Method for tracking third-order strict feedback chaotic trajectory based on global integral sliding mode

An integral sliding mode and trajectory tracking technology, which is applied in the direction of instruments, adaptive control, control/regulation systems, etc., to achieve the effect of increasing speed and good robustness

Inactive Publication Date: 2019-01-18
NORTHEASTERN UNIV
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Problems solved by technology

Sliding mode control is divided into approaching mode and sliding mode. The ordinary sliding mode controller using linear sliding mode surface is only robust in sliding mode, but not robust in approaching mode.

Method used

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  • Method for tracking third-order strict feedback chaotic trajectory based on global integral sliding mode
  • Method for tracking third-order strict feedback chaotic trajectory based on global integral sliding mode
  • Method for tracking third-order strict feedback chaotic trajectory based on global integral sliding mode

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Experimental program
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specific Embodiment 1

[0058] The specific process is as Figure 8 Shown:

[0059] Step 1: According to the state equation and expected trajectory of the third-order strict feedback chaotic system, a trajectory tracking error system is established;

[0060] The third-order strict feedback chaotic system is multi-scroll Jerk chaotic system. Multi-volume Jerk chaotic system with modeling uncertainties and external disturbance signals, the state equation is:

[0061]

[0062] Among them, f 1 (x)=-x 1 -x 2 -0.6x 3 +sgn(x 1 )+sgn(x 1 +2)+sgn(x 1 -2), modeling uncertain △f 1 (x) is set to △f 1 (x)=0.6sin(x 2 )sin(x 3 ), due to |△f 1 (x)|≤d 1 , then d 1 =0.6, the external interference signal d(t) is set as d(t)=0.6cos(2t), because |d(t)|≤d 2 , then d 2 = 0.6. The initial state of the multi-scroll Jerk chaotic system is set to x 1 (0)=1, x 2 (0)=1, x 3 (0)=0.8.

[0063] Multi-scroll Jerk chaotic system state variable x 1 The expected trajectory of x d =sin(ωt), state variable x 2...

specific Embodiment 2

[0085] The specific process is as Figure 8 Shown:

[0086] Step 1: According to the state equation and expected trajectory of the third-order strict feedback chaotic system, a trajectory tracking error system is established;

[0087] The third-order strict feedback chaotic system is Genesio-Tesi chaotic system. For a Genesio-Tesi chaotic system with modeling uncertainties and external disturbance signals, the state equation is:

[0088]

[0089] Among them, f 1 (x)=-6x 1 -2.92x 2 -1.2x 3 +x 1 2 , modeling uncertainty △f 1 (x) is set to △f 1 (x)=0.6sin(x 1 )cos(x 2 ), due to |△f 1 (x)|≤d 1 , then d 1 =0.6, the external interference signal d(t) is set as d(t)=0.4cos(3t), because |d(t)|≤d 2 , then d 2 = 0.4. The initial state of the Genesio-Tesi chaotic system is set to x 1 (0)=1, x 2 (0)=1, x 3 (0)=0.8.

[0090] Genesio-Tesi chaotic system state variable x 1 The expected trajectory of x d =sin(ωt), state variable x 2 The expected trajectory of state...

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Abstract

The invention provides a method for tracking a third-order strict feedback chaotic trajectory based on a global integral sliding mode. The method includes the following steps that S1, a trajectory tracking error system is established according to a state equation and a desired trajectory of a third-order strict feedback chaotic system; S2, a global integral sliding mode surface and an adaptive exponential approach law are designed; and S3, a global integral sliding mode controller is designed to control the trajectory tracking error system and form a closed-loop system, and the closed-loop control system can realize trajectory tracking control of a third-order strict feedback chaos in different initial states. Stability of the closed-loop system is proved through a Lyapunov stability theory, under the condition of uncertain modeling and external disturbance signals, only a single global integral sliding mode controller is used, and trajectory tracking control of the third-order strictfeedback chaos in different initial states is realized. Experimental simulation results show that the effectiveness of the method is achieved, the trajectory tracking speed is very high, and good robustness and reliability are achieved.

Description

technical field [0001] The invention belongs to the technical field of automatic control, and in particular relates to a third-order strict feedback chaotic track tracking method based on a global integral sliding mode. Background technique [0002] Chaos is the link connecting deterministic motion and random motion, and it exists widely in nature and human society. The control and synchronization of chaos is a research subject that has attracted much attention in the field of nonlinear science. Third-order strict feedback chaos (such as Genesio-Tesi chaos and Arneodo chaos) can realize trajectory tracking control only with a single control input, and has broad application prospects in secure communication. [0003] Sliding mode control has strong robustness to modeling uncertainty and external disturbance signals, and has the advantages of fast response and easy implementation, and is widely used in the control of nonlinear systems. Sliding mode control is divided into ap...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G05B13/04
CPCG05B13/042
Inventor 赵海滨刘冲陆志国
Owner NORTHEASTERN UNIV
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