Static Output Feedback Control Method and Storage Medium for Forklift Stability Control

Abstract

A static output feedback control method and storage medium for forklift stability control according to the present invention. The control method includes setting up a fuzzy system model, a singular observer module, a generalized observer module, a residual generator module, and a static output feedback control method module for forklift stability control. The singular observer estimates the state and faults of the system simultaneously; the generalized observer is used to generate a residual signal that is as sensitive as possible to faults and insensitive to disturbances; the residual generator minimizes the sensitivity of the system to disturbances and maximizes the sensitivity to faults; the static output feedback control method for forklift stability control uses the measurable signals such as faults and states provided by the observer to control the dynamic system. The present invention can, after a fault occurs in the system, based on the estimated state and fault vector, ensure the reconfiguration of the control law and restore the performance of the system before the fault as much as possible, greatly improving the lateral stability and active safety of the forklift.

Description

Technical Field

[0001] The present invention relates to the field of vehicle safety control, and particularly to a static output feedback control method and a storage medium for forklift stability control. Background Art

[0002] In the field of active safety technology for forklifts, although the rollover prevention system is becoming increasingly perfect, the fault-tolerant control technology for sensor faults in the rollover prevention system of counterbalanced forklifts has not been applied. If a sensor fault occurs in the forklift rollover prevention system, the system cannot receive the required forklift operation information normally, and the system loses its operating state during operation. At the same time, the safety and stability of the forklift during driving cannot be guaranteed. Therefore, the fault-tolerant control of the forklift rollover prevention system is essential. Summary of the Invention

[0003] A static output feedback control method and a storage medium for forklift stability control proposed by the present invention can solve the above technical defects.

[0004] To achieve the above object, the present invention adopts the following technical solutions:

[0005] A static output feedback control method for forklift stability control includes the following steps:

[0006] Construct a continuous-time forklift rollover prevention fuzzy system model using Equation (1):

[0007]

[0008] In Equation (1-1), x(t) represents the state vector at time t; f(t) ∈ R s is the sensor fault vector; d(t) ∈ R nd is the unknown bounded disturbance vector; the matrices B d and D f have appropriate dimensions, and at the same time, D f is assumed to be full column rank;

[0009] Set the continuous-time fuzzy system model with the excitation function u i (ξ(t)) as the input of the system, and there are both sensor faults and unknown bounded disturbances at the same time;

[0010] Set a singular observer to estimate the state of the counterbalanced forklift rollover prevention fuzzy system and the output fault

[0011] Set a generalized observer to measure the state and fault estimation of the counterbalanced forklift rollover prevention system in continuous time, and generate a residual signal L2 that is as sensitive as possible to the fault f(t) and insensitive to the disturbance d(t);

[0012] By setting up a residual generator and using the residual signal L2 to control the removal of H ∞ The control problem is extended to the non-linear case, observing the minimization of the disturbance signal r d (t) to obtain the gain of the residual signal L2, finding the corresponding positive definite matrix and positive scalar, and then asymptotically estimating the system state and sensor faults;

[0013] Based on the fault and state estimates provided by the above observer, the control law is reconfigured, and sufficient conditions are given in the form of LMIs to ensure the stability of the resulting closed-loop system.

[0014] Furthermore, the singular observer is used to simultaneously estimate the system state and the output fault as follows:

[0015]

[0016] In Equation (1-2), v(t) ∈ R n+p is the auxiliary state vector of the observer; is the estimator of; is the unmeasurable premise variable; S i , E, and L are the observer gains.

[0017] Furthermore, a generalized observer H(t) ∈ L2 is constructed using Equation (1-3)), and the norm of L2 is defined as:

[0018]

[0019] Furthermore, a residual generator r d (t)

[0020]

[0021] Furthermore, the control law of the reconfigured static output feedback controller is designed using Equation (1-5):

[0022]

[0023] In Equation (1-5), K i is the output feedback gain to be determined; y c (t) is the compensated output; is the estimated system output; l = [0 I p .

[0024] On the other hand, the present invention also discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to execute the steps of the above method.

[0025] As can be seen from the above technical solutions, the static output feedback control method and storage medium for forklift stability control of the present invention are expected to improve the fault tolerance of the anti-rollover system of counterbalanced forklifts, thereby ensuring the stability of the forklift anti-rollover system and improving the active safety of forklifts. Specifically, when a sensor fails, the proposed state observer can estimate the signal output by the sensor and the fault state, and its fault signal can be accurately received, and the output signal can be compensated and output in a timely manner according to the static output feedback control method. Then, the system is minimally affected by sensor faults, ensuring the effectiveness of most functions of the controller.

