Non-linear swing-up and stabilizing control of an inverted pendulum system

Bugeja, Marvin K.

doi:10.1109/eurcon.2003.1248235

Cited by 71 publications

(41 citation statements)

References 4 publications

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“…One of these methods, namely heuristic controller, provides a constant voltage in the appropriate direction, and drives the cart along the track repeatedly. Thus, it will repeat this action until the pendulum is close enough to the upright position such that the stabilizing controller can be triggered to maintain this balanced state [1], [4].…”

Section: Inverted Pendulum Modelmentioning

confidence: 99%

“…The goal is to stabilize the IP such that its the position on the track is controlled quickly and accurately such that the pendulum is always erected in its inverted position during such movements. Different control schemes were discussed to swing the pendulum from the downward position to the upright one, as described in [1], [4], [6]. The users are not interested so much in the time to swing-up the pendulum while their objective is its stabilization when it reaches its unstable equilibrium point.…”

Section: Introductionmentioning

confidence: 99%

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Optimal time control to swing-up the inverted pendulum-cart in open-loop form

Merakeb

Messine

2013

2013 IEEE 11th International Workshop of Electronics, Control, Measurement, Signals and Their Application to Mechatronics

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. Abstract-This work deals with simulation on an Inverted Pendulum (IP). The control strategy of an IP is split into two main control phases: (i) swing-up control to bring back the pendulum from the downward position to the upward one, and (ii) upright stabilization control to maintain the pendulum to the upright vertical position. In the case (ii), a feedback or a neuro-fuzzy controller is used to stabilize the pendulum cart, while in the Þrst case (i), a non-linear controller based on the energy of the pendulum is used in order to reach the desired performance with a minimum number of swings. Our contribution is to present a simulation using MatLab of time-optimal control system for swinging-up the pendulum, with a single control law in an open-loop form. From the bang-bang structure of the timeoptimal control resulting from the necessary condition of the Pontryagin Maximum Principle, the solution obtained from direct discretization method is adjusted by using Newton based method.

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Section: Inverted Pendulum Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal time control to swing-up the inverted pendulum-cart in open-loop form

Merakeb

Messine

2013

2013 IEEE 11th International Workshop of Electronics, Control, Measurement, Signals and Their Application to Mechatronics

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“…We consider the task of swing-up inverted pendulum [3] illustrated in Fig.7, consisting of a rod hinged at the top of a cart. The goal of the task is to swing the rod up by moving the cart.…”

Section: Methodsmentioning

confidence: 99%

Efficient data reuse in value function approximation

Hachiya

Akiyama

Sugiyama

et al. 2009

2009 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning

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Abstract-Off-policy reinforcement learning is aimed at efficiently using data samples gathered from a policy that is different from the currently optimized policy. A common approach is to use importance sampling techniques for compensating for the bias of value function estimators caused by the difference between the data-sampling policy and the target policy. However, existing off-policy methods often do not take the variance of the value function estimators explicitly into account and therefore their performance tends to be unstable. To cope with this problem, we propose using an adaptive importance sampling technique which allows us to actively control the trade-off between bias and variance. We further provide a method for optimally determining the trade-off parameter based on a variant of cross-validation. The usefulness of the proposed approach is demonstrated through simulated swing-up inverted-pendulum problem.

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“…Extending the study, in this paper, the feedback controller is designed for the inverted pendulum [18] using both the traditional full state feedback, which is the Ackermann's formula [8], [9], [13], [14] and the state derivative feedback. The resulting feedback gain matrix elements from both the approaches are compared, with a lower value in case of state derivative feedback indicating lesser energy consumption than state feedback.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Pole Placement Problem in Control Systems Using State Derivative Feedback

Hote

Malhotra

2011

Communications in Computer and Information Science

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IntroductionThe pole placement method is a widely used mathematical tool to design linear con- . The tendency of state derivative feedback control systems to result in singularity in case the original system ceases to be state variable system has been overcome recently by employing traditional state feedback approach which provides a solution to both the threat of singularity and to more general time-varying systems[1]. The inspiration for the approach followed in [1] came from controlled vibration absorbers [12]. Due to the specific nature of such systems, use of state derivative feedback is a natural and powerful way to design controllers for them. The motivation for this paper stems from the possibility of reduced energy consumption of the controller when designed using state derivative feedback for a given level of stability. This would expand the scope and range of possible applications of state derivative feedback and provide a new method for generating more energy efficient control system designs.In [1] the scope has been kept limited to developing the theoretical and mathematical analysis of the state derivative feedback approach. Extending the study, in this paper, the feedback controller is designed for the inverted pendulum[18] using both the traditional full state feedback, which is the Ackermann's formula [8], [9], [13],

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Non-linear swing-up and stabilizing control of an inverted pendulum system

Cited by 71 publications

References 4 publications

Optimal time control to swing-up the inverted pendulum-cart in open-loop form

Optimal time control to swing-up the inverted pendulum-cart in open-loop form

Efficient data reuse in value function approximation

Analysis of Pole Placement Problem in Control Systems Using State Derivative Feedback

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