, 2014;Parulski et al, 2021;Spong, 1994;Tuan et al, 2012Tuan et al, , 2013. However, unlike the studies that use the partial feedback linearization to stabilize underactuated mechanical systems, in this work, there is no need to evaluate the internal dynamics (and zero dynamics) of the underactuated system under analysis.…”

Section: Nonlinear Control: Partial Feedback Linearizationmentioning

confidence: 99%

Mathematical modeling and partial feedback linearization control of a constrained and underactuated space tether

Fenili

2022

Journal of Vibration and Control

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This paper investigates the application of the nonlinear control technique called collocated partial feedback linearization to the position and stretching control of a planar underactuated mechanical system. This system is designed to emulate under certain conditions the behavior of a space tether connected to one mass (representing a satellite) at each of its extremities. The flexible cable is approximated by two rigid bodies (thin rods) with springs and dampers attached to represent the cable stiffness and structural damping. The control objective is to move both satellites to its desired positions and to guarantee that on the final configuration the tether is completely stretched. The stability of the closed-loop system is verified and it is proved that the system has global asymptotic stability. The performance of the proposed nonlinear control technique is analyzed via numerical simulations for two cases: one case considering three different values for the damping coefficients and one case considering three different values for the stiffness coefficients. The simulation results show that the collocated partial feedback linearization plus a proportional-derivative control is able to move the satellites to the desired positions and to keep the cable stretched.

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Section: Nonlinear Control: Partial Feedback Linearizationmentioning

confidence: 99%

Mathematical modeling and partial feedback linearization control of a constrained and underactuated space tether

Fenili

2022

Journal of Vibration and Control

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“…In addition to UMS, many types of pendulums are often used in research, such as The Furuta pendulum or rotational inverted pendulum [29] it is a prototype underactuated nonlinear system used as a test bed for various control schemes [30], the inertia-wheel pendulum [31], the acrobat and pendubot [32], and the rotating pendulum [33], the cart pole system [34], the BBS [35], the ball and balancer system [36], the translational oscillator with a rotational actuator TORAsystem [37], and many others. Focusing on control-an observer-based nonlinear robust controller for the BBS has been successfully developed [38].…”

Section: Introductionmentioning

confidence: 99%

Stabilization and tracking control of underactuated ball and beam system using metaheuristic optimization based TID-F and PIDD2–PI control schemes

Zafar,

Malik,

Ali

et al. 2024

PLoS ONE

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In this paper, we propose two different control strategies for the position control of the ball of the ball and beam system (BBS). The first control strategy uses the proportional integral derivative-second derivative with a proportional integrator PIDD2-PI. The second control strategy uses the tilt integral derivative with filter (TID-F). The designed controllers employ two distinct metaheuristic computation techniques: grey wolf optimization (GWO) and whale optimization algorithm (WOA) for the parameter tuning. We evaluated the dynamic and steady-state performance of the proposed control strategies using four performance indices. In addition, to analyze the robustness of proposed control strategies, a comprehensive comparison has been performed with a variety of controllers, including tilt integral-derivative (TID), fractional order proportional integral derivative (FOPID), integral–proportional derivative (I-PD), proportional integral-derivative (PI-D), and proportional integral proportional derivative (PI-PD). By comparing different test cases, including the variation in the parameters of the BBS with disturbance, we examine step response, set point tracking, disturbance rejection analysis, and robustness of proposed control strategies. The comprehensive comparison of results shows that WOA-PIDD2-PI-ISE and GWO-TID-F- ISE perform superior. Moreover, the proposed control strategies yield oscillation-free, stable, and quick response, which confirms the robustness of the proposed control strategies to the disturbance, parameter variation of BBS, and tracking performance. The practical implementation of the proposed controllers can be in the field of under actuated mechanical systems (UMS), robotics and industrial automation. The proposed control strategies are successfully tested in MATLAB simulation.

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“…Although, the linear approximation of the Pendubot at an equilibrium point is controllable, the system is not fully linearizable using state and input transformations. Furthermore, as discussed precisely in [30], there are also significant obstructions in the application of the partial linearization approach, while this method cannot be directly employed for stabilization due to the presence of singular points [31].…”

Section: Introductionmentioning

confidence: 99%

Sub-Optimal Stabilizers of the Pendubot Using Various State Space Representations

et al. 2022

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This paper considers the issue of linear-quadratic regulator (LQR) design for nonlinear systems with the use of smooth state and input transformations. The proposed design methodology is considered in the stabilisation task of the Pendubot, which is based on the concept of feedback equivalent control systems. It turns out that it is possible to find a controller that ensures comparable dynamics of the closed-loop system in the vicinity of the set point regardless of the state-space representation adopted. In addition, the synthesis of suboptimal controllers according to the LQR strategy ensuring equal dynamics at the equilibrium point is presented. The properties of the studied controllers were investigated in a simulation environment and using experimental tests. The detailed forms of transformations and linear approximations given can be regarded as ready-made procedures that can be applied to stabilise similar mechanical systems in robotics.

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Evaluation of Linearization Methods for Control of the Pendubot

Cited by 7 publications

References 17 publications

Mathematical modeling and partial feedback linearization control of a constrained and underactuated space tether

Mathematical modeling and partial feedback linearization control of a constrained and underactuated space tether

Stabilization and tracking control of underactuated ball and beam system using metaheuristic optimization based TID-F and PIDD2–PI control schemes

Sub-Optimal Stabilizers of the Pendubot Using Various State Space Representations

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