[0026] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0027] 1. It can ensure that corresponding state and fault vectors can still be obtained when the system premise variables are unmeasurable.

[0028] 2. After a fault occurs in the system, it can ensure the reconfiguration of the control law based on the estimated state and fault vectors, and restore the performance of the system before the fault as much as possible.

[0029] 3. It improves the fault tolerance of the forklift anti-rollover system, greatly improving the lateral stability and active safety of the forklift. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 is a control system diagram for sensor fault tolerance of the forklift anti-rollover system;

[0031] Figure 2 is a diagram of the fault fa signal and its estimated value signal;

[0032] Figure 3 is a diagram of the fault fb signal and its estimated value signal;

[0033] Figure 4 is a fault-tolerant control input state diagram of static output feedback;

[0034] Figure 5 is a diagram of the lateral deviation angle of the forklift body and its estimated value without fault tolerance;

[0035] Figure 6 is a diagram of the yaw angular velocity of the forklift body and its estimated value without fault tolerance;

[0036] Figure 7 is a diagram of the lateral deviation angle of the forklift body and its estimated value under fault-tolerant control;

[0037] Figure 8 It is a graph of the yaw rate of the forklift body and its estimated value under fault tolerance control. Specific implementation manners

[0038] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention.

[0039] As Figure 1 shown, the static output feedback control method for forklift stability control described in this embodiment includes setting a continuous-time fuzzy system model, a singular observer, a generalized observer, a residual generator, and a static output feedback controller; specifically, it includes the following steps:

[0040] Use Equation (1) to construct a continuous-time forklift rollover prevention fuzzy system model:

[0041]

[0042] In Equation (1-1), x(t) represents the state vector at time t; f(t) ∈ R s is the sensor fault vector; d(t) ∈ R nd is the unknown bounded disturbance vector; the matrices B d and D f have appropriate dimensions, and at the same time D f is assumed to be full column rank;

[0043] By setting a continuous-time fuzzy system model with the excitation function u i (ξ(t)) as the input of the system, and there are sensor faults and unknown bounded disturbances at the same time;

[0044] Set a singular observer to simultaneously estimate the state and output fault

[0045] Set a generalized observer to measure the state and fault estimation of the forklift rollover prevention system in continuous time, and generate a residual signal L2 that is as sensitive as possible to the fault f(t) and insensitive to the disturbance d(t);

[0046] Set a residual generator to use the residual signal L2 control to generalize the H ∞ control problem to the nonlinear case, observe the gain of the residual signal L2 by minimizing the interference signal r d (t), find the corresponding positive definite matrix and positive scalar, and then asymptotically estimate the system state and sensor faults;

[0047] Based on the fault and state estimation provided by the above-mentioned observer, the control law is reconfigured, and sufficient conditions are given in the form of LMIs to ensure the stability of the resulting closed-loop system.

[0048] The following will specifically describe the design of the continuous-time fuzzy system model step by step as follows:

[0049] Step 11: When the forklift body tilts, the forklift tires will deform accordingly. Similarly, when the forklift makes a high-speed turn, the deformation of the forklift tires will also increase, resulting in a relatively large side slip angle of the tires. Since the force characteristic curves of forklift tires cannot all be approximated linearly. Therefore, the present invention adopts a typical non-linear tire model in vehicle research, which is more common in vehicle stability research, namely the Magic Formula model. Thus, the lateral forces F yf , F yr can be expressed as:

[0050]

[0051]

[0052] In the formula, α f and α r are the side slip angles of the front and rear forklift tires respectively. In addition, for the parameters D i , L i , G i and V i (i = f, r), their values are affected by many factors, and the key ones mainly include the traveling speed, wheel adhesion, and wheel force characteristics.

[0053] Step 12: Based on the T-S fuzzy model, for the estimation of the non-linear characteristics of the front lateral force, the sliding region M1 is used; for the estimation of the non-linear characteristics of the rear lateral force, the sliding region M2 is used; if |α f | belongs to M1, then:

[0054]

[0055] If |α f | belongs to M2, then:

[0056]

[0057] In formulas (3) and (4), C fi (i = 1, 2) and C ri (i = 1, 2) are the side slip stiffnesses of the front and rear tires respectively, and their values are affected by many factors, including tire width, load mass, wheel adhesion, and vehicle speed.

