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An Optimal Integral Sliding Mode Control Method

A control method and integral sliding mode technology, applied in the field of control, can solve problems such as the inability to effectively compromise the system response time and overshoot, and the inability to achieve finite time convergence of the system state.

Inactive Publication Date: 2017-09-08
BEIJING INSTITUTE OF TECHNOLOGYGY
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  • Description
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  • Application Information

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Problems solved by technology

[0005] The conventional infinite-time state-dependent Riccati equation (SDRE) control method can only guarantee the gradual convergence of the system state, but cannot achieve the finite-time convergence of the system state; at the same time, it cannot effectively compromise the contradiction between the system response time and the overshoot

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Embodiment 1

[0083] This embodiment is aimed at the description of the nominal system without disturbance, and mainly explains the advantages of the improved control method based on the state-dependent Riccati equation (ISDRE). An optimal integral sliding mode control method disclosed in this embodiment includes the following steps :

[0084] Step 1, establish a dynamic model of the second-order nonlinear system. The dynamic model of the second-order nonlinear system is shown in formula (1).

[0085] System initial value x 0 =[-4,2] T . f(x)=0.3sin(x 1 +2x 2 )-2x 1 +x 2 , g(x)=0.5sin(x 1 +x 2 )+1.

[0086] Extending the linearization of this nonlinear system, the form of the state correlation coefficient SDC (state-dependent coefficient) is obtained as shown in formula (2), where the parameter matrix is ​​constructed in the following form:

[0087]

[0088]

[0089] Step 2, by improving the state-dependent Riccati equation (ISDRE), the finite time convergence of the system...

Embodiment 2

[0102] This embodiment is due to the advantages of the improved optimal sliding mode control method based on the state-dependent Riccati equation (ISDRE) proposed by the present invention, such as Figure 7 As shown, an optimal integral sliding mode control method disclosed in this embodiment includes the following steps:

[0103] Step 1, establish the dynamic model of the second-order nonlinear system with disturbance. The dynamic model of the second-order nonlinear system is shown in formula (9). Wherein the system parameters are the same as in Embodiment 1, and the disturbance term d(x, t)=0.6sin(10t)+0.2cos(0.5x 1 +7x 2 ). The disturbance term d(x,t) satisfies the matching condition and is bounded, and the upper bound of |d(x,t)| has a maximum value △d max = 0.8.

[0104] Step 2. For the nominal system without the disturbance term d(x,t), a control law based on the improved state-dependent Riccati equation (ISDRE) is given. The steps and forms for solving the control...

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Abstract

The invention discloses an optimal integral sliding mode control method, relates to an integral sliding mode control method, and belongs to the technical field of control. The present invention comprises the following steps: Step 1, establishing the dynamic model of the second-order nonlinear system; Step 2, realizing the finite time convergence of the system state by improving the state-dependent Riccati equation (ISDRE), and solving the problem of effective compromise system response time and super The contradiction between the adjustments; step 3, combining the improved state-dependent Riccati equation (ISDRE) with the integral sliding mode to further improve the robustness of the system under disturbance. The invention can realize the finite time convergence of the system state, and can effectively compromise the contradiction between the system response time and the overshoot. In addition, the combination of the improved state-dependent Riccati equation (ISDRE) and the integral sliding mode can further improve the system robustness. The invention has universal applicability, for example, it can be applied to control systems of aircrafts, inverted pendulums and the like.

Description

technical field [0001] The invention relates to an integral sliding mode control method, in particular to an optimal integral sliding mode control method, and belongs to the technical field of control. Background technique [0002] As an important branch of modern control theory, optimal control has achieved great development. The control method uses the optimization strategy to obtain the control quantity that meets the specific performance index, and can obtain the expected system dynamics, which effectively improves the response characteristics of the system. For linear systems, research on optimal control algorithms based on quadratic performance indicators has been fully developed, and rich theoretical basis and design experience have been accumulated. However, for nonlinear systems, due to the complexity of the system form, for the general quadratic performance index optimization problem, it is impossible to obtain the optimal problem analytical solution through algeb...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G05B13/04
Inventor 盛永智巩轶男刘向东
Owner BEIJING INSTITUTE OF TECHNOLOGYGY
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