An asynchronous non-fragile h-infinity control method and system for a rotating inverted pendulum

Abstract

This invention discloses an asynchronous, non-fragile H∞ control method and system for a rotating inverted pendulum, belonging to the field of robust control technology for DC motor rotating inverted pendulums. Addressing the problems of modal asynchrony, controller gain perturbation, time-varying delay, and quantization error in DC motor rotating inverted pendulum systems, this invention proposes an asynchronous, non-fragile H∞ control framework. The main steps include: constructing a Markov jump singular perturbation system model with time-varying delay and variable quantization density; designing an asynchronous, non-fragile output feedback controller for the rotating inverted pendulum, compatible with controller gain perturbation and quantization uncertainty; and deriving the linear matrix inequality conditions through modal-dependent Lyapunov functions to ensure the system's exponential stability in finite time and to meet the preset H∞ performance index. This invention can effectively improve the robustness and stability of DC motor rotating inverted pendulums under attack and parameter perturbation scenarios.

Description

Technical Field

[0001] This invention belongs to the field of robust control technology for rotating inverted pendulums, specifically relating to an asynchronous non-fragile H∞ control method and system for rotating inverted pendulums, applicable to balancing control scenarios of rotating inverted pendulums with modal asynchrony, controller gain perturbation, network attacks, time-varying delays, and bandwidth constraints. Background Technology

[0002] The rotating inverted pendulum is a typical experimental platform for multivariable, nonlinear, underactuated, and non-minimum phase applications. It is widely used to verify the effectiveness of control algorithms and has significant engineering value in robot balancing, servo systems, and aircraft attitude control. However, in practical applications, the rotating inverted pendulum faces multiple challenges: system parameter perturbations, unmodeled dynamics, and external disturbances lead to model uncertainty; network transmission introduces time-varying delays, packet loss, and quantization errors, limiting bandwidth; the physical implementation of the controller exhibits gain perturbations, making it vulnerable; the system modes, quantization modes, and controller modes are asynchronous; and the network environment is susceptible to DoS and spoofing attacks.

[0003] Existing H∞ control systems often assume that the controller and system modes are synchronized, the gain is precise, there are no network attacks, or the quantization is fixed. This makes it difficult to simultaneously achieve asynchronous operation, non-fragility, variable quantization, and attack suppression. Therefore, designing asynchronous, non-fragile H∞ control for a rotating inverted pendulum, ensuring stability and disturbance rejection under complex network and parameter uncertainty conditions, has significant theoretical and engineering implications. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides an asynchronous, non-fragile H∞ control method and system for a rotating inverted pendulum, achieving robust and stable control under conditions of modal asynchrony, controller gain perturbation, time-varying delay, variable quantization density, and network attacks.

[0005] In a first aspect, an asynchronous non-fragile H∞ control method for a rotating inverted pendulum is characterized by comprising the following steps:

[0006] Step S1: Based on the dynamic characteristics of the rotating inverted pendulum, construct a Markov jump singular perturbation system model with time-varying delay, variable quantization density, and DoS attack.

[0007] Step S2: Design an asynchronous, non-fragile H∞ output feedback controller, considering controller gain perturbation, random quantization, and Bernoulli deception attack characteristics;

[0008] Step S3: Based on the modally dependent Lyapunov function, derive the sufficient condition for the linear matrix inequality, and prove that the closed-loop system is exponentially stable in finite time and satisfies H∞ performance.

[0009] 1. The asynchronous non-fragile H∞ control method for a rotating inverted pendulum according to claim 1, characterized in that the continuous dynamic model of the DC motor rotating inverted pendulum in step S1 is:

[0010] ,

[0011] Where x1(t) is the pendulum deflection angle, x2(t) is the pendulum angular velocity, x3(t) is the motor armature current; g is the gravitational acceleration, l is the pendulum length, N is the reduction ratio, and K... m K is the motor torque coefficient. b R is the back electromotive force coefficient. a L a Let u(t) be the armature resistance and inductance, u(t) be the control input, and w(t) be the external disturbance.

