In this paper, a horizontally moving suspended mass pendulum base is designed and controlled using robust control theory. H infinity optimal loop shaping with first and second order desired loop shaping function controllers are used to improve the performance of the system using Matlab/Simulink Toolbox. Comparison of the H infinity optimal loop shaping with first and second order desired loop shaping function controllers for the proposed system have been done to track the desired angular position of the pendulum using step and sine wave input signals and a promising result has been obtained succesfully.

This paper mainly analyzes the design and control of the rotational inverted pendulum, and presents a state space expression. Since the system is highly unstable a feedback control system is used. Augmentations with weighting functions based mixed sensetivity and H2 optimal control methods are used to make the system stable for uprise position. The rotational inverted pendulum have been simulated and compared with the proposed controllers and a promising results have been analyzed sussesfuly.

In this paper, modelling design and analysis of a triple inverted pendulum have been done using Matlab/Script toolbox. Since a triple inverted pendulum is highly nonlinear, strongly unstable without using feedback control system. In this paper an optimal control method means a linear quadratic regulator and pole placement controllers are used to stabilize the triple inverted pendulum upside. The impulse response simulation of the open loop system shows us that the pendulum is unstable. The comparison of the closed loop impulse response simulation of the pendulum with LQR and pole placement controllers results that both controllers have stabilized the system but the pendulum with LQR controllers have a high overshoot with long settling time than the pendulum with pole placement controller. Finally the comparison results prove that the pendulum with pole placement controller improve the stability of the system.

GNSS receivers are nowadays commonly used in monitoring applications, e.g., in estimating crustal and infrastructure deformations. This is basically due to the recent improvements in GNSS instruments and methodologies that allow high precision positioning, 24 h availability and semiautomatic data processing. In this paper, GNSS estimated deformations on a dam structure have been analyzed and compared with pendulum data. This study has been carried out for the Eleonora D’Arborea (Cantoniera) dam, which is in the Sardinia Island. Time series of pendulum and GNSS over a time span of 2.5 years have been aligned so to be comparable. Analytical models fitting these time series have been estimated and compared. Those models were able to properly fit pendulum data and GNSS data, with standard deviation of residuals smaller than one millimeter. This encouraging results led to the conclusion that GNSS technique can be profitably applied to dam monitoring allowing a denser description, both in space and time, of the dam displacements than the one based on pendulum observations.

This paper is primarily focused on the robust control of an inverted pendulum system based on the policy iteration in reinforcement learning. First, a mathematical model of the single inverted pendulum system is established through a force analysis of the pendulum and trolley. Second, based on the theory of robust optimal control, the robust control of the uncertain linear inverted pendulum system is transformed into an optimal control problem with an appropriate performance index. Moreover, for the uncertain linear and nonlinear systems, two reinforcement-learning control algorithms are proposed using the policy iteration method. Finally, two numerical examples are provided to validate the reinforcement learning algorithms for the robust control of the inverted pendulum systems.

Volcanic ash deposited on paved surfaces during volcanic eruptions often compromises skid resistance, which is a major component of safety. We adopt the British pendulum test method in laboratory conditions to investigate the skid resistance of road asphalt and airfield concrete surfaces covered by volcanic ash sourced from various locations in New Zealand. Controlled variations in ash characteristics include type, depth, wetness, particle size and soluble components. We use Stone Mastic Asphalt (SMA) for most road surface experiments but also test porous asphalt, line-painted road surfaces, and a roller screed concrete mix used for airfields. Due to their importance for skid resistance, SMA surface macrotexture and microtexture are analysed with semi-quantitative image analysis, microscopy and a standardised sand patch volumetric test, which enables determination of the relative effectiveness of different cleaning techniques. We find that SMA surfaces covered by thin deposits (~1 mm) of ash result in skid resistance values slightly lower than those observed on wet uncontaminated surfaces. At these depths, a higher relative soluble content for low-crystalline ash and a coarser particle size results in lower skid resistance. Skid resistance results for relatively thicker deposits (3-5 mm) of non-vesiculated basaltic ash are similar to those for thin deposits. There are similarities between road asphalt and airfield concrete, although there is little difference in skid resistance between bare airfield surfaces and airfield surfaces covered by 1 mm of ash. Based on our findings, we provide recommendations for maintaining road safety and effective cleaning techniques in volcanic ash environments.

Improper design of friction pendulum bearings can lead to poor seismic reduction performance and may result in the failure of local vulnerable components. And the parameter design of friction pendulum bearings mainly relies on experience and verification calculations at present. This paper proposes an adaptive genetic algorithm considering the overall evolution state of the population, adjusting crossover and mutation probabilities adaptively based on individual fitness and population diversity. Compared to traditional algorithms, it exhibits better global search capabilities and convergence efficiency. Combining the improved genetic algorithm with finite element models, a parameter optimization method is proposed. The parameters of friction pendulum bearings are optimized, providing reference for the design of seismic isolation devices.

In the present study, a simple approximation expression is given for the relationship between the period and amplitude of a simple pendulum under magnetic action. The analytical solution presented for the given problem. Two numerical quadrature methods Simpson's and Boole's method were utilized to demonstrate a new approximation of the problem. The results of the numerical quadrature have been compared to the exact solution. Absolute and relative mistakes of the problem have been presented. The Matlab program 2013R has created a numerical method that is used to analyze the outcome, It has been determined that the comparison's outcomes attest to the method's suitability and correctness. Moreover, the results show that numerical solution is suitable for the problem.

