Rotations of Pendulum When Its Pivot Oscillates Chaotically

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Sze-Hong Teh ◽  
Ko-Choong Woo ◽  
Hazem Demrdash
Keyword(s):  
Control Method ◽  
Piecewise Linear ◽  
Control Input ◽  
Velocity Control ◽  
Chaotic Oscillations ◽  
Vertical Excitation ◽  
Stiffness Characteristic ◽  
Adjustable Mechanism ◽  
Piecewise Linear Stiffness ◽  
Excitation Conditions

This paper investigates the possibility of energy generation via pendulum rotations when the source of vertical excitation is chaotic in nature. The investigations are conducted using an additional height-adjustable mechanism housing a secondary spring to optimize a configuration of experimental pendulum setup. Chaotic oscillations of the pendulum pivot are made possible at certain excitation conditions due to a piecewise-linear stiffness characteristic introduced by the modification. A velocity control method is applied to maintain the rotational motion of the pendulum as it interacts with the vertical oscillator. The control input is affected by a motor, and a generator is used to quantify the energy extraction. The experimental results imply the feasibility of employing a pendulum device in a chaotic vibratory environment for energy harvesting purpose.

A Nonlinear Optimal Control Approach for the Vertical Take-off and Landing Aircraft

2021 ◽  
pp. 2150012
Author(s):  
G. Rigatos
Keyword(s):  
Optimal Control ◽  
Control Method ◽  
Nonlinear Optimal Control ◽  
The Body ◽  
Algebraic Riccati Equation ◽  
Control Input ◽  
Time Step ◽  
Control Approach ◽  
Vtol Aircraft ◽  
Optimal Control Approach

The paper proposes a nonlinear optimal control approach for the model of the vertical take-off and landing (VTOL) aircraft. This aerial drone receives as control input a directed thrust, as well as forces acting on its wing tips. The latter forces are not perpendicular to the body axis of the drone but are tilted by a small angle. The dynamic model of the VTOL undergoes approximate linearization with the use of Taylor series expansion around a temporary operating point which is recomputed at each iteration of the control method. For the approximately linearized model, an H-infinity feedback controller is designed. The linearization procedure relies on the computation of the Jacobian matrices of the state-space model of the VTOL aircraft. The proposed control method stands for the solution of the optimal control problem for the nonlinear and multivariable dynamics of the aerial drone, under model uncertainties and external perturbations. For the computation of the controller’s feedback gains, an algebraic Riccati equation is solved at each time-step of the control method. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the VTOL aircraft, under moderate variations of the control inputs. The stability properties of the control scheme are proven through Lyapunov analysis.

Chaotic Gyros Synchronization

2011 ◽  
pp. 183-209
Author(s):  
M. Roopaei ◽  
M. J. Zolghadri ◽  
B. S. Ranjbar ◽  
S. H. Mousavi ◽  
H. Adloo ◽  
...  
Keyword(s):  
Sliding Mode Control ◽  
Control Method ◽  
Fuzzy Controller ◽  
Sliding Mode ◽  
Dead Zone ◽  
Control Input ◽  
Mode Control ◽  
Fuzzy Sliding Mode ◽  
Robust Adaptive ◽  
Fuzzy Parameter

In this chapter, three methods for synchronizing of two chaotic gyros in the presence of uncertainties, external disturbances and dead-zone nonlinearity are studied. In the first method, there is dead-zone nonlinearity in the control input, which limits the performance of accurate control methods. The effects of this nonlinearity will be attenuated using a fuzzy parameter approximator integrated with sliding mode control method. In order to overcome the synchronization problem for a class of unknown nonlinear chaotic gyros a robust adaptive fuzzy sliding mode control scheme is proposed in the second method. In the last method, two different gyro systems have been considered and a fuzzy controller is proposed to eliminate chattering phenomena during the reaching phase of sliding mode control. Simulation results are also provided to illustrate the effectiveness of the proposed methods.

scholarly journals Fuzzy adaptive nonlinear stochastic control for vehicle suspension with electromagnetic actuator

2020 ◽  
Vol 53 (7-8) ◽  
pp. 1364-1375
Author(s):  
Feng Cao ◽  
Yongming Li
Keyword(s):  
Control Method ◽  
Reference Model ◽  
Design Procedure ◽  
Lyapunov Stability Theory ◽  
Vehicle Suspension ◽  
Mean Value Theorem ◽  
Electromagnetic Actuator ◽  
Control Input ◽  
Fuzzy Logic Systems ◽  
Stochastic Disturbance

