Fan control system fault-tolerant control method considering random time delay

Abstract

A fan control system fault-tolerant control method considering random time delay comprises: considering the influence of external disturbance, establishing a state space equation of a fan torque control system, considering the actuator fault in a network control system, applying input time delay and Bernoulli distribution to obtain an improved system state equation; adopting Lyapunov stability analysis method to obtain a constraint condition matrix of a controller; and calculating a state feedback controller gain matrix through matrix inequality calculation.The present application considers a fan torque control system with actuator fault and random time delay, establishes a closed-loop control system model, gives a solution method of asymptotic stability and fault-tolerant control of the closed-loop system, establishes a Lyapunov-Krasovskii function containing random time delay information, analyzes and processes the time delay based on an extended complementary convex optimization matrix method, obtains a sufficient condition for system stability, significantly reduces the conservativeness of the system, and obtains good performance characteristics.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of fan control system control, in particular, to a sampling data control method of a fan control system considering random time delay and actuator failure, which can make the system stable and meet the performance, and perform fault-tolerant control. BACKGROUND

[0002] The fan control system connects sensors, controllers, controlled objects and other units through a communication network. In the fan control system, various disturbances will inevitably be encountered, which may cause the system to be unstable and the performance to be degraded. The traditional control method is realized by continuous-time signals, while in the fan control system, digital signals are often required to be realized. As is known to all, most controllers in actual systems are designed by using digital technology. Therefore, the sampling data control method which can directly design a digital controller for a continuous-time system is widely used. At present, there are three methods for studying sampling data control: discretization method, pulse model method and input time delay method. Compared with the first two methods, the input time delay method reconstructs the traditional sampling data system into a time delay system, which has the advantage that the sampling interval does not need to be constant. For the sampling control system with input time delay, researchers have proposed many advanced matrix inequality to establish the stability condition of the system. Among these methods, the complementary convex matrix inequality obtains an accurate convex inequality by combining non-convex terms into an expression, which has been proved to be an effective method to improve the stability criterion.

[0003] However, it is worth noting that the existing sampling control method is designed under the assumption of deterministic sampling and no system failure. But due to various external random factors or communication interference in the actual control system, the time delay actually appears in a random form. Moreover, the structure of the system cannot be fixed, because the failure in the fan control system is inevitable and unpredictable, which will cause the system to be unstable and the performance to be degraded.

[0004] In summary, how to design a controller to make the closed-loop system asymptotically stable and the controlled output and external input lower than the specified performance index, to make the fan torque control system stable when failure occurs, and to have good robustness and lower conservatism, has become a technical problem to be solved in the prior art. SUMMARY

[0005] The purpose of the present application is to propose a fault-tolerant control method of a fan control system considering random time delay, and to give a state feedback controller to make the system stable when failure occurs and to obtain smaller conservatism and good robustness.

[0006] To achieve this purpose, the present application adopts the following technical solutions:

[0007] A fault-tolerant control method for a wind turbine control system considering random time delay is characterized by comprising the following steps:

[0008] State-space equation control step S110:

[0009] Considering the influence of external disturbances, the state-space equations of the wind turbine torque control system are established as follows:

[0010]

[0011] in Represents the system's state variables. Indicates the controlled output of the system. Indicates control input, Indicates external disturbances, where Let A, B, C, Q, and D represent the Euclidean spaces of dimensions n, l, p, and q, respectively, and let A, B, C, Q, and D be known parameter matrices of suitable dimensions.

[0012] Sampling H ∞ Controller construction step S120:

[0013] Considering actuator failure in a networked control system, a control signal u is introduced. F (t), the application uses the input time delay in the control to process the discrete sampling time t. m By applying the Bernoulli distribution to describe the stochastic time delay, an improved system state equation is obtained.

[0014]

[0015] Constraint matrix design steps S130:

[0016] Integrating relevant lemmas, and employing Lyapunov stability analysis based on a model with stochastic time delays and actuator failures, we obtain an asymptotically stable network control system that satisfies H0. ∞ The constraint matrix of a fault-tolerant controller with robust stability.

