Chaotic trajectory tracking method with pole assignment improved

A trajectory tracking and pole configuration technology, which is applied in the direction of instruments, adaptive control, control/regulation systems, etc., can solve the problems that the trajectory tracking error cannot converge to zero, the system cannot be stable, and the impact cannot be ignored, so as to eliminate chattering Phenomenon, fast response, good robustness effect

Active Publication Date: 2018-10-12
NORTHEASTERN UNIV
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Problems solved by technology

The pole allocation method is only suitable for chaotic systems with precise mathematical models. When there are uncertainties and external interference signals in the system, the stability of the system cannot be gu

Method used

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  • Chaotic trajectory tracking method with pole assignment improved
  • Chaotic trajectory tracking method with pole assignment improved
  • Chaotic trajectory tracking method with pole assignment improved

Examples

Experimental program
Comparison scheme
Effect test

Embodiment 1

[0063] Taking the 3D Lorenz chaotic system as an example, the trajectory tracking control is carried out.

[0064] Step 1: According to the state equation and expected trajectory of the chaotic system, establish a trajectory tracking error system, including steps 1.1 to 1.3:

[0065] Step 1.1: The state equation of the chaotic system is: the chaotic system is a Lorenz chaotic system, that is, a 3-dimensional chaotic system. The state equation of the Lorenz chaotic system is:

[0066]

[0067] Among them, the parameter x i is the state variable of the system, i=1,2,3, x=[x 1 ,x 2 ,x 3 ] T . When a=10, b=28, c=8 / 3, the Lorenz chaotic system enters the chaotic state.

[0068] with modeling uncertainty △f i (x,t) and external interference signal m i The Lorenz chaotic system of (t) is expressed as

[0069]

[0070] Formula (14) is a chaotic system. The initial state of the chaotic system is set to x 1 (0)=-2.5,x 2 (0)=-1.4,x 3 (0)=5. In equation (14), the mode...

Embodiment 2

[0100] Taking the 4-dimensional hyperchaotic Chen system as an example, the trajectory tracking control is carried out.

[0101] Step 1: According to the state equation and expected trajectory of the chaotic system, establish a trajectory tracking error system, including steps 1.1 to 1.3:

[0102] Step 1.1: The state equation of the hyperchaotic Chen system is:

[0103]

[0104] Among them, the parameter x i is the state variable of the system, i=1,2,3,4, x=[x 1 ,x 2 ,x 3 ,x 4 ] T . when a 1 =35, b 1 = 3,c 1 = 12, d 1 =7, r 1 = 0.16, the hyperchaotic Chen system is in a hyperchaotic state.

[0105] with modeling uncertainty △f i (x,t) and external interference signal m i The hyperchaotic Chen system of (t) is expressed as:

[0106]

[0107] Formula (26) is the hyperchaotic system. The initial state of the hyperchaotic system is set to x 1 (0)=2, x 2 (0)=-1,x 3 (0)=3, x 4 (0)=1. In Equation (26), the modeling uncertainty △f i (x,t) is set as:

[010...

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Abstract

The invention provides a chaotic trajectory tracking method with pole assignment improved,and belongs to the technical field of automatic control. The chaotic trajectory tracking method specifically comprises the steps that a trajectory tracking error system is set up according to a state equation and expected trajectory of a chaotic system; a pole assignment method and a self-adaptation sliding mode controller are combined to design a controller,a self-adaption rate is designed for estimating modeling uncertainty and the upper bound of external interference signals,and the controller controlsthe trajectory tracking error system. The modeling uncertainty and the upper bound of the external interference signals are estimated through the self-adaptation rate,the controller is designed to carry out trajectory tracking control over different initial state chaos,the advantages of the pole assignment method are brought into play,the influence of the modeling uncertainty and the external interference signals is overcome,and very good robustness and very high reliability are achieved. The Lyapunov stability theory proves that the trajectory tracking error is asymptotically converged to zero,and chaotic system trajectory tracking can be achieved. The method is suitable for all chaotic systems,and the trajectory tracking speed is very high.

Description

technical field [0001] The invention belongs to the technical field of automatic control, and in particular relates to a chaotic trajectory tracking method with improved pole configuration. Background technique [0002] Chaos is an inherent characteristic of nonlinear dynamical systems, and is extremely sensitive to initial conditions. It is a ubiquitous phenomenon in nonlinear systems and widely exists in nature and human society. The key to the study of chaos theory lies in the control and utilization of the chaotic system. For the control of chaos, Ott, Grebogi and Yorke of Maryland State University proposed the famous OGY method. Chaos theory has been widely studied and applied in many fields, has great research value and attractive application prospect, and is a hot research topic at present. The pole allocation method has the advantages of simple design and fast convergence speed in chaotic trajectory tracking control. The pole allocation method is only suitable for...

Claims

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Application Information

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IPC IPC(8): G05B13/04
CPCG05B13/042
Inventor 赵海滨陆志国刘冲
Owner NORTHEASTERN UNIV
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