[0058] Step 13. The lateral forces of the front and rear tires of the forklift are expressed as follows:

[0059]

[0060] In Equation (5), λ i (|α f |)(i = 1, 2) is a weighted function with respect to the variable |α f |, and these weighted functions satisfy the following properties: 0 ≤ λ i (|α f |) ≤ 1 and

[0061] Step 14. Assuming that the sideslip angles of the front and rear tires of the forklift are very small, we can obtain α f = β - (aω / v x ) and α r = δ - β - (bω / v x ). Considering the forklift dynamics model, the overall anti-rollover T-S fuzzy model of the forklift is as follows:

[0062]

[0063] In Equation (6) u(t) = F(t), and z(t) = [LTR] are the state, control input, disturbance input, and control output of the above system model respectively, and the relevant matrices are as follows:

[0064]

[0065]

[0066]

[0067]

[0068] Step 15. For the anti-rollover sensor fault system of the counterbalanced forklift, an extended description system can be constructed:

[0069]

[0070]

[0071]

[0072] C0 = [C 0],

[0073]

[0074] In the anti - rollover fault system of a counterbalanced forklift, the normal operation of the controller is crucial. Sensor faults will cause deviations in the sensor input signals of the controller, and in severe cases, there may even be no signal input. Therefore, if the fault signal of the sensor can be accurately received after a sensor fault occurs, and compensation output can be carried out in a timely manner according to the controller output signal, then the controller will not be affected by the sensor fault and can ensure its normal operation.

[0075] In specific implementation, in order to estimate the state and faults of the system simultaneously, a singular observer structure is designed as follows:

[0076]

[0077] In Equation (1 - 2), \(v(t)\in R\) n+p is the auxiliary state vector of the system singular observer, and is the estimator in the above - described extended - description system . is an unmeasurable premise variable, which depends partially or completely on the estimated state Now, simplify the design of the observer to find the gains \(S\) i , \(E\) and \(L\) so that the state and fault error estimates conform to a stable generation system. In the above - mentioned singular observer, the derivative term of \(y(t)\) does not exist, so this kind of observer is easier to implement in actual engineering.

[0078] Sensor faults and unknown disturbances are assumed in the system model. In order to study the fault estimation and state estimation of the forklift anti - rollover sensor fault system model under continuous time, various general situations will be analyzed.

[0079] In specific implementation, the norm of the generalized observer is defined as:

[0080]

[0081] In the above situation, the design task of the generalized observer is to generate a residual signal that is as sensitive as possible to faults and insensitive to disturbances, so that the fault diagnosis is robust. In fact, the problem of residual generation can be studied through control (generalize the \(H\) ∞ control problem to the non - linear case).

[0082] In specific implementation, design the residual signal generator according to the following steps:

[0083] Step 41: Design by minimizing the gain from the interference signal \(r\) d (t) to the residual signal :

[0084]

[0085] For this purpose, the following theorem is proposed:

[0086] Theorem 1: If positive definite symmetric matrices P 11 , P 12 , P i 2 exist, as well as matrices N1, N2 and positive scalar η, then the state observer (1-2) can estimate the system state and sensor faults, and minimize the scalar γ under the following LMI constraints (see (2-8)).

[0087]

[0088]

[0089]

[0090]

[0091] Step 42: Obtain the observer gain by the following method:

[0092]

[0093] In equation (2-9), Ω ∈ R n.p and are two free matrices, and a non-singular matrix E can be obtained:

[0094]

[0095]

[0096] Step 43: Give the attenuation level of the external disturbance signal residue:

[0097]

[0098] Assume that D f has full column rank, then the estimated value of the sensor can be obtained by the above method, and the integrity of the fault estimated value is ensured at the same time.

[0099] In order to achieve fault-tolerant control for the forklift anti-rollover sensor fault-tolerant system, a static output feedback controller is designed for sensor faults and external disturbances. As Figure 1 shown, the observer provides fault and state estimation. Therefore, the corresponding control law must be redistributed. Linear matrix inequalities will give sufficient conditions to ensure the stability of the resulting closed-loop system.

