Driving wheel longitudinal force estimation method based on sliding mode observer

Abstract

The invention provides a driving wheel longitudinal force estimation method based on a sliding-mode observer. The method comprises the following steps of S1, deducing a sliding-mode observer structure of a bounded disturbance quantity of a first-order system with system input, the bounded disturbance quantity and a system disturbance term; s2, deriving a driving wheel longitudinal force sliding-mode observer structure based on the unmanned mine car quarter vehicle dynamics model and a sliding-mode observer structure of bounded disturbance quantity; and S3, carrying out parameter self-adaption on feedback gain in the driving wheel longitudinal force observer by utilizing TS fuzzy logic. According to the method, the longitudinal force of the driving wheel is estimated based on the sliding-mode observer, calculation of the driving torque and the rolling resistance coefficient of the driving wheel is omitted, the TS fuzzy logic is applied to the traditional sliding-mode observer, self-adaptive adjustment is conducted on the feedback gain in the observer, and the observer can be rapidly and stably converged to a real value.

Description

Technical Field

[0001] The invention belongs to the field related to vehicle chassis control, and in particular relates to a driving wheel longitudinal force estimation method based on a sliding mode observer. Background Art

[0002] Mines are an important resource production area in my country, and mine cars are the core equipment for material transportation. Under the traditional transportation mode, manual operation of mine cars has safety hazards such as fatigue driving and slow response; the use of unmanned driving technology can effectively reduce human errors, reduce the probability of accidents, and improve operating efficiency. Especially in recent years, with the promotion of national policies in the construction of intelligent mines, the unmanned and clustered operation of intelligent mine cars has become a new trend in the mining industry.

[0003] However, in the operation scenario of unmanned mine cars, they often encounter slippery roads caused by rain and snow, which causes the driving wheels of unmanned mine cars to slip and lock due to the low road adhesion coefficient, further causing the mine car to skid and lose stability. Further, the path tracking accuracy is greatly reduced, the transportation operation of the mine car is greatly affected, and the safety cannot be guaranteed. Therefore, it is particularly important to accurately estimate the adhesion coefficient between the driving wheel and the road surface. By obtaining the accurate road adhesion coefficient, further design can obtain the optimal slip rate corresponding to the real-time change of the road surface. In this way, the driving wheel slip rate is controlled with reference to the optimal slip rate to maximize the use of the road adhesion capacity and ensure the best lateral and longitudinal stability of the wheel. The estimation of the adhesion coefficient needs to be based on the variable of the driving wheel longitudinal force. However, in the unmanned mine cars that have been mass-produced, the driving wheel longitudinal force cannot be directly measured by the on-board sensor. Therefore, how to accurately obtain the driving wheel longitudinal force becomes the key to the anti-skid and anti-lock braking of the mine car. Summary of the invention

[0004] The purpose of the present invention is to provide a driving wheel longitudinal force estimation method based on a sliding mode observer. The method estimates the longitudinal force of the driving wheel based on the sliding mode observer, omitting the calculation of the driving torque and rolling resistance coefficient of the driving wheel, and applies TS fuzzy logic to the traditional sliding mode observer to adaptively adjust the feedback gain in the observer, which is conducive to the observer to converge to the true value quickly and stably. The specific steps are as follows:

[0005] Step S1: Derive the structure of the bounded disturbance sliding mode observer for a first-order system with system input, bounded disturbance and system disturbance term. Specifically:

[0006] Step S1.1: Select a symbolic function and use the Lyapunov direct method stability criterion to prove that the observer error will converge stably.

[0007] Step S1.2: According to the observer error finally being stabilized to 0, derive the sliding mode observer expression of the bounded disturbance of the system.

[0008] Step S1.3: When the system error changes around 0, causing the system to vibrate, in order to avoid the observer error caused by the vibration phenomenon, the saturation function is used to approximate the sign function.

[0009] Step S2: derive the sliding mode observer expression of the driving wheel longitudinal force based on the quarter vehicle dynamics model of the unmanned mining vehicle.

[0010] Step S3: Utilize TS fuzzy logic to perform parameter adaptation on the feedback gain in the driving wheel longitudinal force observer. Specifically:

[0011] Step S3.1: Use the slope of the linear function as the output of the TS fuzzy logic, select the wheel speed measurement value and the observed value error and the error change rate as the input of the fuzzy logic, determine the domain of the input and output quantities, and perform fuzzification on them.

