Optimization algorithm and simulation analysis of feedback control parameters of equilibrium point about linear spring-connected double inverted pendulum

2011 ◽  
Author(s):  
Xianglin Hou ◽  
Cong Chen ◽  
Ye Fei
Keyword(s):  
Feedback Control ◽  
Equilibrium Point ◽  
Optimization Algorithm ◽  
Inverted Pendulum ◽  
Simulation Analysis ◽  
Control Parameters ◽  
Linear Spring

IMPLICIT CRITERIA OF EIGENVALUE ASSIGNMENT AND TRANSVERSALITY FOR BIFURCATION CONTROL IN FOUR-DIMENSIONAL MAPS

2004 ◽  
Vol 14 (10) ◽  
pp. 3489-3503 ◽  
Author(s):  
GUILIN WEN ◽  
DAOLIN XU
Keyword(s):  
Feedback Control ◽  
Unit Circle ◽  
Jacobian Matrix ◽  
Transversality Condition ◽  
Delayed Feedback Control ◽  
High Dimensional ◽  
Control Parameters ◽  
Washout Filter ◽  
New Criteria ◽  
Eigenvalue Assignment

In anti-control of bifurcations, it is common to create different types of bifurcations by adjusting the control parameters. For maps, the type of bifurcation is determined by the eigenvalue assignment on the unit circle at the bifurcation parameter point. Thus, an unavoidable problem in the creation of bifurcations is to desirably assign some eigenvalues at the specified locations on the unit circle, and the others inside the unit circle. However, for relatively complicated and high dimensional maps, the explicit expressions of eigenvalues are usually not available so that the implementation of the eigenvalue assignment becomes very difficult. To solve this problem, we proposed the new criteria of eigenvalue assignment without using eigenvalues. The criteria give implicit conditions to specify the eigenvalue assignments in terms of some simple algebraic equalities and inequalities associated with the elements of Jacobian matrix, i.e. eventually associated with the control parameters. Bifurcation occurs with another critical condition, the transversality condition. The computation of the transversality condition is usually nontrivial in high dimensional maps because it is related to the partial differentiation of the eigenvalues on the unit circle. We also present the implicit expression of the transversality condition in the form of the derivative of the Jacobian matrix and its eigenvectors that are computable at the bifurcation point. The proposed criteria cover most known types of bifurcations in four-dimensional maps and serve as the preferable methods for designing the critical bifurcation conditions in anti-control of bifurcations. The application to a modified Hénon map is illustrated in conjunction with the use of the delayed-feedback control and the washout-filter-aided feedback control.

Modified PD Control of Rotary Inverted Pendulum

2009 ◽  
Author(s):  
Naserodin Sepehry ◽  
Mahnaz Shamshirsaz
Keyword(s):  
Feedback Control ◽  
Inverted Pendulum ◽  
Break Point ◽  
State Feedback Control ◽  
Pd Controller ◽  
Loop Transfer Function ◽  
Full State ◽  
Full State Feedback ◽  
Rotary Inverted Pendulum ◽  
Space Method

The inverted pendulum, a classical mechatronic application, exists in many different forms. In despite that many works have been done to balance the pendulum link on end of this device using feedback control but few studies have been developed to control this rotary inverted pendulum using PD controller. In classical methods, using PD, PI or PID control, difficulties appear due to one of the coefficients becomes zero in closed loop transfer function denominator and consequently the system becomes unstable. In this study, an arbitrary pole is placed in order to create a break point in root locus, so by this way a PD controller can be designed for this new system. Also, disturbance rejection has been investigated by state space method in this paper. The results of this modified PD controller are compared with full state feedback control and optimal control, so the method used in this study has been validated.