[0017] State feedback controller gain matrix Calculation step S140:

[0018] The gain matrix of the state feedback controller is obtained by calculating using matrix inequalities.

[0019] The present invention further discloses a storage medium for storing computer-executable instructions, characterized in that:

[0020] When the computer-executable instructions are executed by the processor, they perform the aforementioned fault-tolerant sampling control method for a wind turbine torque control system that takes into account random time delays and actuator failures.

[0021] The application has the following advantages:

[0022] 1) The application is directed to a fan torque control system considering actuator faults and random time delays, and the influence of external disturbances in the system is also considered. A closed-loop control system model is established, and a solution to the asymptotic stability and fault-tolerant control of the closed-loop system is given.

[0023] 2) The application considers the case of random time delay in the fan torque control system, establishes a Lyapunov-Krasovskii function containing random time delay information, analyzes and processes the time delay based on the extended complementary convex optimization matrix method, obtains a sufficient condition for system stability, and significantly reduces the conservativeness of the system.

[0024] 3) The application is applied to a typical fan torque control system, and good performance characteristics can be obtained, which proves the effective application prospect of the application in actual fan torque control systems. BRIEF DESCRIPTION OF DRAWINGS

[0025] Figure 1 is a flowchart of a fan control system fault-tolerant control method considering random time delay according to an embodiment of the application;

[0026] Figure 2 is a schematic diagram of the Bernoulli probability distribution of ζ(t) according to an embodiment of the application;

[0027] Figure 3 is a schematic diagram of system control performance according to an embodiment of the application. DETAILED DESCRIPTION

[0028] The application will be further described in detail below in conjunction with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the application, and not to limit the application. In addition, it should be noted that only the parts related to the application are shown in the drawings for ease of description.

[0029] The application proposes a fan control system fault-tolerant control method considering random time delay, which fully considers the problems of random time delay, actuator faults and external disturbances in the fan torque control system. Through Lyapunov stability theory and extended complementary convex matrix inequality technology, a state feedback controller design method is given to make the system stable when faults occur and obtain smaller conservativeness and good robustness.

[0030] Specifically, see Figure 1 , which shows a flowchart of a fan control system fault-tolerant control method considering random time delay according to an embodiment of the application. The method includes the following steps:

[0031] State space equation control step S110:

[0032] Considering the influence of external disturbance, the state space equation of the fan torque control system is established:

[0033]

[0034] wherein represents the state variable of the system, represents the controlled output of the system, represents the control input, represents the external disturbance, wherein respectively represent the Euclidean space of n, l, p, q dimensions, A, B, C, Q, D are known parameter matrices of suitable dimensions;

[0035] Sampling H ∞ Controller construction step S120:

[0036] Considering the actuator fault in the network control system, the control signal u F (t) is introduced, the discrete sampling time t m is processed by applying the input time delay in the control, and the improved system state equation is obtained by applying the Bernoulli distribution to describe the random time delay.

[0037] Specifically, this step includes the following sub-steps:

[0038] Introducing the control signal u F (t) sub-step S121:

[0039] Since there is a control signal fault in the fan torque control system, the traditional state feedback control design is not suitable for the fan torque control system. This sub-step considers the actuator fault in the fan torque control system, introduces u F (t) to describe the control signal, which is used to represent the fault condition in the system model:

[0040] u F (t) = Gu(t) (34)

[0041] wherein G is an actuator fault matrix, which is a diagonal matrix composed of g1, g2,..., g m , satisfies 0 ≤ g r ≤ 1, g r = 1 indicates that the rth actuator is normal, if 0 < g r < 1 indicates that the rth actuator has a partial fault, and g r = 0 indicates that the rth actuator is completely damaged.