[0100] In specific implementation, design the static output feedback controller according to the following steps:

[0101] Step 51: Based on parallel distributed compensation, the control law of static output feedback is designed as follows:

[0102]

[0103] In Equation (2-13), K i is the output feedback gain to be determined in the i-th local model, and y c (t) represents the compensated output, which is defined as:

[0104]

[0105]

[0106] The goal of static output feedback is to control the dynamic system only by using the knowledge of measurable signals. Therefore, it is required that the decision variables depend only on the control input signal u(t), the actual output signal y(t), and ultimately on the measurable state variables. In the case of unmeasurable premise variables, a stable static output feedback controller can still be designed. In the following calculation of the structure of the fault-tolerant control law, the states derived from the observer and the sensor fault signal estimation are considered simultaneously

[0107] Step 52: Analyze the stability of the closed-loop system. The system state estimation error is generated by combining the above differential equation (2-9) with the following formula:

[0108]

[0109] Substituting the static output feedback control law (2-13) into the above formula, the conclusion can be drawn that:

[0110]

[0111] Adding and subtracting Formula (2-17) can be rewritten as:

[0112]

[0113] In Equation (2-18) Therefore, the above LMI constraint formula is equivalent to:

[0114]

[0115] Rewrite the entire model in the state-space representation using the following formula:

[0116]

[0117]

[0118]

[0119]

[0120] Define the augmented state vector:

[0121]

[0122] Obtain the following closed-loop system:

[0123]

[0124] Step 53. Find the corresponding observer and controller to minimize the influence of the external disturbance d(t) on the closed-loop system. The emergence of this problem leads to the necessity to solve the standard control under the linear matrix inequality constraints provided by the following theorem.

[0125] Lemma 1: Consider two real matrices X, Y with appropriate dimensions and F(t). For any scalar δ, the following inequality is proven:

[0126] X T FY + Y T F T X ≤ δX T X + δ -1 Y T Y, δ > 0 (2-22)

[0127] Lemma 2: If there exist symmetric positive definite matrices P 11 , P 12 , P 2i , matrices Q1, Q2 and positive scalar ψ, and δ i , i = 1, …, 7 satisfying the following conditions for i, j = 1, 2, …, r and i ≠ j, then the forklift anti-rollover sensor fault-tolerant control system based on the singular observer is asymptotically stable.

[0128] min ψ (2-23)

[0129] W ii <0 (2-24)

[0130]

[0131] where:

[0132]

[0133]

[0134]

[0135]

[0136] Y (2,2) = - diag(δ1 + δ5δ2(δ3 + δ4 + δ2) -1 ×δ3δ4δ1 -1 δ6δ7(δ5 + δ6 + δ7) -1 ) (2 - 30)

[0137] Then, the observer gain is obtained through Ω in the above formula (2 - 9) and the following formula obtained.

[0138]

[0139]

[0140] Step 54: Conduct stability proof.

[0141] To obtain a non - conservative condition, the following non - quadratic Lyapunov function is adopted:

[0142]

[0143] In the above formula, Λ i = diag[P1 P 2i , where P1, P 2i are symmetric positive - definite matrices. The closed - loop system with fault - tolerant control is stable, and if then η can limit the gain from d(t) to e(t). The derivative of the Lyapunov function V(x a (t)) is expressed as:

[0144]

[0145] This condition is negative - definite if

[0146]

[0147] where:

[0148]

[0149] In formula (2 - 36):

[0150]

[0151] Using Lemma 1 proposed above, there exist positive scalars δ i , i = 1, …, 7

[0152] such that:

[0153]

[0154] In Equation (2-38):

[0155]

[0156] For the BMI term and applying the Schur complement, the sufficient linear matrix inequality conditions proposed in Theorem 2 hold.

[0157] Embodiment

[0158] For the forklift anti-rollover sensor fault-tolerant system, the above effective control strategy is designed so that the forklift anti-rollover system can still ensure the stability of the entire system in the presence of sensor faults. In this section, numerical simulations are used to prove the effectiveness and applicability of the proposed method for the forklift anti-rollover sensor fault-tolerant system. The T-S model constructed in the previous text is used to construct an observer, representing the forklift anti-rollover sensor fault-tolerant system with the premise variables depending on the unmeasurable state variables. In the design, the parameters of the entire forklift considered are shown in Table 1.

[0159] Table 1

[0160]

[0161]

[0162] Considering the fault signal f(t)=(f a (t), f b (t)) T affects the system output behavior and is described as follows:[[]]

[0163]

[0164]

[0165] For the forklift anti-rollover system, a gyroscope sensor is used. The gyroscope sensor can only measure the yaw angular velocity of the forklift. For the lateral velocity, the recommended observer is used for estimation. Solving the optimization problem under the linear matrix inequality constraints in the above Theorem (2), the following observer and controller gain matrices with the nominal attenuation level ψ = 0.843 are obtained.