[0012] Step S3.2: Establish the membership function of the input quantity.

[0013] Step S3.3: Design the fuzzy rule table.

[0014] Step S3.4: Perform fuzzy reasoning based on the fuzzy rule table.

[0015] Step S3.5: Defuzzification to obtain the slope parameter of the linear function

[0016] Step S3.6: Update the feedback gain according to the linear function.

[0017] Step S3.7: Continue to observe the longitudinal force of the driving wheel.

[0018] Compared with the prior art, the advantages of the present invention are:

[0019] 1. The longitudinal force of the driving wheel is estimated based on the sliding mode observer, eliminating the need to calculate the driving torque and rolling resistance coefficient of the driving wheel;

[0020] 2. Based on TS fuzzy logic, the feedback coefficient of the sliding mode observer is adaptively adjusted, so that the observer error converges quickly and stably. At the same time, compared with traditional fuzzy logic, it is more stable in dealing with nonlinear problems. The changing trend of the unknown nonlinear system is replaced by multiple linear functions, which has higher accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is a flow chart of the driving wheel longitudinal force estimation method based on sliding mode observer;

[0022] Figure 2 This is a comparison chart of the saturation function and the sign function.

[0023] Figure 3 This is the dynamic force diagram of 1 / 4 of the vehicle.

[0024] Figure 4(a) to Figure 4(b) It is the membership function diagram of fuzzy logic input quantity.

[0025] Figure 5 It is a fuzzy regular surface graph.

[0026] Figure 6 The graph of feedback gain coefficient variation is approximated by a linear function obtained by using the slope of fuzzy logic output. DETAILED DESCRIPTION

[0027] The method for estimating the longitudinal force of the driving wheel based on the TS fuzzy enhanced sliding mode observer of the present invention will be described in more detail below in conjunction with a schematic diagram, wherein a preferred embodiment of the present invention is shown, and it should be understood that those skilled in the art can modify the present invention described herein while still achieving the advantageous effects of the present invention. Therefore, the following description should be understood as being widely known to those skilled in the art, and not as a limitation to the present invention.

[0028] like Figure 1 As shown, the driving wheel longitudinal force estimation method based on TS fuzzy enhanced sliding mode observer includes the following steps:

[0029] Step S1, deriving a bounded disturbance sliding mode observer structure of a first-order system with a system input, a bounded disturbance and a system disturbance term.

[0030] The goal is to ensure that the observer can quickly and accurately track the actual trajectory while being robust to internal and external disturbances. Specifically:

[0031] Step S1.1, select a symbolic function and use the Lyapunov direct method stability criterion to prove that the observer error will converge stably, so that the observer's value can be used to replace the true value.

[0032] For the following first-order system:

[0033]

[0034] In formula (1), x is the state variable of the system;

[0035] u - input of the system;

[0036] d- unknown and bounded input, i.e. the state quantity to be estimated;

[0037] ψ - other interference terms;

[0038] B and P are coefficient matrices, respectively;

[0039] Next, we construct an observer, that is, to estimate d through the measured and estimated values ​​of the system's state variables.

[0040] Define the systematic error as

[0041] in, Represents the observed value (estimated value) of the system's state variables;

[0042] In this paper, the system error is selected as the sliding surface function, that is:

[0043]

[0044] Where, S in formula (2) and (3) represents the sliding surface function;

[0045] Construct a Lyapunov stability function:

[0046] V=S 2 / twenty three)

[0047] Derivation of formula (3) yields:

[0048]

[0049] According to the system state equation, that is, formula (1), the observer is constructed:

[0050]

[0051] Among them, L-feedback gain coefficient, which is also the target parameter to be adjusted later;

[0052] - represents the estimated value of the bounded perturbation d.

[0053] Substituting equation (1) and equation (5) into equation (4), we get:

[0054]

[0055] For bounded input d, it is easy to see that satisfy:

[0056]

[0057] Substituting formula (7) into formula (6), we get:

[0058]

[0059] In order to ensure the stability of the observer,

[0060] In formula (8), sgnS is a sign function, expressed as:

[0061]

[0062] According to the above judgment, we can get

[0063] So far, the sliding mode observer is in the form of:

[0064]

[0065] Combining equation (1) and equation (10), we get:

[0066]

[0067] Step S1.2: Based on the observer error finally stabilizing to 0, derive the bounded disturbance of the system The observer expression of .

