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Feedback controller design method of time-varying delay system based on convex combination method

A time-varying time-delay and design method technology, applied in the direction of adaptive control, general control system, control/regulation system, etc., can solve the problems of deteriorating system performance, system loss of stability, incorrect design scheme, etc.

Inactive Publication Date: 2017-07-21
HENAN POLYTECHNIC UNIV
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Problems solved by technology

[0003] The occurrence of time-delay may deteriorate the system performance and even make the system lose stability. If the influence of time-delay is ignored in the analysis, it will lead to incorrect design schemes; therefore, in recent years, the uncertainty, stability and control of time-delay systems Related issues such as device design have been widely concerned by many experts and scholars

Method used

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  • Feedback controller design method of time-varying delay system based on convex combination method
  • Feedback controller design method of time-varying delay system based on convex combination method
  • Feedback controller design method of time-varying delay system based on convex combination method

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example 1

[0193] Example 1. Consider the time-varying delay system (1), whose coefficient matrix is:

[0194]

[0195] When μ=0.5, the lower bound of the delay h is given d , and when i=N in Theorem 1, find the maximum time-delay upper bound that can guarantee the asymptotic stability of the system. for linear systems with time-varying delays compared with literature b: Robust stability criteria for uncertain linear systems with intervaltime-varying delay, figure 1 gives h d When different values ​​are taken, the value of the upper bound of the delay is from figure 1 It can be seen that compared with other systems using the time-delay partition method, Theorem 1 has fewer variables and is easier to calculate; by comparing with literature a and literature b, when μ = 0.5, the lower bound of the system time-delay h d =1, the maximum upper bound of the time delay is obtained, and the document b is 2.3912, and applying theorem 1, when N=2, the result is 2.4526, when N=4, the result is...

example 2

[0196] Example 2. Consider the time-varying delay system (1), whose coefficient matrix is:

[0197]

[0198] When μ is unknown, the lower bound of delay h is given d , and when i=N in Theorem 1, find the upper bound of the maximum delay that can guarantee the asymptotic stability of the system, and compare this theorem with the literature c: Further improvement on delay-range-dependent stability results for linear systems with interval time- Varying delays are compared with literature d: A novel approach to delay–fractional–dependent stability criterion forlinear systems with interval delay, such as figure 2 ; when h d = 0, given the value of μ, and when i=N in Theorem 1, find the maximum time-delay upper bound that can guarantee the asymptotic stability of the system, and compare this theorem with the literature e: Newstability criteria for continuous time systems with interval Time-varyingdelay is compared with literature f: Improved delay-range-dependent stability cri...

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Abstract

The invention provides a feedback controller design method of a time-varying delay system based on a convex combination method. The method includes: based on the Lyapunov stability theory, a delay interval is decomposed into a plurality of equidistant small intervals by employing a delay partitioning method, a Lyapunov-krasovskii generic function with triple integral terms is constructed, and a stability criteria with lower conservative property is obtained based on the convex combination method; and a feedback controller is designed on the basis, non-linear terms are processed by employing a linearization processing method, and the existence condition and the concrete form of the controller are provided. The beneficial effects of the method are that based on delay partitioning, the triple integral terms are constructed, delay lower bound information is fully utilized, a promoted integral inequality is employed; and the characteristics reduce the system conservative property; and compared with other delay partitioning methods, according to the method, less matrix variables are introduced, the calculation complexity is reduced, and the existence condition of the controller based on the LMI can be obtained.

Description

technical field [0001] The invention relates to the field of controller design, in particular to a design method of a feedback controller for a time-varying time-delay system based on a convex combination method. Background technique [0002] Time lag widely exists in communication systems, chemical engineering, biological systems, nuclear reactors, process control and networked control systems, etc. [0003] The occurrence of time-delay may deteriorate the system performance and even make the system lose stability. If the influence of time-delay is ignored in the analysis, it will lead to incorrect design schemes; therefore, in recent years, the uncertainty, stability and control of time-delay systems Related issues such as device design have been widely concerned by many experts and scholars. [0004] At present, the stability research of time-varying time-delay systems generally first derives the stability criterion of the system by constructing a suitable Lyapunov-kraso...

Claims

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Application Information

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IPC IPC(8): G05B13/04
CPCG05B13/042
Inventor 钱伟苑曼曼黄凯征王俊峰李冰锋刘海波
Owner HENAN POLYTECHNIC UNIV
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