Multistability in the Centrifugal Governor System Under a Time-Delay Control Strategy

2019 ◽  
Vol 14 (11) ◽  
Author(s):  
Shuning Deng ◽  
Jinchen Ji ◽  
Shan Yin ◽  
Guilin Wen
Keyword(s):  
Time Delay ◽  
Control Strategy ◽  
Large Amplitude ◽  
Stability Boundary ◽  
Physical Parameters ◽  
Time Delay Control ◽  
Delay Control ◽  
Delayed Feedback Controller ◽  
Trivial Equilibrium ◽  
The Stability

Abstract The centrifugal governor system plays an indispensable role in maintaining the near-constant speed of engines. Although different arrangements have been developed, the governor systems are still applied in many machines for its simple mechanical structure. Therefore, the large-amplitude vibrations of the governor system which can lead to the function failure of the system should be attenuated to guarantee reliable operation. This paper adopts a time-delay control strategy to suppress the undesirable large-amplitude motions in the centrifugal governor system, which can be regarded as the practical application of the delayed feedback controller in this system. The stability region of the trivial equilibrium of the controlled system is determined by investigating the characteristic equation and generic Hopf bifurcations. It is found that the dynamic behavior of multistability can be induced by the Bautin bifurcation, arising on the stability boundary of the trivial equilibrium with a constant delay. More specifically, a coexistence of two desirable stable motions, i.e., an equilibrium or a small-amplitude periodic motion, can be observed in the controlled centrifugal governor system without changing the physical parameters. This is a new feature of the motion control in the centrifugal governor systems, which has not yet been reported in the existing studies. Finally, the results of theoretical analyses are verified by numerical simulations.

Control of Uncertain LTI Systems Based on an Uncertainty and Disturbance Estimator

2004 ◽  
Vol 126 (4) ◽  
pp. 905-910 ◽  
Author(s):  
Qing-Chang Zhong ◽  
David Rees
Keyword(s):  
Time Delay ◽  
Robust Control ◽  
Robust Stability ◽  
Control Strategy ◽  
Time Delay Control ◽  
Delay Control ◽  
Uncertainty And Disturbance Estimator ◽  
Derivatives Of ◽  
Siso Systems ◽  
Disturbance Estimator

This paper proposes a robust control strategy for uncertain LTI systems. The strategy is based on an uncertainty and disturbance estimator (UDE). It brings similar performance as the time-delay control (TDC). The advantages over TDC are: (i) no delay is introduced into the system; (ii) there are no oscillations in the control signal; and (iii) there is no need of measuring the derivatives of the state vector. The robust stability of LTI-SISO systems is analyzed, and simulations are given to show the effectiveness of the UDE-based control with a comparison made with TDC.

Stability of Uncertain Linear Systems With Time Delay

1991 ◽  
Vol 113 (4) ◽  
pp. 558-567 ◽  
Author(s):  
K. Youcef-Toumi ◽  
J. Bobbett
Keyword(s):  
Time Delay ◽  
Linear Time ◽  
Sufficient Condition ◽  
Single Input Single Output ◽  
Time Delay Control ◽  
Linear Time Invariant ◽  
Single Output ◽  
Uncertain Dynamics ◽  
Delay Control ◽  
The Stability

The control of systems with uncertain dynamics and unpredictable disturbances has raised some challenging problems. This is particularly important when high system performance is to be guaranteed at all times. Recently, Time Delay Control has been suggested as an alternative control scheme. The proposed control system does not require an explicit plant model nor does it depend on the estimation of specific plant parameters. Rather, it combines adaptation with past observations to directly estimate the effect of the plant dynamics. This paper outlines the Time Delay Control law for a class of linear dynamic systems and then presents a sufficient condition for stability of linear uncertain systems with time delay. The ideas of Nyquist and Kharitonov are used in the development of a sufficient condition, which does not resort to using approximations for time delay. Like Nyquist, the condition depends on maps of the Nyquist path and, like Kharitonov, stability depends on four functions each yielding a stable system. In this paper we combine these ideas to determine the stability of systems where the Time Delay Controller is applied to single input single output, linear time-invariant plants whose coefficients are known to vary within certain defined intervals. The development is carried out in the context of Time Delay Control but it can be applied in more general cases. Two examples will illustrate the approach and the usefulness of the technique.

scholarly journals Velocity-Free Adaptive Time Delay Control of Robotic System

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Shini Chen ◽  
Xia Liu
Keyword(s):  
Time Delay ◽  
Large Time ◽  
Complex Dynamics ◽  
Time Delay Estimation ◽  
Robotic System ◽  
Time Delay Control ◽  
System A ◽  
Delay Control ◽  
Adaptive Time ◽  
The Stability

To improve the trajectory tracking performance of a complex nonlinear robotic system, a velocity-free adaptive time delay control is proposed. First, considering that conventional time delay control (TDC) may cause large time delay estimation (TDE) error under nonlinear friction, a TDC with gradient estimator is designed. Next, since it is complicated and time-consuming to adjust gains manually, an adaptive law is designed to estimate the gain of the gradient. Finally, in order to avoid the measurement of velocity and acceleration in the controller while enabling the robot to implement position tracking, an observer is designed. The proposed control can not only offset the nonlinear terms in the complex dynamics of the robotic system but also reduce the TDE error, estimate the gain of the gradient online, and avoid the measurement of velocity and acceleration. The stability of the system is analyzed via Lyapunov function. Simulations are conducted on a 2-DOF robot to verify the effectiveness of the proposed control.