[0166]

[0167]

[0168] K1 = [-0.0019 0.0020], K2 = [-0.0020 0.0020] (2-44)

[0169]

[0170] As an embodiment of the present invention, Figure 2 and Figure 3 Figure 4 are respectively the fault f a signal and its estimated value signal, the fault f b signal and its estimated value signal, and the fault-tolerant control input state of static output feedback. Figure 5 and Figure 6 are respectively the forklift body sideslip angle without fault tolerance and its estimated value, and the yaw rate and its estimated value, Figure 7 and Figure 8 are respectively the forklift body sideslip angle and its estimated value, and the yaw rate and its estimated value under fault-tolerant control.

[0171] For the case using the static output feedback fault-tolerant control strategy, it can be noted that when the system sensors fail, although there are faults and external disturbances in the system, the forklift rollover prevention system still remains stable, and its sideslip angle and yaw rate have a maximum value fluctuation not exceeding 3% of the maximum value of the angle without using the static output feedback fault-tolerant control strategy when a fault occurs. Therefore, it shows that the static output feedback fault-tolerant control strategy proposed in this paper is effective.

[0172] On the other hand, the present invention also discloses a computer-readable storage medium storing a computer program, which when executed by a processor causes the processor to execute the steps of any of the above methods.

[0173] On yet another aspect, the present invention also discloses a computer device including a memory and a processor, where the memory stores a computer program, and when the computer program is executed by the processor, it causes the processor to execute the steps of any of the above methods.

[0174] In yet another embodiment provided by the present application, there is also provided a computer program product including instructions, which when run on a computer causes the computer to execute the steps of any of the above embodiments.

[0175] It can be understood that the system provided by the embodiments of the present invention corresponds to the method provided by the embodiments of the present invention. For the explanations, examples and beneficial effects of the relevant content, reference can be made to the corresponding parts in the above method.

[0176] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The program can be stored in a non-volatile computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, storage, database, or other medium used in the embodiments provided in this application can include non-volatile and / or volatile memories. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM), etc.

[0177] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this specification.

[0178] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A static output feedback control method for forklift stability control, characterized in that, It includes the following steps: Construct a continuous-time forklift anti-rollover fuzzy system model by using Equation (1): (1-1) In Equation (1-1), represents the state vector at time t; is the sensor fault vector; is the unknown bounded disturbance vector; the matrices and are of appropriate dimensions, and at the same time is assumed to have full column rank, is the state matrix, is the control input matrix, is the actual output signal; By setting a continuous-time fuzzy system model as the excitation function as the input of the system, and there are simultaneously sensor faults and unknown bounded disturbances; By setting up a singular observer to simultaneously estimate the states of the anti-rollover fuzzy system of a counterbalanced forklift and the output faults ; By setting up a generalized observer to measure the states and fault estimation of the anti-rollover system of a counterbalanced forklift in continuous time, a residual signal is generated that is as sensitive as possible to faults and as insensitive as possible to disturbances ; ; By setting up a residual generator to utilize the residual signal Control to transfer The control problem is extended to the non-linear case, and by observing the minimization of the interference signal The residual signal is obtained The gain of, find the corresponding positive definite matrix and positive scalar, and then asymptotically estimate the system state and sensor faults; Reconfigure the control law based on the fault and state estimates provided by the above observer, and give sufficient conditions in the form of LMIs to ensure the stability of the resulting closed-loop system; The singular observer is used to simultaneously estimate the system state and the output fault , as follows: (1-2) In formula (1-2) is the auxiliary state vector of the observer; is the estimator of; is the unmeasurable premise variable; , , are the observer gains.

2. The static output feedback control method for forklift stability control according to claim 1, characterized in that: Construct a generalized observer using Equation (1-3)) , The norm of is defined as: (1-3)。 3. The static output feedback control method for forklift stability control according to claim 1, characterized in that: Construct a residual generator using Equation (1-4) : (1-4)。 4. The static output feedback control method for forklift stability control according to claim 1, characterized in that: Design the control law of the reconfigured static output feedback controller by using Equation (1-5): (1-5) In formula (1-5) is the output feedback gain to be determined; is the compensation output; is the estimated system output; .

5. A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the processor is caused to execute the steps of the method according to any one of claims 1 to 4.

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