Stabilization Of Inverted Pendulum Research Articles

Синергетическая теория управления и вибромеханика: концептуальная связь

The paper established a deep conceptual relation between vibro-mechanics and synergetic control theory. This conceptual relation is revealed in emergence of new phenomena in complex systems, namely: expansion and compression of phase flow; transition of point representing system into internal attracting manifolds, on which new dynamic properties of system are formed. In vibro-mehanics control actions are carried out usually as a function of time by selecting corresponding vibration actions, but synergetic theory of control actions is synthesized in feedback function, ensuring desired oscillation and vibration processes. These new research areas complement each other in meeting today's major technological challenges of controlling complex objects of different nature. We prove that with an example of a complete solution of famous P. L. Kapitza's problem of the inverted pendulum stabilization.

Taylor Series Method for Continuous Linear-Quadratic Regulators

A simple and eficient algorithm for finite-horizon continuous time LQR feedback control computation is presented. The method uses only basic linear algebra and does not require the solution of algebraic Riccati equation. The developed algorithm is applied to the benchmark problem of double inverted pendulum stabilization.

Modeling and PID Control of Single-Stage Inverted Pendulum System

The dynamic model is obtained based on researching the structure of single inverted pendulum system in this paper. Mathematical model of inverted pendulum that is close to the working point is deduced by linearization. A PID control algorithm is put forward by analyzing the factor of influencing inverted pendulum stability. The effectiveness of proposed algorithm is verified by simulation. This algorithm has the features of high control precision and good stability.

Simplifications of the Rule base for the stabilization of Inverted Pendulum System

Control of an inverted pendulum on a carriage which moves in a horizontal path, is one of the classic problems in the area of control. The basic aim of our work was to design appropriate controller to control the angle of the pendulum and the position of the cart in order to stabilize the inverted pendulum system. The main objective of this paper to keep the stabilization of the inverted pendulum based on the simplification of rule base. The proposed fuzzy control scheme successfully fulfills the control objectives and also has an excellent stabilizing ability to overcome the external impact acting on the pendulum system. The effectiveness of this controller is verified by experiments on a simple inverted pendulum with fixed cart length.

Natural Frequency based Swing up and GA tuned Pole Placement with integral Control based Stabilization of Rotary Inverted Pendulum

This paper aims at the applications of natural frequency of inverted pendulum and genetic algorithm (GA) tuned pole placement with integral control in the swing up and stabilization of Rotary inverted pendulum (RIP) respectively. RIP is an important multivariable system in control to test the performance of any controller due to its nonlinear, unstable, non-minimum phase and under actuated nature. The technique used in this paper for swing up of pendulum from downward position to upright position is based on natural frequency of pendulum. It can be calculated either experimentally or based on equation of time period of pendulum. Classical method only places the dominant pair of poles to desired location hoping that higher order poles do not affect the second order approximation. This disadvantage is overcome by pole placement technique which places the entire poles at desired locations. Integral action is required to remove the steady state error. In between the swing up and stabilization a mode controller is used which is basically a condition check on the angle of the pendulum rod. Finally Simulink based experimental results are used to verify and validate the performance of the above controllers on RIP system.

Design of Parameter Adaptive Fuzzy Controller for the Planar Double Inverted Pendulum

In this paper, The mathematical model is established using analytical dynamics method for planar double inverted pendulum, based on optimal control theory, parameter adaptive fuzzy controller is designed by use of variable fusion technology, thereby it can reduce the dimension of the input variables of the fuzzy controller, greatly decrease the number of the fuzzy rules, and the impact of the quantization factor on the control effectiveness is studied. The designed controller for system is applied in simulation experiments, the results show that the fuzzy controller can guarantee good control precision, fast response, control planar inverted pendulum stability.

Simulating Robots Without Conventional Physics: A Neural Network Approach

The construction of physics-based simulators for use in Evolutionary Robotics (ER) can be complex and time-consuming. Alternative simulation schemes construct robotic simulators from empirically-collected data. Such empirical simulators, however, also have associated challenges. This paper therefore investigates the potential use of Artificial Neural Networks, henceforth simply referred to as Neural Networks (NNs), as alternative robotic simulators. In contrast to physics models, NN-based simulators can be constructed without requiring an explicit mathematical model of the system being modeled, which can simplify simulator development. The generalization abilities of NNs, along with NNs’ noise tolerance, suggest that NNs could be well-suited to application in robotics simulation. Investigating whether NNs can be effectively used as robotic simulators in ER is thus the endeavour of this work. Two robot morphologies were selected on which the NN simulators created in this work were based, namely a differentially steered robot and an inverted pendulum robot. Accuracy tests indicated that NN simulators created for these robots generally trained well and could generalize well on data not presented during simulator construction. In order to validate the feasibility of the created NN simulators in the ER process, these simulators were subsequently used to evolve controllers in simulation, similar to controllers developed in related studies. Encouraging results were obtained, with the newly-evolved controllers allowing experimental robots to exhibit obstacle avoidance, light-approaching behaviour and inverted pendulum stabilization. It was thus clearly established that NN-based robotic simulators can be successfully employed as alternative simulation schemes in the ER process.

