Switched controllers are being used frequently for control of complex systems. However, they introduce new challenges for verification of stability, of which a great deal of work in the hybrid systems domain has been formalizing recently. This work is a stability case study of the classical inverted pendulum, in this case controlled using the Simplex architecture of [1], combining to form a com...

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The strategies involved in swinging up and balancing the inverted pendulum are discussed. The nonlinear swing-up controller drives the system input according to the energy of the pendulum. The balancing controller is a digital linear quadratic regulator that is based on a model of the plant that has been linearized about the pendulum’s upright equilibrium position. Relays with hysteresis are em...

The problem of stabilizing the double inverted pendulum has been solved using two different techniques which were the Pole Placement and Linear Quadratic Regulator techniques to design controls for the system. Copyright c ©2003 Yang’s Scientific Research Institute, LLC. All rights reserved.

Recent research efforts are considering the problem of performing control of dynamical systems over wireless sensor and actuator networks. However, existing results lack an experimental evaluation in real platforms. In this demonstration an inverted pendulum system is controlled over an IEEE 802.15.4 wireless sensor and actuator network. This platform can evaluate several sensor networks and co...

The rotary inverted pendulum, also named Furuta Pendulum, has been studied extensively for control performance evaluation in under-actuated mechanisms. The H∞ control invoking Linear Matrix Inequality (H∞-LMI) has been also wide employed for linear control design. This paper deals with the feasibility ofH∞-LMI technique to stabilize the rotary inverted pendulum around its unstable equilibrium p...

We analyse the stability of the spring inverted pendulum with the vertical oscillations of the suspension point. An important factor in the stability analysis is the interaction between radial and oscillating modes. In addition to the small oscillations near the upper position, the nonlinearity of the problem leads to the appearance of limit-cycle oscillations of finite amplitudes.

The observation that time-delayed feedback can stabilize an inverted pendulum motivates the formulation of models of human balance control in terms of delay differential equations (DDEs). Recently the intermittent, digital-like nature of the neural feedback control of balance has become evident. Here, semidiscretization methods for DDEs are used to investigate an unstable dynamic system subject...

The standard approach to vibrational control applies first-order averaging methods to find an openloop periodic input that stabilizes an unstable equilibrium point. While the capability of stabilization without feedback is appealing, this formulation has drawbacks from a design perspective. An alternative design framework based on stability maps for second-order linear periodic systems is not a...

This paper obtains feedback stabilization of an inverted pendulum on a rotor arm by the “method of controlled Lagrangians”. This approach involves modifying the Lagrangian for the uncontrolled system so that the Euler-Lagrange equations derived from the modified or “controlled” Lagrangian describe the closed-loop system. For the closed-loop equations to be consistent with available control inpu...