Rollover prevention of partially-filled tank trucks is an industry teaser, with the core challenge being real-time perception and observation of the liquid state inside the tank. In order realize re-liable observation of sloshing liquid, this article firstly proposes a sloshing modeling method based on multi-degree-of-freedom pendulum model, and derives the double mass trammel pendulum model (DMTP, 2DOF) accordingly, which accurately reflects the sloshing dynamics under more pervasive working conditions. Secondly, a free surface fluctuation sensor is designed based on magnetostriction, capable of measuring the inclination and height of the liquid level inside tanks filled with hazardous chemical. Finally, the unscented Kalman filter (UKF) is utilized to synthesize the information of the two, establishing a credible real-time observation of the sloshing liquid. Verified through vehicle-fluid coupled co-simulation, under condition of con-secutive double lane change, observation error of the proposed method is only 25.9% that of the open-loop calculation, providing a secure guarantee for the observation of the state variables of the single pendulum model (SP) used for most kinds of anti-rollover controller.

In this paper, the stability control of the inverted pendulum on a cart with a disturbance forces has been done using observer based and full state feedback H2 controllers. The Lagrangian equation has been used to model the system equation of motions and linearized the system to the unstable upward position. Comparison of the system stability has been simulated by comparing the proposed controllers using Matlab/Scripts and a promising results has been analyzed successfully.

Classically the walk in biped robotics was obtained controlling balance during the whole step, i.e. guaranteeing that the pressure point under the soles always stayed in the polygon of the supporting feet. However, this assumed that the feet were able to transfer torque to the ground during the whole gait cycle. In spite of the fact that the amount of transferrable torque in the feet-ground contact is limited, it is possible only during some phases of the step, and the overall process is energetically inefficient. On the other side, starting from the passive motion of the rimless wheel falling on an inclined surface, and ending to the inverted pendulum with a compass, balance in the whole was proven in spite of dynamical instability inside each step. Along this line results of Foot Placement Estimation (FPE) in 2-D and 3-D showed how energy efficient walk was possible, emulating the human walk with a free fall on the swing foot and energy restitution at the foot collision with the ground for the next step. This model assumes pointy feet, so without torque transfer to the ground. In the realm of FPE, in previous papers the present author adopted the 3-D inverted pendulum in polar coordinates (Spherical Inverted Pendulum - SIP) to introduce omnidirectional walks with arbitrarily changing characteristics. No torque control was used during the step, i.e the pendulum was always in free fall at each step, the only control actions were at the beginning of the next step. These actions are: the change of angular velocities at the start of a new step, with respect to those given after the collision (emulating the torque action in the brief double stance period), to recover for the losses, and the preparation of the position in the frontal and sagittal planes of the swing foot for the next collision. The present paper improves this paradigm, proposing a general model to account for all characteristics of the biped and of the gait, with adding a minimum of dynamical complexity with respect to the SIP. This model allows, not only to walk omnidirectionally on a flat surface, but also to go up and down staircases.

This work explores state-of-the-art approaches for stabilizing an inverted pendulum on a cart system, which has been used for over a century to demonstrate ideas in nonlinear and linear control theory, owing to its simple practical implementation yet complex system dynamics. We introduce energy-based control methods and propose a simple linear controller to quickly force the system to the downward equilibrium before swing-up. By constraining the system to start from a stable equilibrium configuration, the problem of global stability is reduced to ensuring that the system can follow all heteroclinic orbits that start very close to the downward equilibrium. Multiple Lyapunov functions are employed to ensure non-zero tracking, increasing the system's domain of attraction than is achieved by traditional controllers based on a single Lyapunov function. We stabilize our inverted pendulum system in the upright configuration through pole placement using a linear quadratic regulator known for fast settling times and smooth system response and through sliding mode controllers known for their robustness to disturbances and model uncertainties. While sliding mode controllers exhibit faster stabilization of the pendulum angle, they fail to stabilize the cart position in a reasonable amount of time. The paper concludes by suggesting various controller techniques that can enhance the swing-up and stabilization controller architectures, leaving room for future exploration. To facilitate further research and education, an open-source MATLAB simulation code is provided, encapsulating the system dynamics and controller designs. This resource offers flexibility for customization, making it a valuable tool for both researchers and educators working with inverted pendulum systems.

In this paper a full state feedback control of a double inverted pendulum on a cart (DIPC) are designed and compared. Modeling is based on Euler-Lagrange equations derived by specifying a Lagrangian, difference between kinetic and potential energy of the DIPC system. A full state feedback control with H infinity and H 2 is addressed. Two approaches are tested: open loop impulse response and a double inverted pendulum on a cart with full state feedback H infinity and H 2 controllers. Simulations reveal superior performance of the double inverted pendulum on a cart with full state feedback H infinity controller.

In this paper we give approximations to the Mittag-Leffler functions in terms of elementary functions using different methods. This allowed us to establish a practical method we called integerization principle. This principle states that many fractional nonlinear oscillators may be solved by means of the solution to some integer-order Duffing oscillator equation. The accuracy of the obtained results is illsutrated in concrete examples. Formulas for estimating the errors in the approximations are also provided.