Swing-up control of a triple pendulum on a cart with experimental validation

Glück, Tobias; Eder, Alexander; Kugi, Andreas

doi:10.1016/j.automatica.2012.12.006

Cited by 68 publications

(45 citation statements)

References 10 publications

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“…x x x(t) = θ 0 (t)θ 0 (t) θ 1 (t)θ 1 (t) T (11) and the same holds for the vector of desired trajectories…”

Section: Design Of the Control Algorithm For Tracking Desired Trajectmentioning

confidence: 83%

“…An example application of the latter was notably published in [9] and [10] where Graichen et al studied the swing-up manoeuver problem for a double pendulum on the cart-based combined feedforward/feedback control scheme resulting in a two-point boundary value problem (BVP) of the in-ternal dynamics of the system. The BVP solution for the pendulum swing-up for the triple pendulum on the cart was introduced in [11].…”

Section: Introductionmentioning

confidence: 99%

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Inverted Pendulum With Linear Synchronous Motor Swing Up Using Boundary Value Problem

et al. 2019

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Research in the field of underactuated systems shows that control algorithms which take the natural dynamics of the system’s underactuated part into account are more energy-efficient than those utilizing fully-actuated systems. The purpose of this paper to apply the two-degrees-of-freedom (feedforward/feedback) control structure to design a swing-up manoeuver that involves tracking the desired trajectories so as to achieve and maintain the unstable equilibrium position of the pendulum on the cart system. The desired trajectories are obtained by solving the boundary value problem of the internal system dynamics, while the optimal state-feedback controller ensures that the desired trajectory is tracked with minimal deviations. The proposed algorithm is verified on the simulation model of the available laboratory model actuated by a linear synchronous motor, and the resulting program implementation is used to enhance the custom Simulink library Inverted Pendula Modeling and Control, developed by the authors of this paper.

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“…x x x(t) = θ 0 (t)θ 0 (t) θ 1 (t)θ 1 (t) T (11) and the same holds for the vector of desired trajectories…”

Section: Design Of the Control Algorithm For Tracking Desired Trajectmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Inverted Pendulum With Linear Synchronous Motor Swing Up Using Boundary Value Problem

et al. 2019

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show abstract

“…Finally, direct methods are commonly used to discretise the problem, typically by using multiple or single-shooting discretisations [8,9]. The (double) inverted pendulum is a complex multivariable nonlinear system that presents many challenges such as input-output constraints as well as underactuated, unstable and non-minimum phase dynamics [10]. For this reason, it has been used extensively for benchmarking of NMPC, though mostly for simulation works such as [1,3,7], and similar systems such as cranes studied in [6].…”

Section: Introductionmentioning

confidence: 99%

Fast hybrid dual mode NMPC for a parallel double inverted pendulum with experimental validation

González

Rossiter

2020

IET Control Theory & Appl

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This paper presents a novel Fast Nonlinear Model Predictive Control approach for a parallel double inverted pendulum. The approach uses dual mode closed-loop predictions to obtain numerically robust optimal solutions. Moreover, it uses the Real-Time Iteration Scheme to reduce the computational burden and achieve real-time performance. Furthermore, two main modifications are proposed which significantly improve the performance of the RTI Scheme in the presence of large disturbances, namely; additional energy-based costs, and a hybrid switching scheme. Finally, the approach is combined with an Online System Identification scheme to address parameter uncertainty, and with an Extended Kalman Filter for state-estimation. The resulting performance is validated through both simulations and experimental results.

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“…Notably, their features such as swing up, stabilization problem, higher order, nonlinear, robust coupling, and multivariate have been attracted more and more attention from control researchers for the last decades. Moreover, inverted pendulum system is widely used in the field of robotics and aerospace field, and so has essential significance both in the field of the theoretical study research and practice [1]- [3]. There are a lot of researchers about most popular types inverted pendulums such as the rotational single arm pendulum, the cart inverted pendulum, and the double inverted investigated the inverted pendulum by switching two different control laws [3], and in [4] LQR, double-PID and pole placement control techniques are used to control a cart inverted pendulum system.…”

Section: Introductionmentioning

confidence: 99%

Using real interpolation method for adaptive identification of nonlinear inverted pendulum system

Tin¹,

Minh²,

Trang³

et al. 2019

IJECE

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<p>In this paper, we investigate the inverted pendulum system by using real interpolation method (RIM) algorithm. In the first stage, the mathematical model of the inverted pendulum system and the RIM algorithm are presented. After that, the identification of the inverted pendulum system by using the RIM algorithm is proposed. Finally, the comparison of the linear analytical model, RIM model, and nonlinear model is carried out. From the results, it is found that the inverted pendulum system by using RIM algorithm has simplicity, low computer source requirement, high accuracy and adaptiveness in the advantages.</p>

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Swing-up control of a triple pendulum on a cart with experimental validation

Cited by 68 publications

References 10 publications

Inverted Pendulum With Linear Synchronous Motor Swing Up Using Boundary Value Problem

Inverted Pendulum With Linear Synchronous Motor Swing Up Using Boundary Value Problem

Fast hybrid dual mode NMPC for a parallel double inverted pendulum with experimental validation

Using real interpolation method for adaptive identification of nonlinear inverted pendulum system

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