Stabilization of the Inverted Pendulum on a Skate

In the classical control theory literature, the inverted pendulum stabilization problem has been addressed in two ways: as an application of the vibrational control principle, or by imagining that the pivot is on a cart moved according to a suitable feedback law. Several other stabilization methods have been recently proposed.In this paper we propose a new approach: the pendulum is assembled on an ice skate, subject to some constraints and equipped with a driving device. The upper equilibrium position is stabilized provided that the speed of the skate is sufficiently large.

Stabilization of the inverted pendulum on a skate

In the classical control theory literature, the inverted pendulum stabilization problem has been addressed in two ways: as an application of the vibrational control principle, or by imagining that the pivot is on a cart moved according to a suitable feedback law. Several other stabilization methods have been recently proposed. In this paper we propose a new approach: the pendulum is assembled on an ice skate, subject to some constraints and equipped with a driving device. The upper equilibrium position is stabilized provided that the speed of the skate is sufficiently large.

Global stabilization of a double inverted pendulum with control at the hinge between the links

We study the plane motion of a double pendulum with fixed suspension point. The pendulum is controlled by a single moment applied to the internal hinge between the links. The moment is assumed to be bounded in absolute value. We construct a feedback control law bringing the pendulum from the position in which both links hang vertically downwards into the unstable upper position in which both links are inverted. The same feedback ensures the asymptotic stability of the pendulum in the upper equilibrium position. Since the pendulum can be brought to the lower equilibrium position from any initial states, it follows that the constructed control law ensures the global stability of the inverted pendulum.

Friction and the Inverted Pendulum Stabilization Problem

We consider an experimental system consisting of a pendulum, which is free to rotate 360deg, attached to a cart. The cart can move in one dimension. We study the effect of friction on the design and performance of a feedback controller, a linear quadratic regulator, that aims to stabilize the pendulum in the upright position. We show that a controller designed using a simple viscous friction model has poor performance—small amplitude oscillations occur when the controller is implemented. We consider various models for stick slip friction between the cart and the track and measure the friction parameters experimentally. We give strong evidence that stick slip friction is the source of the small amplitude oscillations. A controller designed using a stick slip friction model stabilizes the system, and the small amplitude oscillations are eliminated.

Stabilization Control for a Serial Double Inverted Pendulum with Observation-Time-Delay Using Delayed Feedback

In this paper, the stabilization problem of a plant with known delay in observation is studied. Although several methods, the Smith predictor or the state predictive control, have already been proposed about the control of plant with time delay, theoretical limitations and the practical inconvenience were left to be solved; e. g., the Smith predictor can only treat the stable systems, and the numerical integration of the exponential function is difficult in the state predictive control. The presented method combines the state feedback control with the delayed feedback control, which can stabilize the unstable systems and can be easily performed. The numerical simulation of the stabilization of the serial double inverted pendulum shows that the proposed method can he applied to stabilization of the unstable system and is effective for the impulsive disturbance.

1012 マシンビジョン技術を用いた倒立振子の安定化

1012 マシンビジョン技術を用いた倒立振子の安定化

Subharmonic resonances of the parametrically driven pendulum

A simple qualitative physical explanation is suggested for the phenomenon of subharmonic resonances of a rigid planar pendulum whose axis is forced to oscillate with a high frequency in the vertical direction. An approximate quantitative theory based on the suggested approach is developed. The spectral composition of the subharmonic resonances is investigated quantitatively, and the boundaries of these modes in the parameter space are determined. New related modes of regular behaviour are described and explained. The conditions of the inverted pendulum stability are determined with greater precision than previous results. A computer program simulating the physical system supports the analytical investigation.

Almost global stabilization of the inverted pendulum via continuous state feedback

Continuous state feedback laws are presented for “almost” global stabilization of the planar inverted pendulum on a cart. The synthesis is carried out exploiting energy-shaping techniques and a suitable smooth switching between positive and negative feedback. Some of the employed ideas could be possibly generalized to the problem of stabilization of systems with multiple equilibrium points.

メモリ型ファジイネットワークによる回転型倒立振子の安定化制御

メモリ型ファジイネットワークによる回転型倒立振子の安定化制御

Inverted Pendulum Stabilization of Submarines in Free Positive Buoyancy Ascent

The problem of steady-state vertical ascent of a submarine with excess buoyancy is analyzed. All possible vertical plane solutions are computed and their stability is established in both in-plane and out-of-plane perturbations. Divergence of trajectories, sensitivity of solutions to initial conditions, and stable inverted pendulum configurations are shown to exist for certain ranges of parameters.