[0068] Consider that when the system is stable, there is Therefore, according to formula (11), the final estimated value of the unknown input quantity d can be expressed as follows:

[0069]

[0070] Where, M is sliding mode gain.

[0071] Step S1.3, when the error fluctuates around 0, in order to avoid the chattering phenomenon that causes the sign function value to switch discontinuously between, the saturation function is used to approximate the sign function. For example Figure 2 shown.

[0072]

[0073] In formula (13), b is a small positive number, which is 0.1 here. In this case, the continuous saturation function can suppress chattering.

[0074] Step S2: deriving a sliding mode observer expression for the longitudinal force of the driving wheel based on a quarter vehicle dynamics model of the unmanned mining vehicle.

[0075] That is, based on the research object, the unmanned mining car, a quarter vehicle dynamics model is built (such as Figure 3 As shown in the figure, the expression of the driving wheel longitudinal force observer is derived, and the driving wheel longitudinal force is regarded as a bounded disturbance.

[0076] Depend on Figure 3 According to the driving wheel torque balance, we get:

[0077]

[0078] The parameters in formula (14) are Figure 3Correspondingly, the derivation process of formula (14) belongs to the prior art.

[0079] T-driving torque acting on the driving wheel;

[0080] J-tire moment of inertia;

[0081] f - rolling resistance coefficient;

[0082] r - tire rolling radius;

[0083] F Z - the load carried by the tire;

[0084] F X - tire longitudinal force; w - driving wheel speed.

[0085] According to equation (10), and ignoring the second term in equation (14), the sliding mode observer of the driving wheel speed is written as:

[0086]

[0087] That is, based on formula (1), let d=F X ; u=T;

[0088] Then, by combining formula (10), we can obtain formula (15).

[0089] In formula (15), F X It is both the system position input and the state quantity to be estimated.

[0090] According to equations (12) and (13), the final estimated expression of this paper is:

[0091]

[0092] in,

[0093] -Observed values.

[0094] In this way, the longitudinal force sliding mode observer of the driving wheel is obtained.

[0095] The actual speed of the driving wheel is measured by the wheel speed sensor of the unmanned mine wheel, and the initial estimated value of the driving wheel speed is Given by humans, the longitudinal force of the driving wheel is observed according to formula (16): Then, the differential of the estimated value of the driving wheel speed is calculated by equation (15), and then integrated to update the obtained driving wheel speed. Then, based on the updated speed, the estimated value of the driving wheel longitudinal force is updated according to equation (16), and the cycle is iterated.

[0096] Next, TS fuzzy logic is used to perform parameter adaptation on the feedback gain coefficient L.

[0097] Step S3: Utilize TS fuzzy logic to perform parameter adaptation on the feedback gain in the driving wheel longitudinal force observer.

[0098] Step S3.1: If the independent variable is time and the dependent variable is the gain coefficient L of the sliding mode observer, for each frame of control time, we only care about the change in L. Combined with the initial value set for L, we can get the L value of the next frame.

[0099] The error between the wheel speed measurement value and the observed value and the error change rate between the wheel speed measurement value and the observed value are selected as the input of the fuzzy logic, and the linear change slope of the feedback gain coefficient is selected as the output of the fuzzy logic.

[0100] The domain of input and output quantities is determined according to engineering practice, and fuzzy processing is performed on them during actual observation.

[0101] The observer error range is generally within [0rad / s, 12.5rad / s], and the observer error change rate range is generally within [0ras / s 2 ,10rad / s 2 ]. Therefore, the domain of error e is set to [0,12.5], and the domain of error change rate ec is set to [0,10].

[0102] During fuzzy processing, the domain is divided into 5 subsets, namely {VS (extremely small), S (small), M (medium), L (large), VL (maximum)}, and the domain of the linear change slope of the feedback gain coefficient is {10, 50, 100, 150, 200}.

[0103] Step S3.2: Establish the membership function of the input quantity, i.e., the error between the wheel speed measurement value and the observed value and the error change rate. In order to make the output surface as smooth as possible, the Gaussian function is used as the membership function, see Figure 4(a)-Figure 4(b) .

[0104] Step S3.3, design a fuzzy rule table.

[0105] The independent variables are the subset to which the error between the wheel speed measurement value and the observed value belongs and the subset to which the error change rate belongs. The dependent variable is the fuzzy logic output variable and the slope value k of the linear function, see Table 1.