[0042] Processing the discrete sampling time t m sub-step S122:

[0043] Assume that the controller u(t) is sampled based on the zero-order hold circuit and the sampling procedure before entering the network, t m (m = 0, 1,...) represents the sampling time, satisfying 0 < t0< t1<... < t m <... and The state feedback controller is then described as:

[0044]

[0045] The state feedback gain matrix is denoted as K, thus the system dynamic equation can be described as:

[0046]

[0047] The above closed-loop system contains both continuous signals and discrete signals, and the input time delay method is used to handle this case by using the sampling data transformation, the sampling time t m is defined as:

[0048] t m = t - (t - t m ) = t - h(t) (37)

[0049] The controller is then described as u(t) = u(t m ) = u(t - h(t)), t m ≤ t ≤ t m+1 , where u(t m ) is the discrete-time control input, h(t) is the time-varying time delay, satisfying h0≤ h(t) ≤ h2, h0and h2are given constants.

[0050] Bernoulli distribution is applied to improve the system state equation sub-step S123:

[0051] Due to various external random factors or communication interference in the fan torque control system, the time delay usually occurs in a random form. Random time delay signals can cause system instability, oscillation and some other poor performance problems. Therefore, it is very valuable to consider the influence of random time delay in networked control systems.

[0052] In this sub-step, Bernoulli distribution is used to describe the random time delay, and two sets are introduced to describe the probability distribution of h(t):

[0053]

[0054] where h1∈ [h0, h2], represents the case that h(t) ∈ [h0, h1). h(t)∈[h1, h2] occurs,

[0055] Assume that the probabilities of the two cases are and Then introduce a Bernoulli distributed sequence ξ(t):

[0056]

[0057] That is, ξ(t) satisfies the probability where denotes the mathematical expectation of ξ(t), and ξ0 is a constant belonging to the interval [0, 1], and it can be seen that denotes the probability of the event occurring;

[0058] Introduce two time delay variables and satisfy h0≤h1(t)≤h1 and h1≤h2(t)≤h2, and by considering the random time delay, the system state equation can be expressed as:

[0059]

[0060] Its equivalent form can be expressed as:

[0061]

[0062] The constraint condition matrix design step S130:

[0063] Integrate the relevant lemmas, and according to the Lyapunov stability analysis method of the model with random time delay and actuator fault, the network control system is asymptotically stable and satisfies H ∞ The constraint condition matrix of the fault-tolerant controller with robust stability performance of the controller.

[0064] Specifically, it includes the following sub-steps:

[0065] The lemma arrangement sub-step S131:

[0066] Arrange the following three lemmas necessary for proving the main conclusions,

[0067] Lemma 1: For any given matrix R>0, given scalars m and n and m

[0068]

[0069] where τ1=x(n)-x(m),

[0070] Lemma 2: For any given matrix R > 0, given scalars m and n with m < n, for any integrable function x: [m, n], the following inequality holds:

[0071]

[0072] Lemma 3: For positive scalars β, λ ∈ (0, 1), when β + λ = 1, for any matrices W1, W2, and matrices R1 > 0 and R2 > 0, the inequality holds:

[0073]

[0074] where and

[0075] The Lyapunov stability analysis method introduces a sub-step S132:

[0076] The robust H ∞ sampling control problem is studied. Given the disturbance attenuation coefficient σ, the state feedback controller is designed to make the network control system satisfy the following two requirements:

[0077] c) The closed-loop system is asymptotically stable when the external disturbance input d(t) = 0;

[0078] d) Under zero initial conditions, for any non-zero disturbance d(t) ≠ 0, the controller output L(t) satisfies

[0079] The Lyapunov-Krasovskii function is constructed:

[0080] V(x(t)) = V1(x(t)) + V2(x(t)) + V3(x(t)) + V4(x(t)) (45)

[0081] where

[0082]

[0083]

[0084]

[0085] where h 10 = h1 - h0 and h 21 = h2 - h1, the symmetric matrix

[0086] By combining Lemma 1, 2, 3, the derivative of the Lyapunov function is estimated after scaling the integral term, and the derivative of the Lyapunov function can be estimated as:

[0087]

[0088] where,

[0089]

[0090] By Lemma 3, the expectation of

[0091]

[0092] where,

[0093]

[0094]

[0095]

[0096] Adding zero matrix inequality condition:

[0097]

[0098] When , the condition is satisfied, i.e., the system is asymptotically stable, i.e.,

[0099]

[0100]

[0101] Solve H ∞ fault-tolerant controller gain matrix, according to H ∞ performance constraint condition, under the zero initial condition:

[0102]

[0103] By Schur complement lemma, the condition is satisfied,

[0104] Integrating the above equation from 0 to +∞, we get:

[0105]

[0106] i.e., ||L(t)|| 2 < σ 2 ‖d(t)‖ 2 , which means that the closed-loop fault-tolerant control system satisfies H ∞ performance index σ, and the closed-loop system is asymptotically stable.

