Modelling and robust stabilisation of a closed-link 2-dof inverted pendulum with gain scheduled control

Ishii, Chiharu; Nishitani, Yosuke; Hashimoto, Hiroshi

doi:10.1504/ijmic.2009.024739

Cited by 4 publications

(12 citation statements)

References 14 publications

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“…Unlike many studies [9,10] in which the rotational axes are parallel to each other and the rotational motion occurs on a single plane, the spatial inverted pendulum is designed so that two rotational axes are orthogonal to each other and the pendulum is prevented from rotating around its own axis and can easily tilt over any direction in 3D space. Spatial inverted pendulum systems are classified in three basic groups depending on the mechanism used to stabilize the pendulum [11]. The studies of Soto [12] and Ishii [11] can also be added in these three categories as a fourth type.…”

Section: Introductionmentioning

confidence: 99%

“…Spatial inverted pendulum systems are classified in three basic groups depending on the mechanism used to stabilize the pendulum [11]. The studies of Soto [12] and Ishii [11] can also be added in these three categories as a fourth type. The first type among this classification is a system where a spatial inverted pendulum connected to the X-Y table is controlled by applying linear motions in x and y directions in horizontal plane parallel to the ground [13].…”

Section: Introductionmentioning

confidence: 99%

“…In the fourth type, a spatial inverted pendulum is mounted on a five-bar planar mechanism highly studied in the literature. In these systems, the pendulum is controlled by the motion generated through a mechanism with two rotational inputs [11,12].…”

Section: Introductionmentioning

confidence: 99%

“…There are only a few studies in literature on the spatial inverted pendulum actuated five bar mechanism. The researchers designed the controllers for the stabilization of the pendulum based on H ∞ robust control method and the linear quadratic regulator over the linearized model respectively [11,12].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Design and control of spatial inverted pendulum with two degrees of freedom

Bayram

Kara

2020

J Braz. Soc. Mech. Sci. Eng.

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The inverted pendulum systems have inherently unstable dynamics. In order to stabilize the inverted pendulum at upright position, an actuation mechanism should generate fast-reactive motions at the pivot point of the system. This paper addressed the design and control of a spatial inverted pendulum with two degrees of freedom (DOF). The first part of the study consists of designing a novel planar two-DOF (PRRRR) actuation mechanism in order to balance the spatial inverted pendulum. The system is underactuated and has inherently extreme nonlinearity and also the restrictions on the actuators. Then, in the second part, a second-order sliding-mode and a linear quadratic Gaussian (LQG) controller have been proposed to control the pendulum within the equilibrium position. Finally the simulation results evaluated in terms of the robustness, time response and stability show that the second-order sliding-mode controller is more robust and has fast response performances in re-stabilizing the spatial inverted pendulum, while LQG controller is better in terms of keeping the system in equilibrium during the long period of time. Keywords Two degrees of freedom inverted pendulum • Spatial inverted pendulum • Sliding-mode control • Linear quadratic Gaussian * Atilla Bayram

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Design and control of spatial inverted pendulum with two degrees of freedom

Bayram

Kara

2020

J Braz. Soc. Mech. Sci. Eng.

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“…In addition, there are a large number of uncertainty descriptions from robust control theory such as parametric uncertainty sets (Bhattacharyya et al, 1995), real parametric uncertainties (Zhou and Doyle, 1998;Vinnicombe, 2000), H ∞ norm bounded additive or multiplicative uncertainty on the plant model and uncertainties bounded in the gap metric or v-gap metric. Both in the robustness analysis and in the robust synthesis problems, the choice for an appropriate model uncertainty structure is important (Ishii et al, 2009). Nevertheless, there are no arguments favouring one structure over another.…”

Section: Introductionmentioning

confidence: 99%

Improved intelligent identification of uncertainty bounds: design, model validation and stability analysis

Akmeliawati

Raafat

Martono

2012

IJMIC

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Identification of uncertainty bounds in robust control design is known to be a critical issue that attracts the attention of research in robust control field recently. Nevertheless, the practical implementation involves a trial and error procedure, which depends on the designer prior knowledge and the available information about the system under study. Artificial intelligent techniques provide a suitable solution to such a problem. In this paper a new intelligent identification method of uncertainty bound using an adaptive neuro-fuzzy inference system (ANFIS) in an enhanced feedback scheme is proposed. The proposed ANFIS structure enables accurate determination of the uncertainty bounds and guarantees robust stability and performance. In our proposed technique, the validation of the intelligent identified uncertainty weighting function is based on the measurement of both the v-gap metric and the stability margin that result from the corresponding robust controller design. Additionally, these two indices are used to improve the accuracy of the intelligent estimation of uncertainty bound in conjunction with the robust control design requirements. The enhanced intelligent identification of uncertainty bound is demonstrated on a servo positioning system. Simulation and experimental results prove the validity of the applied approach; more reliable and highly efficient estimation of the uncertainty weighting function for robust controller design.

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Modelling and control of a spherical pendulum via a non–minimal state representation

Campa

Soto

Martínez

2021

Mathematical and Computer Modelling of Dynamical Systems

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A spherical pendulum is a 2 degree-of-freedom mechanism consisting on a rod whose tip moves on the surface of a sphere. It is common to use two angular coordinates to describe such a system. This paper proposes the use of a non-minimal set of coordinates for modelling and controlling a fully-actuated torque-driven spherical pendulum. These coordinates is merely for the purpose of showing the application of unit quaternions as a useful tool for dealing with the orientation of rigid bodies. First, we recall the properties of unit quaternions, and explain how they can be employed for the definition of such non-minimal pendulum coordinates. Later, the control objective for orientation regulation is established and an inversedynamics controller, which uses joint displacement and velocity measurements but also some non-minimal states for the orientation error, is proposed. The stability analysis shows the fulfilment of the control objective and is validated through simulations.

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Modelling and robust stabilisation of a closed-link 2-dof inverted pendulum with gain scheduled control

Cited by 4 publications

References 14 publications

Design and control of spatial inverted pendulum with two degrees of freedom

Design and control of spatial inverted pendulum with two degrees of freedom

Improved intelligent identification of uncertainty bounds: design, model validation and stability analysis

Modelling and control of a spherical pendulum via a non–minimal state representation

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