Nonlinear control of a swinging pendulum

Chung, Chung Choo; Hauser, John

doi:10.1016/0005-1098(94)00148-c

Cited by 201 publications

(91 citation statements)

References 3 publications

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“…As explained in the previous section, the phase ϕ is only approximately time linear. Consequently, the accelerationr according to the approximate control law (8) does not only contain the desired oscillation of frequency ω, but also higher order harmonics, which disturb the sign condition. In order to attenuate the higher harmonics and to be able to obey a restricted workspace, Yoshida defines a reference trajectory [10] …”

Section: B Model Based Swing-up Controllermentioning

confidence: 99%

“…267877 (www.shrine-project.eu) and in part by the Technische Universität München -Institute for Advanced Study (www.tumias.de), funded by the German Excellence Initiative into account restricted pivot travel are e.g. [8], [9], [10]. Lozano et al present a passivity based design of a swingup controller and show asymptotic stability of the inverted pendulum at zero cart displacement [9].…”

Section: Introductionmentioning

confidence: 99%

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Adaptive simple pendulum swing-up controller based on the closed-loop fundamental dynamics

Donner

Christange

Buss

2015

2015 European Control Conference (ECC)

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Abstract-An adaptive energy-based swing-up controller for simple pendulums is presented. A state transformation from cartesian to polar phase space followed by approximation steps leads to the fundamental dynamics of the controlled simple pendulum. Based on the fundamental dynamics, the unknown natural frequency is estimated and a control gain is adjusted such that the system energy follows desired reference dynamics. We prove convergence of the natural frequency estimate to the true value as well as convergence of the system energy to the desired energy level under the fundamental dynamics assumption. The implications of the fundamental dynamics approximation are evaluated in simulation. Noise affected angle measurements simulate a realistic inverted pendulum experiment. The successful swing-up into the highly nonlinear regimes of the simple pendulum support the applicability of the fundamental dynamics.

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Section: B Model Based Swing-up Controllermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive simple pendulum swing-up controller based on the closed-loop fundamental dynamics

Donner

Christange

Buss

2015

2015 European Control Conference (ECC)

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show abstract

“…The feedback gains are calculated by trial and error, which makes the process cumbersome for a wide range of operating conditions. Chung Choo Chung et al proposed a nonlinear controller to regulate the swinging energy of the pendulum for a cart and pendulum system [4]. The controller is usually designed to achieve the two tasks.…”

Section: Introductionmentioning

confidence: 99%

Hybrid velocity switching and fuzzy logic control scheme for cable tunnel inspection robot

Meng

et al. 2015

IFS

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Abstract. This paper describes a hybrid anti-swing control scheme of an inspection robot in tunnels for power transmission cables. The hybrid control scheme consists of velocity switching and fuzzy logic control, so that the robot can be operated smoothly without causing excessive swings in acceleration or deceleration motion. In order to ensure control system robustness for greatest movement in the tunnel, fuzzy logic control is used for horizontal anti-swing control. Velocity switching is adopted for incline anti-swing control, in order to obtain sufficient damping as well as a fast response. The stability of the hybrid system has been analyzed. The experimental results present the practicability and effectiveness of the proposed method.

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“…This system was originally used as a benchmark for educational purposes, see [1,6,15,33,39,43,44,46] .Through the years, this system has attracted attention as an important underactuated mechanical system, because the pendulum angular acceleration cannot be directly controlled [18,42]. As the CPS dynamics resembles that of many underactuated robot systems, it has been studied as a simplified model such systems (see [7,27,30,38,40,43] ).…”

Section: Introductionmentioning

confidence: 99%

Stabilization of the cart pole system: by sliding mode control

Aguilar-Ibáñez¹,

Mendoza-Mendoza²,

Dávila³

2014

Nonlinear Dyn

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This paper presents a control strategy designed as a combination of a PD controller and a twistinglike algorithm to stabilize the damped cart pole system, provided that the pendulum is initially placed within the upper-half plane. To develop the strategy, the original system is transformed into a four-order chain of integrator form, where the damping force is included through an additional nonlinear perturbation. The strategy consists of simultaneously bringing the position and velocity of the pendulum to within a compact region by applying the PD controller. Meanwhile, the system state variables are brought to the origin by the twisting-like algorithm. The corresponding convergence analysis is done using several Lyapunov functions. The control strategy is illustrated with numerical simulations.

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Nonlinear control of a swinging pendulum

Cited by 201 publications

References 3 publications

Adaptive simple pendulum swing-up controller based on the closed-loop fundamental dynamics

Adaptive simple pendulum swing-up controller based on the closed-loop fundamental dynamics

Hybrid velocity switching and fuzzy logic control scheme for cable tunnel inspection robot

Stabilization of the cart pole system: by sliding mode control

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