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Inverted Pendulum (inverted + pendulum)
Selected AbstractsA new controller for the inverted pendulum on a cartINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 17 2008F. Gordillo Abstract This paper presents a complete solution to the problem of swinging-up and stabilization of the inverted pendulum on a cart, with a single control law. The resulting law has two parts: first, an energy-shaping law is able to swing and maintain the pendulum up. Then, the second part introduces additional control to stop the cart and it is based on forwarding control with bounded input. The resulting control law is the sum of both parts and does not commute between different laws although there exist switches inside the controller. Copyright © 2008 John Wiley & Sons, Ltd. [source] A reduction paradigm for output regulationINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 7 2008F. Celani Abstract The goal of this paper is to provide a reduction paradigm for the design of output regulators which can be of interest for nonlinear as well as linear uncertain systems. The main motivation of the work is to provide a systematic design tool to deal with non-minimum-phase uncertain systems for which conventional high-gain stabilization methods are not effective. The contribution of the work is two-fold. First, this work extends a previous reduction paradigm for output regulation of nonlinear systems. Furthermore, in the case of the uncertain controlled dynamics being linear, we show how the proposed framework leads to a number of systematic design tools of interest for non-minimum-phase linear systems affected by severe uncertainties. A numerical control example of a linearized model of an inverted pendulum on a cart is presented. Copyright © 2007 John Wiley & Sons, Ltd. [source] Manually controlled human balancing using visual, vestibular and proprioceptive senses involves a common, low frequency neural processTHE JOURNAL OF PHYSIOLOGY, Issue 1 2006Martin Lakie Ten subjects balanced their own body or a mechanically equivalent unstable inverted pendulum by hand, through a compliant spring linkage. Their balancing process was always characterized by repeated small reciprocating hand movements. These bias adjustments were an observable sign of intermittent alterations in neural output. On average, the adjustments occurred at intervals of ,400 ms. To generate appropriate stabilizing bias adjustments, sensory information about body or load movement is needed. Subjects used visual, vestibular or proprioceptive sensation alone and in combination to perform the tasks. We first ask, is the time between adjustments (bias duration) sensory specific? Vision is associated with slow responses. Other senses involved with balance are known to be faster. Our second question is; does bias duration depend on sensory abundance? An appropriate bias adjustment cannot occur until unplanned motion is unambiguously perceived (a sensory threshold). The addition of more sensory data should therefore expedite action, decreasing the mean bias adjustment duration. Statistical analysis showed that (1) the mean bias adjustment duration was remarkably independent of the sensory modality and (2) the addition of one or two sensory modalities made a small, but significant, decrease in the mean bias adjustment duration. Thus, a threshold effect can alter only a very minor part of the bias duration. The bias adjustment duration in manual balancing must reflect something more than visual sensation and perceptual thresholds; our suggestion is that it is a common central motor planning process. We predict that similar processes may be identified in the control of standing. [source] Structural design of composite nonlinear feedback control for linear systems with actuator constraint,ASIAN JOURNAL OF CONTROL, Issue 5 2010Weiyao Lan Abstract The performance of the composite nonlinear feedback (CNF) control law relies on the selection of the linear feedback gain and the nonlinear function. However, it is a tough task to select an appropriate linear feedback gain and appropriate parameters of the nonlinear function because the general design procedure of CNF control just gives some simple guidelines for the selections. This paper proposes an operational design procedure based on the structural decomposition of the linear systems with input saturation. The linear feedback gain is constructed by two linear gains which are designed independently to stabilize the unstable zero dynamics part and the pure integration part of the system respectively. By investigating the influence of these two linear gains on transient performance, it is flexible and efficient to design a satisfactory linear feedback gain for the CNF control law. Moreover, the parameters of the nonlinear function are tuned automatically by solving a minimization problem. The proposed design procedure is illustrated by applying it to design a tracking control law for the inverted pendulum on a cart system. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] Minimizing operating points for way point tracking of an unstable nonlinear plantASIAN JOURNAL OF CONTROL, Issue 1 2010Guangyu Liu Abstract Stability analysis of way point tracking of an open loop unstable nonlinear system is overwhelmingly ignored in the literature. Taking a spherical inverted pendulum as an example, the stability issue of way point tracking for an unstable nonlinear system is properly addressed and solved by incorporating nonlinear stabilizing controllers that could minimize the number of operating points. The underlying principle in stability analysis of way point tracking easily extends to other unstable nonlinear systems. Effectiveness of the proposed idea is evaluated in computer simulation. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] NETWORK-INDUCED DELAY-DEPENDENT H, CONTROLLER DESIGN FOR A CLASS OF NETWORKED CONTROL SYSTEMSASIAN JOURNAL OF CONTROL, Issue 2 2006Xiefu Jiang ABSTRACT This paper is concerned with the problem of robust H, controller design for a class of uncertain networked control systems (NCSs). The network-induced delay is of an interval-like time-varying type integer, which means that both lower and upper bounds for such a kind of delay are available. The parameter uncertainties are assumed to be normbounded and possibly time-varying. Based on Lyapunov-Krasovskii functional approach, a robust H, controller for uncertain NCSs is designed by using a sum inequality which is first introduced and plays an important role in deriving the controller. A delay-dependent condition for the existence of a state feedback controller, which ensures internal asymptotic stability and a prescribed H, performance level of the closed-loop system for all admissible uncertainties, is proposed in terms of a nonlinear matrix inequality which can be solved by a linearization algorithm, and no parameters need to be adjusted. A numerical example about a balancing problem of an inverted pendulum on a cart is given to show the effectiveness of the proposed design method. [source] | ||||||||||