Swing-up control for an inverted pendulum with restricted cart rail length

Yang, Ji-Hyuk; Shim, Su-Yong; Seo, Jun-Woo; Lee, Young‐Sam

doi:10.1007/s12555-009-0419-x

Cited by 32 publications

(18 citation statements)

References 9 publications

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“…First, we present 3 examples where SAC is applied to the nonlinear cart-pendulum (13) in simulated constrained swing-up. Performance of SAC is demonstrated using the cart-pendulum as it provides a well understood underactuated control problem that has long served as a benchmark for new control methodologies (see [19]- [24]).…”

Section: A Cart-pendulummentioning

confidence: 99%

Sequential Action Control: Closed-Form Optimal Control for Nonlinear and Nonsmooth Systems

2016

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This paper presents a new model-based algorithm that computes predictive optimal controls on-line and in closed loop for traditionally challenging nonlinear systems. Examples demonstrate the same algorithm controlling hybrid impulsive, underactuated, and constrained systems using only high-level models and trajectory goals. Rather than iteratively optimize finite horizon control sequences to minimize an objective, this paper derives a closed-form expression for individual control actions, i.e., control values that can be applied for short duration, that optimally improve a tracking objective over a long time horizon. Under mild assumptions, actions become linear feedback laws near equilibria that permit stability analysis and performance-based parameter selection. Globally, optimal actions are guaranteed existence and uniqueness. By sequencing these actions on-line, in receding horizon fashion, the proposed controller provides a min-max constrained response to state that avoids the overhead typically required to impose control constraints. Benchmark examples show the approach can avoid local minima and outperform nonlinear optimal controllers and recent, case-specific methods in terms of tracking performance, and at speeds orders of magnitude faster than traditionally achievable.3 are nonlinear in state x : R → R n . Though these methods apply more broadly, we derive controls for the case where (1) is linear with respect to the control, u : R → R m , satisfying control-affine form, f (t, x(t), u(t)) = g(t, x(t)) + h(t, x(t)) u(t) .(2)The time dependence in (1) and (2) will be dropped for brevity. The prediction phase simulates motion resulting from some choice of nominal control, u = u 1 . Thus, the nominal predicted motion corresponds to, u 1 (t)).Although the nominal control may be chosen arbitrarily, all examples here use a null nominal control, u 1 = 0. Hence, in the SLIP example, SAC seeks actions that improve performance relative to doing nothing, i.e., letting the SLIP fall.With l 1 : R n → R and m : R n → R, the cost functional,

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Section: A Cart-pendulummentioning

confidence: 99%

Sequential Action Control: Closed-Form Optimal Control for Nonlinear and Nonsmooth Systems

2016

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“…With change in energy depending on and using the Lyapunov function defined by , the control law required to reach the target energy is given by: (17) The above method does not consider the restrictions of the finite cart track length. Introducing the restrictions [14], the Lyapunov function is modified to and thus, the new control law is: (18) where is a parameter to restrict the linear motion of the cart.…”

Section: A Swing-up Using Energy Control Methodsmentioning

confidence: 99%

Comparison of reinforcement learning algorithms applied to the cart-pole problem

Nagendra

Podila

Ugarakhod

et al. 2017

2017 International Conference on Advances in Computing, Communications and Informatics (ICACCI)

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Designing optimal controllers continues to be challenging as systems are becoming complex and are inherently nonlinear. The principal advantage of reinforcement learning (RL) is its ability to learn from the interaction with the environment and provide optimal control strategy. In this paper, RL is explored in the context of control of the benchmark cartpole dynamical system with no prior knowledge of the dynamics. RL algorithms such as temporal-difference, policy gradient actor-critic, and value function approximation are compared in this context with the standard LQR solution. Further, we propose a novel approach to integrate RL and swing-up controllers.

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“…However, the method is effective for only a small area around the target position. In order to realize the motion control of the system in the whole motion space, a controller switching (CS) strategy has been proposed . This strategy designs a swing‐up controller and a balancing controller for two motion subspaces of the cart‐pendulum system.…”

Section: Introductionmentioning

confidence: 99%

“…In order to realize the motion control of the system in the whole motion space, a controller switching (CS) strategy has been proposed. [12][13][14][15][16] This strategy designs a swing-up controller and a balancing controller for two motion subspaces of the cart-pendulum system. In addition, the motion control objective is realized by switching the swing-up controller to the balancing controller.…”

Section: Introductionmentioning

confidence: 99%

Design of motion trajectory and tracking control for underactuated cart‐pendulum system

Zhang

She

Qiu

et al. 2019

Intl J Robust & Nonlinear

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Summary A cart‐pendulum system is a nonlinear underactuated mechanical system with two degrees of freedom. This paper addresses the motion trajectory design and tracking control problems for this underactuated system. First, a friction‐like control law is designed for the system. Then, the characteristics of the closed‐loop control system are analyzed. Second, a new method of constructing an optimal trajectory for the system is developed. Then, a tracking control law is designed to quickly track the constructed trajectory. It guarantees that the motion control of the cart‐pendulum system is achieved along a reference trajectory. Finally, a numerical example is presented to demonstrate the effectiveness of the theoretical results. This study constructs an optimal trajectory for the cart‐pendulum system in its whole motion space and solves the motion control objective by tracking the constructed trajectory. It has many advantages compared with other motion control methods, eg, the optimal motion control objective of the system is achieved by a single control law; and the motion process and transient characteristics (eg, the settling time) of the control system can be accurately predicted.

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Swing-up control for an inverted pendulum with restricted cart rail length

Cited by 32 publications

References 9 publications

Sequential Action Control: Closed-Form Optimal Control for Nonlinear and Nonsmooth Systems

Sequential Action Control: Closed-Form Optimal Control for Nonlinear and Nonsmooth Systems

Comparison of reinforcement learning algorithms applied to the cart-pole problem

Design of motion trajectory and tracking control for underactuated cart‐pendulum system

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