This work solves the stability problem of a vehicle suspension with stochastic disturbance by designing an adaptive controller. The model of a quarter vehicle subjected to noise excitation is considered. The stochastic perturbance is realized by the roughness of the road and the vehicle moving with constant velocity. In the control design procedure, fuzzy logic systems are used to approximate unknown nonlinear functions. Meanwhile, the mean value theorem is employed to ensure the existence of the affine virtual control variables and control input. The backstepping technique is applied to construct the ideal controller. On the basis of Lyapunov stability theory, the proposed control method proves that the displacement and speed of the vehicle is reduced to a level ascertained by a true “desired” conceptual suspension reference model. Finally, the effectiveness of the proposed method is verified by simulation of electromagnetic actuator servo system.

scholarly journals Finite Time Stability of Finance Systems with or without Market Confidence Using Less Control Input

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Chao Ma ◽  
Yujuan Tian ◽  
Zhongfeng Qu
Keyword(s):  
Finite Time ◽  
Chaotic Systems ◽  
Control Method ◽  
Control Input ◽  
Three Dimension ◽  
Time Stability ◽  
Finance System ◽  
Finite Time Stability ◽  
Single Controller ◽  
Simulation Results

In this paper, we make an exploration of a technique to control a class of finance chaotic systems. This technique allows one to achieve the finite time stability of the finance system more effectively with less control input energy. First, the finite time stability of three dimension finance system without market confidence is analyzed by using a single controller. Then, two controllers are designed to stabilize the four-dimension finance system with market confidence. Moreover, the finite time stability of the three-dimension and four-dimension finance system with unknown parameter is also studied. Finally, simulation results are presented to show the chaotic behaviour of the finance systems, verify the effectiveness of the proposed control method, and illustrate its advantages compared with other methods.

scholarly journals Underactuated robotics: A review

2019 ◽  
Vol 16 (4) ◽  
pp. 172988141986216 ◽  
Author(s):  
Bin He ◽  
Shuai Wang ◽  
Yongjia Liu
Keyword(s):  
Control Method ◽  
Constraint Equation ◽  
Research Direction ◽  
Control Flow ◽  
Future Research ◽  
Control Input ◽  
Research Directions ◽  
Loop Control ◽  
Future Research Directions ◽  
Underactuated Robot

Underactuated robotics is an emerging research direction in the field of robotics. The control input of the underactuated robot is less than the degree of freedom of the system. It has the advantages of lightweight, low energy consumption, excellent performance, and broad development prospects. This article reviews the state of the art on underactuated robotics. On the basis of previous studies, this article takes the non-holonomic constraint equation as the entry point to classify and summarize underactuated robot and their common mechanisms. The controllability of underactuated robot is further discussed. The control flow of underactuated robot is described based on the open–closed control method. In the closed-loop control, the control method based on the fuzzy system is mainly used. Finally, the difficulties in the current research of underactuated robot are summarized, and the future research directions are prospected.

scholarly journals A fast vibration-level adjustment method for low-frequency vibration calibration based on modified filtered-x least mean square algorithm

2020 ◽  
Vol 53 (3-4) ◽  
pp. 328-338
Author(s):  
Chao Li ◽  
Zhangwei Chen
Keyword(s):  
Control Method ◽  
Low Frequency ◽  
Successive Approximation Method ◽  
Control Input ◽  
Mean Square ◽  
Least Mean Square ◽  
Vibration Level ◽  
Calibration System ◽  
Low Frequency Vibration ◽  
Least Mean Square Algorithm

Traditionally, successive approximation method is applied to the vibration-level adjustment of vibration calibration system, which leads to a time-consuming work for low-frequency vibration calibration. In this paper, a novel control method for low-frequency vibration calibration system is proposed based on adaptive filter. First, the problem of the traditional vibration-level adjustment for low-frequency signals is depicted. Then, an adaptive control algorithm is presented, in which the control input is composed of two weighted sinusoidal signals with a phase difference of 90°. The weighted vector is updated in real time using a modified filtered-x least mean square algorithm. Unlike filtered-x least mean square algorithm, the proposed modified filtered-x least mean square algorithm does not require a pre-identification of the controlled system and has a reduced computational complexity. The convergence property of the proposed method is analyzed in detail. Finally, the proposed method is implemented on a low-frequency vibration calibration system. Experimental results show that the proposed modified filtered-x least mean square algorithm can significantly reduce the time of the vibration-level adjustment in low-frequency band.

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