Nonlinear optimal control of a triple link inverted pendulum with single control input

Eltohamy, Khaled Gamal; Kuo, Chen-Yuan

doi:10.1080/002071798222811

Cited by 49 publications

(25 citation statements)

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“…By optimizing control sequence U = [u(k), u(k + 1), · · · , u(k + n − 1)], desired state can be obtained together with n sets of [x T (k), u(k)]. Thus, the mapping from x(k) to u(k) can be established as equation 3.…”

Section: Inverse Mapping Modelmentioning

confidence: 98%

“…Equation 3 indicates in essence that there exists an input sequence x(k), which is given by and can produce u(k). Now the problem is how to find g, namely the controller.…”

Section: Inverse Mapping Modelmentioning

confidence: 99%

“…There are many ways to stabilize the pendulum locally at present, such as feedback stabilization [3], fuzzy logic control [4], sliding mode control [5], etc.…”

Section: Introductionmentioning

confidence: 99%

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Swing-Up Control of Double Inverted Pendulum Based on Adaptive Neuro-fuzzy Inference System

Yao

Chai

2007

Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007)

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Neuro-fuzzy controller based on Adaptive Neuro-FuzzyInference System (ANFIS) is proposed for swinging up a double pendulum from its hanging position to the inverted position. The controller is designed through two stages. In learning stage, the controller, which is an inverse mapping model from state variable to controlled quantity, is constructed off-line. While in control stage, control output is derived from the built model. To obtain training samples for inverse mapping model, hybrid genetic algorithms are applied to optimize computation of state variables and control law during the swing-up. Simulation results showed the effectiveness of the controller and the theoretical discussions.

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Section: Inverse Mapping Modelmentioning

confidence: 98%

“…Equation 3 indicates in essence that there exists an input sequence x(k), which is given by and can produce u(k). Now the problem is how to find g, namely the controller.…”

Section: Inverse Mapping Modelmentioning

confidence: 99%

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Swing-Up Control of Double Inverted Pendulum Based on Adaptive Neuro-fuzzy Inference System

Yao

Chai

2007

Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007)

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“…, c 10 of the cubic basis functions are additional degrees of freedom for the construction of the functionα = Φ(t, p). 4 (iii) In order to account for the input constraints (15), it is required to check if the resulting feedforward control…”

Section: A Bvps For Constrained Inputmentioning

confidence: 99%

“…The control task of stabilizing the pendulum in the upward position has been studied e.g. in [13], [4], [19]. Besides the stabilization aspect, the side-stepping maneuver, i.e.…”

Section: Introductionmentioning

confidence: 99%

Fast Side-Stepping of the Triple Inverted Pendulum via Constrained Nonlinear Feedforward Control Design

Graichen

Treuer

Zeitz

Proceedings of the 44th IEEE Conference on Decision and Control

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Abstract-The side-stepping of the triple inverted pendulum serves as a benchmark problem for the presentation of a new feedforward control design technique for finite-time transition problems under consideration of output constraints. The inversion-based design treats the transition task as a twopoint boundary value problem (BVP) defined in the inputoutput coordinates of the pendulum. As a necessary condition for its solvability, a sufficient number of free parameters is provided in a set-up function for the cart acceleration. The new approach allows to directly incorporate output constraints of the pendulum within the BVP, which is solved by a standard MATLAB function. A linear LQR controller is used to stabilize the pendulum along the feedforward side-stepping trajectories. Experimental results for the triple inverted pendulum illustrate the accuracy and robustness of the proposed feedforward/feedback control scheme.

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A Triple Inverted Pendulum Control-system Design

Robust Control Design With MATLAB®

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Nonlinear optimal control of a triple link inverted pendulum with single control input

Cited by 49 publications

References 0 publications

Swing-Up Control of Double Inverted Pendulum Based on Adaptive Neuro-fuzzy Inference System

Swing-Up Control of Double Inverted Pendulum Based on Adaptive Neuro-fuzzy Inference System

Fast Side-Stepping of the Triple Inverted Pendulum via Constrained Nonlinear Feedforward Control Design

A Triple Inverted Pendulum Control-system Design

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