Time-delay control of a switchable stiffness system

2015 ◽  
Vol 23 (15) ◽  
pp. 2375-2390 ◽  
Author(s):  
Thai Tran ◽  
Kefu Liu
Keyword(s):  
Time Delay ◽  
Control Strategy ◽  
Control Strategies ◽  
Oscillation Period ◽  
Control Law ◽  
System Delay ◽  
Single Degree Of Freedom ◽  
Time Delay Control ◽  
Single Degree ◽  
Delay Control

This paper focuses on suppression of free vibration of single degree-of-freedom systems that possess time delay. The switchable stiffness (SS) control strategy is reviewed. The implication of time delay is examined. It shows that the system delay can cause malfunction of the direct SS control. To overcome this problem, the two time-delay control strategies are proposed. The first strategy named as half period delay SS control introduces an intentional delay such that the switch action takes place in a half of oscillation period later. The second strategy named as quarter period delay SS control is to add an intentional delay such that the switch action occurs in a quarter of oscillation period later. In this case, the SS control law is inverted. An apparatus consisting of an electromagnetic (EM) spring is developed to validate the proposed strategies. The stiffness models of the system are established. In computer simulation, three cases have been examined. In case A, the system is simplified as linear and the dynamics of the EMs is neglected. In case B, the stiffness models are used and the dynamics of the EMs is neglected. In case C, the stiffness models are used and the dynamics of the EMs is considered. An experimental study is conducted in real time. The results have validated the observations obtained from the computer simulations.

scholarly journals The Development of Anti-Windup Scheme for Time Delay Control With Switching Action Using Integral Sliding Surface

2003 ◽  
Vol 125 (4) ◽  
pp. 630-638 ◽  
Author(s):  
Sung-Uk Lee ◽  
Pyung Hun Chang
Keyword(s):  
Time Delay ◽  
Sliding Mode ◽  
Control Area ◽  
Time Delay Estimation ◽  
Sliding Surface ◽  
Time Delay Control ◽  
Delay Control ◽  
Switching Action ◽  
Integral Sliding Surface ◽  
The Stability

The Time Delay Control with Switching Action (TDCSA) method, which consists of Time Delay Control (TDC) and a switching action of sliding mode control (SMC), has been proposed as a promising technique in the robust control area where the plant has an unknown dynamics with parameter variations and substantial disturbances are preset. When TDCSA is applied to the plant with saturation nonlinearity, however, the so-called windup phenomenon is observed to arise, causing excessive overshoot and instability. The integral element of TDCSA and the saturation element of a plant cause the windup phenomenon. There are two integral effects in TDCSA. One is the integral effect caused by time delay estimation of TDC. The other is the integral term of an integral sliding surface. To solve this problem, we have proposed an anti-windup scheme method for TDCSA. The stability of the overall system has been proved for a class of nonlinear system. Experimental results show that the proposed method overcomes the windup problem of the TDCSA.

Optimal Time-Delay Control for Multi-Degree-of-Freedom Nonlinear Systems Excited by Harmonic and Wide-Band Noises

2021 ◽  
pp. 2150053
Author(s):  
Rongchun Hu ◽  
Qiangfeng Lü
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Control Strategy ◽  
Wide Band ◽  
Stochastic Averaging ◽  
Degree Of Freedom ◽  
Optimal Time ◽  
Time Delay Control ◽  
Strongly Nonlinear ◽  
Delay Control

In this paper, an optimal time-delay control strategy is designed for multi-degree-of-freedom (multi-DOF) strongly nonlinear systems excited by harmonic and wide-band noises. First, by using the generalized harmonic functions, a stochastic averaging method (SAM) is employed for the time-delay controlled strongly nonlinear system under combined harmonic and wide-band noise excitations, by which a set of partially averaged Itô equations are obtained. Then, by solving the dynamical programming equation associated with the partially averaged Itô equations, the optimal control law can be obtained. Finally, by solving the Fokker–Planck–Kolmogorov (FPK) equation, the responses of the optimally time-delay controlled system are predicted. The analytical results are compared with the Monte Carlo simulation to verify the effectiveness and efficiency of the proposed control strategy.

scholarly journals Time-delay control for stabilization of the Shapovalov mid-size firm model

2020 ◽  
Vol 53 (2) ◽  
pp. 16971-16976
Author(s):  
T.A. Alexeeva ◽  
W.A. Barnett ◽  
N.V. Kuznetsov ◽  
T.N. Mokaev
Keyword(s):  
Time Delay ◽  
Time Delay Control ◽  
Delay Control ◽  
Size Firm ◽  
Firm Model
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