Output error MISO system identification using fractional models

2021 ◽  
Vol 24 (5) ◽  
pp. 1601-1618
Author(s):  
Abir Mayoufi ◽  
Stéphane Victor ◽  
Manel Chetoui ◽  
Rachid Malti ◽  
Mohamed Aoun
Keyword(s):  
System Identification ◽  
Optimization Algorithm ◽  
Simulation Analysis ◽  
Good Efficiency ◽  
Output Error ◽  
Single Output ◽  
Multiple Input ◽  
Fractional Models ◽  
Definition Of ◽  
Initialization Procedure

Abstract This paper deals with system identification for continuous-time multiple-input single-output (MISO) fractional differentiation models. An output error optimization algorithm is proposed for estimating all parameters, namely the coefficients and the differentiation orders. Given the high number of parameters to be estimated, the output error method can converge to a local minimum. Therefore, an initialization procedure is proposed to help the convergence to the optimum by using three variants of the algorithm. Moreover, a new definition of structured-commensurability (or S-commensurability) has been introduced to cope with the differentiation order estimation. First, a global S-commensurate order is estimated for all subsystems. Then, local S-commensurate orders are estimated (one for each subsystem). Finally the S-commensurability constraint being released, all differentiation orders are further adjusted. Estimating a global S-commensurate order greatly reduces the number of parameters and helps initializing the second variant, where local S-commensurate orders are estimated which, in turn, are used as a good initial hit for the last variant. It is known that such an initialization procedure progressively increases the number of parameters and provides good efficiency of the optimization algorithm. Monte Carlo simulation analysis are provided to evaluate the performances of this algorithm.

An optimal control method for time-delay feedback control of 1/4 vehicle active suspension under random excitation

2021 ◽  
pp. 146134842110592
Author(s):  
Kaiwei Wu ◽  
Chuanbo Ren ◽  
Yuanchang Chen
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Control Method ◽  
Harmonic Excitation ◽  
Random Excitation ◽  
Vehicle Body ◽  
Vehicle Suspension ◽  
Control Parameters ◽  
Damping Effect ◽  
Delay Feedback Control

Time-delay feedback control can effectively broaden the damping frequency band and improve the damping efficiency. However, the existing time-delay feedback control strategy has no obvious effect on multi-frequency random excitation vibration reduction control. That is, when the frequency of external excitation is more complicated, there is no better way to obtain the best time-delay feedback control parameters. To overcome this issue, this paper is the first work of proposing an optimal calculation method that introduces stochastic excitation into the process of solving the delay feedback control parameters. It is a time-delay control parameter with a better damping effect for random excitation. In this paper, a 2 DOF one-quarter vehicle suspension model with time-delay is studied. First, the stability interval of time-delay feedback control parameters is solved by using the Lyapunov stability theory. Second, the optimal control parameters of the time-delay feedback control under random excitation are solved by particle swarm optimization (PSO). Finally, the simulation models of a one-quarter vehicle suspension simulation model are established. Random excitation and harmonic excitation are used as inputs. The response of the vehicle body under the frequency domain damping control method and the proposed control method is compared and simulated. To make the control precision higher and the solution speed faster, this paper simulates the model by using the precise integration method of transient history. The simulation results show that the acceleration of the vehicle body in the proposed control method is 13.05% less than the passive vibration absorber under random excitation. Compared with the time-delay feedback control optimized by frequency response function, the damping effect is 12.99%. The results show that the vibration displacement, vibration velocity, and vibration acceleration of the vehicle body are better than the frequency domain function optimization method, whether it is harmonic excitation or random excitation. The ride comfort of the vehicle is improved obviously. It provides a valuable tool for time-delay vibration reduction control under random excitation.

Research on vibration reduction of semi-active suspension system of quarter vehicle based on time-delayed feedback control with body acceleration

2021 ◽  
pp. 146134842110518
Author(s):  
Yong Guo ◽  
Chuanbo Ren
Keyword(s):  
Feedback Control ◽  
Delayed Feedback ◽  
Suspension System ◽  
Delayed Feedback Control ◽  
Vehicle Body ◽  
Vehicle Suspension ◽  
Vertical Acceleration ◽  
Control Parameters ◽  
Vehicle Suspension System ◽  
Time Delayed Feedback