[0012] After linearization and Euler discretization, the discrete-time Markov jump singular perturbation system is obtained:

[0013] ,

[0014] Among them, E ϵ σ(k) is the singular perturbation matrix, σ(k) is the system modal Markov chain, τ(k) is the time-varying delay, and w(k)∈l2[0,∞) is the finite energy perturbation.

[0015] 2. The asynchronous non-fragile H∞ control method for a rotating inverted pendulum according to claim 1, characterized in that the asynchronous non-fragile controller in step S2 is designed as follows:

[0016] ,

[0017] Where α(k) follows a Bernoulli distribution, characterizing whether a deception attack occurs; φ(k) is a controller modal Markov chain, asynchronous with the system modal; ΔK φ (k),ΔK d φ(k) is the controller gain perturbation, which satisfies the bounded norm; q ϖ (k)(⋅) is a mode-dependent quantizer that satisfies the sector-bounded uncertainty q. ϖ (k)(x(k))=(I+Δ ϖ (k))x(k).

[0018] 3. The asynchronous non-fragile H∞ control method for a rotating inverted pendulum according to claim 1, characterized in that the stability determination condition in step S4 is:

[0019] If there exists a symmetric positive definite matrix P ap >0, U ap A value greater than 0 makes the following linear matrix inequality hold:

[0020] ,

[0021] The closed-loop system is then stochastic finite-time exponentially stable and satisfies the H∞ disturbance suppression level μ.

[0022] Secondly, embodiments of the present invention also provide an asynchronous non-fragile H∞ control system for a rotating inverted pendulum, characterized in that it includes: S001 a DC motor rotating inverted pendulum model, S002 a discrete-time TS fuzzy Markov jump system, S003 a sensor, S004 a recursive quantization strategy, S005 a controller, S006 a zero-order hold, and a computer program that can run on a processor, wherein when the processor executes the computer program, it implements a recursive quantization feedback control method for a mass spring damped system as described in the first aspect. Attached Figure Description

[0023] The accompanying drawings are provided to further illustrate the present invention and form part of the specification. They are used together with the embodiments of the present invention to explain the technical solutions of the present invention, but do not constitute a limitation on the technical solutions of the present invention.

[0024] Figure 1 This is a flowchart of an asynchronous non-fragile H∞ control method for a rotating inverted pendulum according to the present invention;

[0025] Figure 2 This is a schematic diagram of the structure of an asynchronous non-fragile H∞ control system for a rotating inverted pendulum according to the present invention; Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0027] It should be noted that although functional modules are divided in the device schematic diagram and a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first," "second," etc., in the specification, claims, or the aforementioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0028] like Figure 1 As shown, this invention provides an asynchronous non-fragile H∞ control method for a rotating inverted pendulum, the method comprising the following steps:

[0029] Step S1: Based on the dynamic characteristics of the rotating inverted pendulum, construct a Markov jump singular perturbation system model with time-varying delay, variable quantization density, and DoS attack.

[0030] According to claim 1, the asynchronous non-fragile H∞ control method for a rotating inverted pendulum is characterized in that the continuous dynamic model of the DC motor rotating inverted pendulum in step S1 is:

[0031] ,

[0032] Where x1(t) is the pendulum deflection angle, x2(t) is the pendulum angular velocity, x3(t) is the motor armature current; g is the gravitational acceleration, l is the pendulum length, N is the reduction ratio, and K... m K is the motor torque coefficient. b R is the back electromotive force coefficient. a L a Let u(t) be the armature resistance and inductance, u(t) be the control input, and w(t) be the external disturbance.

[0033] After linearization and Euler discretization, the discrete-time Markov jump singular perturbation system is obtained:

[0034] ,

[0035] Among them, E ϵ σ(k) is the singular perturbation matrix, σ(k) is the system modal Markov chain, τ(k) is the time-varying delay, and w(k)∈l2[0,∞) is the finite energy perturbation.

