scholarly journals Stabilization of Linear Sampled-Data Systems by a Time-Delay Feedback Control

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
F. Ricardo García ◽  
Baltazar Aguirre ◽  
Rodolfo Suárez
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Sufficient Conditions ◽  
Sampling Period ◽  
Fixed Time ◽  
Feedback Gain ◽  
Data Systems ◽  
Sampled Data ◽  
Sampled Signal ◽  
Time Invariant

We consider one-dimensional, time-invariant sampled-data linear systems with constant feedback gain, an arbitrary fixed time delay, which is a multiple of the sampling period and a zero-order hold for reconstructing the sampled signal of the system in the feedback control. We obtain sufficient conditions on the coefficients of the characteristic polynomial associated with the system. We get these conditions by finding both lower and upper bounds on the coefficients. These conditions let us give both an estimation of the maximum value of the sampling period and an interval on the controller gain that guarantees the stabilization of the system.

Stability Criteria for Distributed Nonlinear Sampled-Data Systems Defined by Green’s Functions

1974 ◽  
Vol 96 (3) ◽  
pp. 315-321 ◽  
Author(s):  
G. Jumarie
Keyword(s):  
Stability Criterion ◽  
Feedback Gain ◽  
Continuous Systems ◽  
Mean Square ◽  
Data Systems ◽  
Sampled Data ◽  
Input Output ◽  
Output Stability ◽  
Lumped Parameter ◽  
The Mean

Sampled-data, nonlinear, distributed systems, which exhibit a structure similar to that of the standard closed loop with lumped parameter, are investigated from the viewpoint of their input-output stability. These systems are governed by operational equations involving discrete Laplace-Green kernels. Their feedback gains are bounded by upper and lower values which depend explicitly on the time and the distributed parameter. The main result is: an input-output stability theorem is given which applies both in L∞ (O, ∞) and L2 (O, ∞). This criterion, which may be considered as being an extension of the ≪circle criterion≫, involves the mean square value on the bounds of the feedback gain. Stability conditions for continuous systems are derived from this result. In the special case of systems with distributed periodical time-varying feedback gains, a stability criterion is given which applies in Marcinkiewicz space M2 (O, ∞). This result which involves the mean square value of the feedback gain is generally less restrictive than the L2 (O, ∞) stability criterion mentioned above.

Continuous control of sampled data systems with robustness against bounded measurement errors

2017 ◽  
Vol 40 (10) ◽  
pp. 3125-3133
Author(s):  
Milad Ghanbari ◽  
Masoud Bahraini ◽  
Mohammad Javad Yazdanpanah
Keyword(s):  
Measurement Errors ◽  
Control Method ◽  
Linear Time ◽  
Continuous Control ◽  
Data Systems ◽  
Sampled Data ◽  
Linear Time Invariant ◽  
Experimental Implementation ◽  
Time Invariant ◽  
Ultimate Bound

This paper considers the design of a generalized hold function to be used for the control of sampled-data systems. The proposed method suggests a continuous controller for sampled data systems. Ultimate boundedness of the proposed method in the presence of bounded measurement errors is also shown for linear and nonlinear systems. In linear time invariant cases, a cost function is suggested for the sake of ultimate bound minimization. In addition, this can answer how we choose a sensor for a real system to get a desired control outcome. Eventually, the effectiveness of the proposed control method is investigated through simulation and experimental implementation.

Minimum Time Control of Second Order Pulse-Width-Modulated Sampled-Data Systems

1962 ◽  
Vol 84 (1) ◽  
pp. 101-109 ◽  
Author(s):  
E. Polak
Keyword(s):  
Pulse Width ◽  
Phase Plane ◽  
Sampling Period ◽  
Second Order ◽  
Data Systems ◽  
Sampled Data ◽  
Relay System ◽  
Pulse Width Modulated ◽  
Minimal Time ◽  
Time Control

This paper treats the minimal time control problem for two second order pulse-width-modulated sampled-data systems, one with a double integrator type plant and one with a plant described by an integral and a time constant. Such plants are encountered in systems with hydraulic components. It is shown rigorously that for minimal time control the phase plane can be divided into two regions: a striplike region around the optimal switching trajectory for a continuous relay system with the same plants, in which the pulse width must be adjusted for optimal action; and the rest of the phase plane in which an optimal p.w.m. system of the type described behaves like a continuous optimal relay system, the pulse duration being equal to the sampling period. A brief description of an electromechanical computer capable of implementing minimal time control for these systems is also given.

STABILIZATION OF CHAOTIC SYSTEMS USING LINEAR SAMPLED-DATA CONTROLLER

2007 ◽  
Vol 17 (06) ◽  
pp. 2021-2031 ◽  
Author(s):  
H. K. LAM ◽  
F. H. F. LEUNG
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Design Procedure ◽  
Sampling Period ◽  
Feedback Gain ◽  
Sampled Data ◽  
Lyapunov Approach ◽  
And Performance ◽  
Data Controller

This paper proposes a linear sampled-data controller for the stabilization of chaotic system. The system stabilization and performance issues will be investigated. Stability conditions will be derived based on the Lyapunov approach. The findings of the maximum sampling period and the feedback gain of controller, and the optimization of system performance will be formulated as a generalized eigenvalue minimization problem. Based on the analysis result, a stable linear sampled-data controller can be realized systematically to stabilize a chaotic system. An example of stabilizing a Lorenz system will be given to illustrate the design procedure and effectiveness of the proposed approach.

Time-Delayed Sampled-Data Feedback Control of Differential Systems Undergoing Hopf Bifurcation

2021 ◽  
Vol 31 (01) ◽  
pp. 2150004
Author(s):  
Huan Su ◽  
Jing Xu
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
Blood Transfusion ◽  
Sampling Period ◽  
Delayed Feedback Control ◽  
Control Technique ◽  
Blood Collection ◽  
Sampled Data ◽  
Differential Systems ◽  
Data Feedback

In this paper, time-delayed sampled-data feedback control technique is used to asymptotically stabilize a class of unstable delayed differential systems. Through the analysis for the distribution change of eigenvalues, an effective interval of the control parameter is obtained for a given sampling period. Here an indirect strategy is taken. Specifically, the system of continuous-time delayed feedback control is studied first by Hopf bifurcation theory. And then, the result and implicit function theorem are used to analyze the system of time-delayed sampled-data feedback control with a sufficiently small sampling period. Considering the practical criterion for the size of sampling period, the upper bound of sampling period is estimated. Finally, an application example, an unstable Mackey–Glass model, is asymptotically stabilized by introducing a blood transfusion item with time-delayed sampled-data feedback control. The blood transfusion speed and blood collection test period are derived from the main results. Some simulations and comparisons show the correctness and advantages of the main theoretical results.

Set-Valued Feedback Control and Its Application to Event-Triggered Sampled-Data Systems

2020 ◽  
Vol 65 (11) ◽  
pp. 4965-4972
Author(s):  
Yi Jiang ◽  
Dawei Shi ◽  
Jialu Fan ◽  
Tianyou Chai ◽  
Tongwen Chen
Keyword(s):  
Feedback Control ◽  
Data Systems ◽  
Sampled Data ◽  
Event Triggered
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