[0107] where V(0) and V(+∞) represent the state of Lyapunov function x(t)=0 and x(t)=+∞.

[0108] The constraint matrix derivation sub-step S133:

[0109] By using Lyapunov stability theory and extended complementary convex optimization matrix inequality analysis method, the network control system is gradually stable and meets H ∞ The sufficient condition of fault-tolerant controller:

[0110] For given positive scalar ε1,ε2,ξ0 and 0≤h0<h1<h2, when there exists a symmetric positive definite matrix Real matrix And the matrix of appropriate dimension Make the matrix inequality (54) ~ (57) hold, then the closed-loop fault-tolerant control system of network control system with random time-varying time delay is gradually stable when the actuator fails, and H ∞ Fault-tolerant control is realized.

[0111]

[0112]

[0113]

[0114]

[0115] Where * represents the transpose of the symmetric position matrix,

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

[0137] It is worth noting that the controller gain is coupled with F, so further processing is needed to calculate the matrix

[0138] the state feedback controller gain matrix The calculation step S140 is:

[0139] The state feedback controller gain matrix is calculated by matrix inequality

[0140] Specifically, let When the matrix inequalities (58) ~ (61) are established, the state feedback controller gain matrix

[0141]

[0142]

[0143]

[0144]

[0145] Wherein:

[0146]

[0147]

[0148]

[0149]

[0150]

[0151]

[0152]

[0153]

[0154] By solving the above matrix inequality, the closed-loop network control system meets the H ∞ State feedback controller gain matrix under fault-tolerant control condition

[0155] Further, the application further discloses a storage medium for storing computer executable instructions, characterized in that:

[0156] The computer executable instructions perform the fault-tolerant sampling control method of the fan torque control system considering random time delay and actuator faults when executed by the processor.

[0157] Embodiment:

[0158] Taking a typical fan torque control system as an example:

[0159]

[0160] Among them:

[0161] Q = [0 0 0.542]

[0162] The actuator failure rate G is selected as 0.5, the maximum controlled output torque is 5 N·m, the maximum control input u max = 10, and other parameters ε1 = 1, ε2 = 0.2, for ξ0 = 0.1, h0 = 0.01 s, h1 = 0.02 s, h2 = 0.04 s. The following table shows that as the integral upper limit h2 decreases, the H ∞ performance index σ also increases.

[0163] In order to further evaluate the performance of the system, the existence of external disturbance is considered:

[0164]

[0165] By applying the application to a typical fan torque control system, the minimum H ∞ performance index σ is 11.7782, and the allowable controller gain matrix is calculated as:

[0166]

[0167] Referring to Figure 2 Bernoulli probability distribution reflecting ξ(t), Figure 3 Reflects the system control performance. It can be seen from the figure that when the actuator fails, the fan torque control system can still operate stably, and the performance requirements |L(t)|<1 and |u F (t)|<|u max | are met. Compared with the traditional fan torque control system fault-tolerant control method, the application has less conservatism and better constraint performance. It shows that the fault-tolerant controller designed by the application can make the fan torque control system considering random time delay have good robust integrity when the actuator fails.

[0168] The application has the following advantages:

[0169] 1) The application is aimed at the fan torque control system considering actuator failure and random time delay, and the influence of external disturbance in the system is also considered. A closed-loop control system model is established, and a solution method for asymptotic stability and fault-tolerant control of the closed-loop system is given.

[0170] 2) The application considers the random time delay existing in the fan torque control system, establishes a Lyapunov-Krasovskii function containing random time delay information, analyzes and processes the time delay based on the extended complementary convex optimization matrix method, obtains a sufficient condition for system stability, and significantly reduces the conservatism of the system.

