Unified method for swing-up control of double inverted pendulum systems

Henmi, Tomohiro; Deng, Mingcong

doi:10.1109/icamechs.2014.6911611

Cited by 8 publications

(10 citation statements)

References 7 publications

(5 reference statements)

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“…In the case of the single pendulum, controllers have been designed to swing the pendulum up and/or stabilize it in the inverted position [11] , [46] , [47] , [47] , [48] , [49] , [50] , [51] , [52] , [53] , [54] , [55] , [56] , [57] , [58] , [59] . Similar control methods have been developed to swing up the arms of the double and triple pendulums [25] , [28] , [58] , [60] , [61] , [62] , [63] , [64] , [65] , [66] , [67] , [68] , [69] , [70] , [71] , [72] , stabilize their arms in various unstable vertical positions [58] , [60] , [73] , [74] , [75] , and perform time-periodic motion [26] , [27] , [31] , [76] , [77] , [78] . Due to the chaotic nature of multi-armed pendulums, the sensitivity increases as more arms are added to the pendulum, thus making it an increasingly difficult control benchmark.…”

Section: Hardware In Contextmentioning

confidence: 99%

The experimental multi-arm pendulum on a cart: A benchmark system for chaos, learning, and control

Kaheman,

Fasel,

Bramburger

et al. 2023

HardwareX

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Section: Hardware In Contextmentioning

confidence: 99%

The experimental multi-arm pendulum on a cart: A benchmark system for chaos, learning, and control

Kaheman,

Fasel,

Bramburger

et al. 2023

HardwareX

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“…or equivalently θp1 = The following state vector is defined x = [x 1 , x 2 , x 3 , x 4 ] T = [θ p1 , θp1 , θ p2 , θp2 ] T . Thus, the dynamic model of the parallel double inverted pendulum becomes: [23] ẋ1 = x 2 ẋ2 =…”

Section: Dynamic Model Of the Double Parallel Pendulum -Systemmentioning

confidence: 99%

“…However, little has been done so far for treatment of the associated nonlinear optimal control problem [20][21][22]. In this article a novel nonlinear optimal (H-infinity) control method is developed for the parallel double inverted pendulum, and is tested in three different forms of this system: (i) a model with four state variables and one control input, describing the dynamics of a cart with double inverted poles but without including the position of the cart [23], (ii) a model with six state variables and one control input, describing the dynamics of a cart with double inverted poles after including the position of the cart [24], (iii) a model with eight state variables and two control inputs, describing the dynamics of two separate cart and inverted pole systems which are connected through an elastic link [25].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear optimal control of the parallel double inverted pendulum

Rigatos

Pomares

Abbaszadeh

et al. 2023

Preprint

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The article proposes a nonlinear optimal control method for the dynamic model of the parallel double inverted pendulum. Three different forms of this system are considered: (i) two poles mounted on the same cart resulting into a model with four state variables and one control input, (ii) two poles mounted on the same cart resulting into a model with six state variables and one control input, (iii) two different cart-pole systems connected through an elastic link, resulting into a model with eight state variables and two control inputs. To implement the proposed nonlinear optimal control method the dynamic model of the parallel double pendulum undergoes approximate linearization around a temporary operating point which is updated at each sampling instance. This operating point is defined within each sampling period by the present value of the state vector of the parallel double inverted pendulum and by the last sampled value of the control inputs vector. The linearization process is based on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. For the approximately linearized model of the parallel double inverted pendulum a stabilizing H-infinity feedback controller is designed. To compute the feedback gains of this controller an algebraic Riccati equation is also being solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. First it is demonstrated that the H-infinity tracking performance criterion holds, which signifies robustness of the control method under model uncertainty and external perturbations. Moreover, under moderate conditions it is proven that the control loop of the parallel double inverted pendulum is globally asymptotically stable. To implement state estimation-based control the H-infinity Kalman Filter is used as a robust observer. The nonlinear optimal control scheme for the parallel double inverted pendulum achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs.

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“…In the case of the single pendulum, controllers have been designed to swing the pendulum up and/or stabilize it in the inverted position [11,46,47,[47][48][49][50][51][52][53][54][55][56][57][58][59]. Similar control methods have been developed to swing up the arms of the double and triple pendulums [25,28,58,[60][61][62][63][64][65][66][67][68][69][70][71][72], stabilize their arms in various unstable vertical positions [58,60,[73][74][75], and perform time-periodic motion [26,27,31,[76][77][78]. Due to the chaotic nature of multi-armed pendulums, the sensitivity increases as more arms are added to the pendulum, thus making it an increasingly difficult control benchmark.…”

Section: Introductionmentioning

confidence: 99%

The Experimental Multi-Arm Pendulum on a Cart: A Benchmark System for Chaos, Learning, and Control

Kaheman¹,

Fasel²,

Bramburger³

et al. 2022

Preprint

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The single, double, and triple pendulum has served as an illustrative experimental benchmark system for scientists to study dynamical behavior for more than four centuries. The pendulum system exhibits a wide range of interesting behaviors, from simple harmonic motion in the single pendulum to chaotic dynamics in multi-arm pendulums. Under forcing, even the single pendulum may exhibit chaos, providing a simple example of a damped-driven system. All multi-armed pendulums are characterized by the existence of index-one saddle points, which mediate the transport of trajectories in the system, providing a simple mechanical analog of various complex transport phenomena, from biolocomotion to transport within the solar system. Further, pendulum systems have long been used to design and test both linear and nonlinear control strategies, with the addition of more arms making the problem more challenging. In this work, we provide extensive designs for the construction and operation of a high-performance, multi-link pendulum on a cart system. Although many experimental setups have been built to study the behavior of pendulum systems, such an extensive documentation on the design, construction, and operation is missing from the literature. The resulting experimental system is highly flexible, enabling a wide range of benchmark problems in dynamical systems modeling, system identification and learning, and control. To promote reproducible research, we have made our entire system open-source, including 3D CAD drawings, basic tutorial code, and data. Moreover, we discuss the possibility of extending our system capability to be operated remotely to enable researchers all around the world to use it, thus increasing access.

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Unified method for swing-up control of double inverted pendulum systems

Cited by 8 publications

References 7 publications

The experimental multi-arm pendulum on a cart: A benchmark system for chaos, learning, and control

The experimental multi-arm pendulum on a cart: A benchmark system for chaos, learning, and control

Nonlinear optimal control of the parallel double inverted pendulum

The Experimental Multi-Arm Pendulum on a Cart: A Benchmark System for Chaos, Learning, and Control

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