[0036] Step S2: Design an asynchronous, non-fragile H∞ output feedback controller, considering controller gain perturbation, random quantization, and Bernoulli deception attack characteristics;

[0037] According to claim 1, the asynchronous non-fragile H∞ control method for a rotating inverted pendulum is characterized in that the asynchronous non-fragile controller in step S2 is designed as follows:

[0038] ,

[0039] Where α(k) follows a Bernoulli distribution, characterizing whether a deception attack occurs; φ(k) is a controller modal Markov chain, asynchronous with the system modal; ΔK φ (k),ΔK d φ(k) is the controller gain perturbation, which satisfies the bounded norm; q ϖ (k)(⋅) is a mode-dependent quantizer that satisfies the sector-bounded uncertainty q. ϖ (k)(x(k))=(I+Δ ϖ (k))x(k).

[0040] Step S3: Based on the modally dependent Lyapunov function, derive the sufficient condition for the linear matrix inequality, and prove that the closed-loop system is exponentially stable in finite time and satisfies H∞ performance.

[0041] According to claim 1, the asynchronous non-fragile H∞ control method for a rotating inverted pendulum is characterized in that the stability determination condition in step S4 is:

[0042] If there exists a symmetric positive definite matrix P ap >0, U ap A value greater than 0 makes the following linear matrix inequality hold:

[0043] ,

[0044] The closed-loop system is then stochastic finite-time exponentially stable and satisfies the H∞ disturbance suppression level μ.

[0045] like Figure 2 As shown, this embodiment of the invention also provides an asynchronous non-fragile H∞ control system for a rotating inverted pendulum, characterized in that it includes: S001 a DC motor rotating inverted pendulum model, S002 a discrete-time TS fuzzy Markov jump system, S003 a sensor, S004 a recursive quantization strategy, S005 a controller, S006 a zero-order hold, and a computer program that can run on a processor, wherein when the processor executes the computer program, it implements a recursive quantization feedback control method for a mass spring damped system as described in the first aspect.

Claims

1. An asynchronous, non-fragile H∞ control method for a rotating inverted pendulum, characterized in that, Includes the following steps: Step S1: Based on the dynamic characteristics of the rotating inverted pendulum, construct a Markov jump singular perturbation system model with time-varying delay, variable quantization density, and DoS attack. Step S2: Design an asynchronous, non-fragile H∞ output feedback controller, considering controller gain perturbation, random quantization, and Bernoulli deception attack characteristics; Step S3: Based on the modally dependent Lyapunov function, derive the sufficient condition for the linear matrix inequality, and prove that the closed-loop system is exponentially stable in finite time and satisfies H∞ performance.

2. The asynchronous non-fragile H∞ control method for a rotating inverted pendulum according to claim 1, characterized in that, The continuous dynamic model of the DC motor rotating inverted pendulum in step S1 is as follows: ， Where x1(t) is the pendulum deflection angle, x2(t) is the pendulum angular velocity, x3(t) is the motor armature current; g is the gravitational acceleration, l is the pendulum length, N is the reduction ratio, and K... m K is the motor torque coefficient. b R is the back electromotive force coefficient. a L a Let u(t) be the armature resistance and inductance, u(t) be the control input, and w(t) be the external disturbance.

3. After linearization and Euler discretization, the discrete-time Markov jump singular perturbation system is obtained: , Where E ϵ σ(k) is the singular perturbation matrix, σ(k) is the system modal Markov chain, τ(k) is the time-varying delay, and w(k)∈l2[0,∞) is the finite energy perturbation.

4. The asynchronous non-fragile H∞ control method for a rotating inverted pendulum according to claim 1, characterized in that, The asynchronous non-fragile controller in step S2 is designed as follows: , Where α(k) follows a Bernoulli distribution, characterizing whether a deception attack occurs; φ(k) is a controller modal Markov chain, asynchronous with the system modal; ΔK φ (k),ΔK d φ(k) is the controller gain perturbation, which satisfies the bounded norm; q ϖ (k)(⋅) is a mode-dependent quantizer that satisfies the sector-bounded uncertainty q. ϖ (k)(x(k))=(I+Δ ϖ (k))x(k).

5. The asynchronous non-fragile H∞ control method for a rotating inverted pendulum according to claim 1, characterized in that, The stability determination condition in step S4 is: If there exists a symmetric positive definite matrix P ap >0, U ap A value greater than 0 makes the following linear matrix inequality hold: , The closed-loop system is then stochastic finite-time exponentially stable and satisfies the H∞ disturbance suppression level μ.

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