[0106] Table 1 TS fuzzy rule table

[0107]

[0108] For the design of TS fuzzy system, taking a continuous nonlinear system with n state variables as an example, its TS fuzzy model can be described as shown in formula (17): rA fuzzy rule.

[0109]

[0110] In formula (17), x j represents the jth state variable of the system, represents the jth membership function of the ith rule, x(t) is the state vector, x(t) = [x 1 (t),x 2 (t)…x n (t)] T ∈R n , k i The constant slope of the linear function of the fuzzy logic output set by the expert knowledge, r is the number of fuzzy rules.

[0111] Based on the above rules, the relationship surface between the longitudinal force observation error and the longitudinal force observation error change rate, and the slope of the linear function of the feedback gain coefficient change can be obtained, see Figure 5 .

[0112] Step S3.4: During the actual driving wheel longitudinal force observation process, fuzzy reasoning is performed based on the fuzzy rule table.

[0113] Step S3.5, defuzzify and obtain the slope of the linear function.

[0114] According to the definition of fuzzy system defuzzification, the total output of fuzzy logic is as shown in formula (18).

[0115]

[0116] In formula (18), K is the final output of fuzzy logic, that is, the slope of the linear change function of the feedback gain coefficient of the sliding mode observer, ω i is the membership value of each fuzzy rule, Represents the state vector x j (t) The membership value of the j-th membership function for the ith rule.

[0117] Step S3.6: Update the feedback gain coefficient L according to the linear function.

[0118] K new =K (19)

[0119] In formula (19), K new That is, the linear change slope of L.

[0120] L new =LK new T (20)

[0121] In formula (20), L newis the updated sliding mode observer feedback gain coefficient, and T is the observation time frame. The observer feedback gain coefficient update process is shown in Figure 6 The curve in the figure represents the nonlinear curve of L change, and each straight line represents the approximation of nonlinear change. The slope of the straight line is K new , K new That is the final output of the TS fuzzy logic used in the present invention.

[0122] Step S3.7, continue to observe the longitudinal force of the driving wheel, and repeat in a cycle.

[0123] The above is only a preferred embodiment of the present invention and does not limit the present invention in any way. Any technician in the relevant technical field, without departing from the scope of the technical solution of the present invention, makes any form of equivalent replacement or modification to the technical solution and technical content disclosed in the present invention, which does not depart from the content of the technical solution of the present invention and still falls within the protection scope of the present invention.

Claims

1. A driving wheel longitudinal force estimation method based on sliding mode observer, characterized in that: The following steps are involved: Step S1, deriving a bounded disturbance sliding mode observer structure of a first-order system with a system input, a bounded disturbance and a system disturbance term; Step S2: derive a driving wheel longitudinal force sliding mode observer structure based on a quarter vehicle dynamics model of the unmanned mining vehicle and a sliding mode observer structure of bounded disturbance.

2. The driving wheel longitudinal force estimation method based on sliding mode observer according to claim 1, characterized in that: Step S1 includes the following steps: Step S1.1: Select a symbolic function and use the Lyapunov direct method stability criterion to prove that the observer error will converge stably. Step S1.2: According to the observer error finally being stabilized to 0, derive the sliding mode observer expression of the bounded disturbance of the system. Step S1.3: When the system error changes around 0, causing the system to vibrate, in order to avoid the observer error caused by the vibration phenomenon, the saturation function is used to approximate the sign function.

3. The driving wheel longitudinal force estimation method based on sliding mode observer according to claim 1, characterized in that: The step S2 further includes the following steps: Step S3: Utilize TS fuzzy logic to perform parameter adaptation on the feedback gain in the driving wheel longitudinal force observer.

4. The driving wheel longitudinal force estimation method based on sliding mode observer according to claim 3 is characterized in that: Step S3 includes the following steps: Step S3.1: Use the slope of the linear function as the output of the TS fuzzy logic, select the wheel speed measurement value and the observed value error and the error change rate as the input of the fuzzy logic; determine the domain of the input and output quantities, and perform fuzzification processing on them; Step S3.2: Establishing the membership function of the input quantity; Step S3.3: Design fuzzy rule table; Step S3.4: performing fuzzy reasoning based on the fuzzy rule table; Step S3.5: Defuzzification to obtain the slope parameter of the linear function; Step S3.6: Update the feedback gain according to the linear function; Step S3.7: Continue to observe the longitudinal force of the driving wheel.

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