In this paper, the mechanical model of two-degree-of-freedom vehicle semi-active suspension system based on time-delayed feedback control with vertical acceleration of the vehicle body was studied. With frequency-domain analysis method, the optimization of time-delayed feedback control parameters of vehicle suspension system in effective frequency band was studied, and a set of optimization method of time-delayed feedback control parameters based on “equivalent harmonic excitation” was proposed. The time-domain simulation results of vehicle suspension system show that compared with the passive control, the time-delayed feedback control based on the vertical acceleration of the vehicle body under the optimal time-delayed feedback control effectively broadens the vibration absorption bandwidth of the vehicle suspension system. The ride comfort and stability of the vehicle under random road excitation are significantly improved, which provides a theoretical basis for the selection of time-delayed feedback control strategy and the optimal design of time-delayed feedback control parameters of vehicle suspension system.

Optimal design of adaptive and proportional integral derivative controllers using a novel hybrid particle swarm optimization algorithm

2020 ◽  
Vol 42 (8) ◽  
pp. 1492-1510
Author(s):  
Elham Yazdani Bejarbaneh ◽  
Arash Hosseinian Ahangarnejad ◽  
Ahmad Bagheri ◽  
Behnam Yazdani Bejarbaneh ◽  
Binh Thai Pham ◽  
...  
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Algorithm ◽  
Inverted Pendulum ◽  
Particle Swarm Optimization Algorithm ◽  
Particle Swarm ◽  
Swarm Optimization ◽  
Pendulum System ◽  
Hybrid Particle ◽  
Inverted Pendulum System ◽  
Hybrid Particle Swarm Optimization

Controlling of a rotational inverted pendulum is considered as a challenging problem, mainly due to the system’s inherent nonlinear and unstable dynamics. In fact, the goal of this control is to maintain the pendulum vertically upward regardless of external disturbances. This paper aims to optimally design a model reference adaptive proportional integral derivative (PID) control for rotary inverted pendulum system based on a novel hybrid particle swarm optimization algorithm, combining sine cosine algorithm and levy flight distribution. Evaluation of the performance quality of the proposed adaptive controller is accomplished based on the stabilization and tracking control of rotary inverted pendulum system. In addition, two other PID controllers are designed to get a better understanding of the performance and robustness of the proposed controller. To make a complete comparison, the performance of the hybrid particle swarm optimization algorithm is examined against two other optimization techniques known as simple particle swarm optimization and whale optimization algorithm. Finally, the obtained simulation results demonstrate that the proposed optimal adaptive controller is superior to the other controllers, especially in terms of the transient response characteristics and the magnitude of control output signal.

Investigating the Nonlinear Dynamics of Human Balance Using Topological Data Analysis

2020 ◽  
Vol 15 (9) ◽  
Author(s):  
Kyle W. Siegrist ◽  
Ryan M. Kramer ◽  
James R. Chagdes
Keyword(s):  
Time Series ◽  
Postural Stability ◽  
Inverted Pendulum ◽  
Balance Control ◽  
Neuromuscular Diseases ◽  
Neuromuscular Control ◽  
Topological Data Analysis ◽  
Control Parameters ◽  
Human Balance ◽  
Neuromuscular Impairment

Abstract Understanding the mechanisms behind human balance has been a subject of interest as various postural instabilities have been linked to neuromuscular diseases (e.g., Parkinson's, multiple sclerosis, and concussion). This paper presents a method to characterize an individual's postural stability and estimate of their neuromuscular feedback control parameters. The method uses a generated topological mapping between a subject's experimental data and a dataset consisting of time-series realizations generated using an inverted pendulum mathematical model of upright balance. The performance of the method is quantified using a set of validation time-series realizations with known stability and neuromuscular control parameters. The method was found to have an overall sensitivity of 85.1% and a specificity of 91.9%. Furthermore, the method was most accurate when identifying limit cycle oscillations (LCOs) with a sensitivity of 91.1% and a specificity of 97.6%. Such a method has the capability of classifying an individual's stability and revealing possible neuromuscular impairment related to balance control, ultimately providing useful information to clinicians for diagnostic and rehabilitation purposes.

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