The real stabilizability radius of the multi-link inverted pendulum

Lam, Simon; Davison, E.J.

doi:10.1109/acc.2006.1656483

Cited by 28 publications

(33 citation statements)

References 8 publications

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“…System (1) - (4) is different from the known system of equations used to describe motion of an n-link pendulum with a fixed base [3], [4]. Note that system (1) - (4) is under-actuated one.…”

Section: Planar N-link Pendulum On a Wheelmentioning

confidence: 99%

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Unstable Mechanical Objects: Motion Control, Stabilization

Formalskii¹

2017

ujme

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We consider here mechanical objects that have desired operating regime unstable without additional control signal. The resources of control are assumed limited. First of all the motion equations of a multi-link pendulum mounted on a moving base -wheel are designed. Equations that describe only the pendulum motion are separated. The problem of controlling a single inverted pendulum on a wheel is studied. Control law that ensures large basin of attraction of the top unstable equilibrium is developed. The 'inverse' system -the inertia wheel pendulum with fixed suspension point is investigated. For this system the control algorithm is developed to stabilize globally the top equilibrium of the pendulum. This control law is tested successfully in simulation and experiments. The double pendulum with fixed suspension point is considered. The limited in absolute value control torque is applied in the inter-link joint. The control algorithm to ensure global stabilization of the inverted pendulum is designed. For maximizing basin of attraction of unstable system, we use all control resources to suppress the unstable modes. At the end of the paper, the problem of gyroscopic stabilizing of the upright unstable position of a robot-bicycle is studied.

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Section: Planar N-link Pendulum On a Wheelmentioning

confidence: 99%

“…It is not limited with respect to the other two Jordan variables 3 y , 4 y that correspond to the negative eigenvalues …”

Section: Local Stabilization In Top Position With Large Basin Of Attrmentioning

confidence: 99%

Unstable Mechanical Objects: Motion Control, Stabilization

Formalskii¹

2017

ujme

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“…First, we will revisit the pendulum problem in [11] and using the results of this paper, compute a lower bound of the true structured real WeB03.4 controllability radius of the multi-link inverted pendulum. In the second example, we will study cases of when the lower bounds provided by Theorem 3.1 are actually achievable.…”

Section: Applicationsmentioning

confidence: 99%

“…In [11], the real controllability radius was used to study the difficulty of balancing the multi-link inverted pendulum system with v links (see Figure 1), for v = 1, 2, . .…”

Section: A Structured Real Controllability Radius Of the Pendulummentioning

confidence: 99%

“…Then in Section III, we define the restricted real perturbation values of a matrix triplet, and present our main result, which is a formula for computing lower bounds of these values. Finally in Section IV, we will revisit the pendulum problem in [11], and apply the results of this paper to compute the true value of the structured real controllability radius of the multi-link inverted pendulum. Also, we will numerically show that the lower bounds provided in this paper are actually achievable for the cases when L (or N ) has full column (or row) rank and/or is real.…”

Section: Introductionmentioning

confidence: 99%

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Restricted real perturbation values with applications to the structured real controllability radius of LTI systems

Lam

Davison

2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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Abstract-In this paper, the concept of restricted real perturbation values of a complex matrix triplet is introduced, and a formula for computing lower bounds of these values is presented. Restricted real perturbation values are a generalization of the real perturbation values introduced in [1], which is a key concept in evaluating various robustness radii found in the control literature, such as the real controllability/observability radius, the real decentralized fixed-mode radius, the real minimum-phase radius, etc. The generalization to restricted real perturbation values is needed for an extension of these radii to account for more general system perturbation structures. As an example, we will use the results of this paper to compute the true value of the structured real controllability radius of the multi-link inverted pendulum system. Also, we will numerically investigate cases of when the provided lower bounds are achievable.

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