[0171] 3) The application is applied to a typical fan torque control system, and good performance characteristics can be obtained, which proves the effective application prospect of the application in the actual fan torque control system.

[0172] Obviously, those skilled in the art should understand that the units or steps of the application described above can be realized by general computing devices, which can be concentrated on a single computing device, and alternatively, they can be realized by computer device executable program codes, so that they can be stored in storage devices and executed by computing devices, or they can be manufactured into individual integrated circuit modules, or a plurality of modules or steps among them can be manufactured into a single integrated circuit module. Thus, the application is not limited to any specific combination of hardware and software.

[0173] The above is further detailed description of the present application in combination with specific preferred embodiments, and cannot be deemed as limitation of the specific embodiments of the present application to the above. For those skilled in the art of the present application, without departing from the concept of the present application, a number of simple deductions or substitutions can be made, which shall be deemed to fall within the protection scope of the present application determined by the submitted claims.

Claims

1. A fan control system fault-tolerant control method considering random time delay, characterized in that, The method comprises the following steps: Step S110, considering the influence of external disturbance, a state space equation of the fan torque control system is established: wherein denotes a state variable of the system, denotes a controlled output of the system, denotes a control input, denotes an external disturbance, wherein denotes the n-, l-, p-, q-dimensional Euclidean space, respectively; A, B, C, Q are known parameter matrices of suitable dimension. Step S120, a sampled controller with actuator faults and random time delay is constructed: Considering actuator fault in networked control systems, the control signal u F (t) is introduced, and the discrete sampling time t m is dealt with by using input time delay in control. The Bernoulli distribution is applied to describe the random time delay, and the state space equation of the improved fan torque control system is obtained. where ξ0 is a constant belonging to the interval [0, 1], and ξ(t) is a Bernoulli distributed sequence, is the state feedback controller gain matrix, G is the actuator fault matrix, h1(t) and h2(t) are time-delay variables; Step S130, a constraint condition matrix is designed by using Lyapunov stability analysis method: Integrating relevant lemmas, the Lyapunov stability analysis method is adopted to obtain the asymptotic stability of the network control system and the H ∞ The constraint matrix of the controller with robust stability performance of the fault-tolerant controller Step S140, a state feedback controller gain matrix is calculated: The state feedback controller gain matrix is computed by matrix inequality calculation 2. The fan control system fault-tolerant control method according to claim 1, wherein, The step S120 of constructing the sampled controller with actuator faults and random time delay is specifically: Sub-step S121, introducing a control signal u F (t): Considering actuator faults in the fan torque control system, the u F (t) is introduced to describe the control signal, which is used to represent the fault condition in the system model: u F (t) = Gu(t) (3) where G is the actuator fault matrix, is a diagonal matrix composed of g1, g2,..., g m , satisfying 0 < g r < 1, g r = 1 indicates that the rth actuator is normal, if 0 < g r < 1 indicates that the rth actuator has partial failure, and g r = 0 indicates that the rth actuator is completely damaged; Sub-step S122, processing the discrete sampling instants t m : It is assumed that the controller u(t) is sampled before entering the network based on a zero-order hold circuit and a sampling procedure, t m (m = 0, 1,...) denotes the sampling time, satisfying 0 < t0< t1<... < t m <... and The state feedback controller is then described as: The state feedback controller gain matrix K is thus determined, and the state space equation of the fan torque control system can be described as: The closed-loop system contains both continuous signals and discrete signals, and the input time-delay method is used to deal with this situation by using sampling data transformation. The sampling time t m is defined as: t m = t - (t - t m ) = t - h(t) (6) The controller is described as u(t) = u(t m ) = u(t - h(t)), t m ≤ t ≤ t m+1 , where u(t m ) is the discrete-time control input, h(t) is a time-varying time delay, satisfying h0≤ h(t) ≤ h2, h0and h2are given constants; In this substep, the random time delay is described by Bernoulli distribution, and two sets are introduced to describe the probability distribution of h(t): The equivalent form can be expressed as: where h1∈[h0, h2], represents that the case h(t)∈[h0, h1) occurs; represents that the case h(t)∈[h1, h2] occurs, Assume that the probabilities of the two cases are and Next introduce the Bernoulli distributed sequence ξ(t): i.e. ξ(t) satisfies the probability wherein denotes the mathematical expectation of ξ(t), ξ0is a constant belonging to the interval [0, 1], denotes the probability of the event, it can be seen that Introducing two time-delay variables and Satisfying h0≤ h1(t)≤ h1 and h1≤ h2(t)≤ h2, by considering the random time delay, the state space equation of the fan torque control system can be expressed as:

3. The fan control system fault-tolerant control method according to claim 1 or 2, wherein, The step S130 of designing the constraint condition matrix by using Lyapunov stability analysis method is specifically: In this substep, the lemmas 1 to 3 are arranged: The following three lemmas are necessary for arranging the main conclusions of the proofs, Lemma 1: For any given matrix R>0, given scalar m and scalar n and m<n, let the vector x:[m,n] be a derivable function, then the inequality holds: Lemma 2: For any given matrix R>0, given scalar m and scalar n and m<n, for any integrable function x:[m,n], the following inequality holds: where τ1= x(n) - x(m), Lemma 3: For positive scalar β, λ∈(0,1), when β+λ=1, for any matrix W1, W2 and matrix R1>0 and R2>0, the inequality holds: In this substep, the Lyapunov stability analysis method is introduced: wherein and a) The closed-loop system is asymptotically stable when the external disturbance input d(t)=0; Robust H ∞ The sampled-data control problem is investigated. Given a disturbance attenuation level σ, a state feedback controller is designed such that the networked control system satisfies the following two requirements: The Lyapunov-Krasovskii function is constructed: b) under zero initial conditions, for any non-zero disturbance d(t)≠0, the controller output L(t) satisfies V(x(t))=V1(x(t))+V2(x(t))+V3(x(t))+V4(x(t)) (14) By combining the lemmas 1 to 3, the derivative of the Lyapunov function is estimated after the integral term is scaled, and then the derivative of the Lyapunov function can be estimated as: wherein where h 10 = h1- h0and h 21 = h2- h1, the symmetric matrix are all greater than 0, Wherein, The zero matrix inequality condition is added: By Lemma 3, The expectation of X is estimated as: wherein Integrating the above formula from 0 to +∞ can obtain: When the conditions are satisfied, the system is asymptotically stable, i.e.: the conditions are satisfied, the system is asymptotically stable, i.e.: H ∞ fault-tolerant controller gain matrix, according to H ∞ performance constraint condition, defined at zero initial conditions: By Schur complement lemma, provided that the conditions are met, Wherein V(0), V(+∞) represent the state of the Lyapunov function x(t)=0 and the state of the Lyapunov function x(t)=+∞, i.e. ||L(t)| 2 <σ 2 ‖d(t)‖ 2 This means that the closed-loop fault-tolerant control system satisfies H ∞ performance index σ, and the closed-loop system is asymptotically stable; In this substep, the constraint condition matrix is obtained: Wherein★represents the transpose of the symmetric position matrix, By using Lyapunov stability theory and extended complementary convex optimization matrix inequality analysis method, the network control system is asymptotically stable and satisfies H ∞ A sufficient condition of fault-tolerant controller: For given positive scalars ε1,ε2,ξ0 and 0≤h0<h1<h2, when there exists a symmetric positive definite matrix a real matrix and a state feedback gain matrix such that the matrix inequalities (23)-(26) hold, then the closed-loop fault-tolerant control system of the networked control system with random time-varying time delay is asymptotically stable, and H ∞ fault-tolerant control; 4. The fan control system fault-tolerant control method according to claim 3, wherein, The step S140 of calculating the state feedback controller gain matrix is specifically: Wherein: Specifically, let When the matrix inequalities (27) - (30) are satisfied, the state feedback controller gain matrix 5. A storage medium for storing computer executable instructions, wherein: By solving the above matrix inequality, the closed-loop network control system can meet the H ∞ State feedback controller gain matrix under fault-tolerant control conditions The computer executable instructions, when executed by a processor, perform the fan control system fault-tolerant control method considering random time delay according to any one of claims 1-4. ​

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