Method of forming mathematical model of man-operator at tracking of preset steering wheel positions on director device

The invention relates to methods for forming a mathematical model of a human operator (for example, a pilot) while tracking the set positions (deviations) of the control wheel from the error signal on the director. The mathematical model of the human operator is understood to mean the mathematical connection between the error of the steering wheel deflection in the form of the deflection of the arrow of the director and the position of the steering wheel (or the force applied to the steering wheel).

The method is necessary when replacing a human operator with his mathematical model, for example, to simulate the actions of an operator (for example, a pilot) in the mathematical modeling and analysis of the director's control processes of a dynamic object, for example, an airplane.

There is a well-known method of forming a mathematical model for the self-inertia of a human operator (prototype) (see Dobrolensky, Yu.P., Ivanova VI, Pospelov GS Automatics of guided missiles .- M: State Scientific and Technical Publishing House DEFENSE, 1963. - 548 p.) As a transfer function of the serial connection of the link of pure delay, aperiodic and forcing links.

The disadvantage of this model is its incompleteness and inaccuracy, for example, when the operator-operator traces the set steering wheel positions according to different time functions by the director. For example, if the preset position of the hand wheel is a step function, then it becomes necessary to add a prototype of the integrating link to the transfer function (Obolensky Yu.G., Pokhvalensky VL, Teryaev ED, Yakubovich MM Development and study of the action model pilot in the positioning of control knobs for aircraft - Moscow: Nauka // Problems of Machine Building and Machine Reliability, 2004, No. 5. - P. 70-77). However, experiments show that with the exponential function of the preset positions of the handwheel, it is expedient to add an integrating and aperiodic link with a time constant,

The proposed solution is characterized by the fact that the mathematical model of estimating the state variables of the assumed dynamic model of the generator-generator of the preset positions of the steering wheel is formed and additionally connected, corresponding, for example, to the Laplace image of the real time function of the given positions, so that the output signal of the mathematical model of the self- the gain factors are summed with the input signals of each integrator of the mathematical model of estimating the state variables of the problem snip-generator, i.e., with the derivatives of its state variables, as in known observing devices, and the weighted sum of these estimates, corresponding to the dynamic model of the generator-generator, is the output of the complete mathematical model of the human operator and the input of the handwheel.

The essence of the proposed solution is explained Fig. 1, which shows a flowchart simulating the process of tracking by a human operator on the director of the given position of the steering wheel with the proposed addition to the model of the operator's own inertia of the operator.

Referring to Fig. 2 shows the transient processes of tracking the stepped preset positions of the wheel in the bench experiment with the real participation of the human operator.

Referring to Fig. 3 shows transient processes of simulation simulation of the same process as in Fig. 2, with the corresponding input signal by the mathematical model of the human operator and the helm model with the selected gain between two parts of the transfer function of the human operator.

Referring to Fig. 4 shows the transient processes of tracking the exponential preset positions of the wheel in the bench experiment with the real participation of the human operator.

Referring to Fig. 5 shows the transient processes of simulation simulation of the same process as in Fig. 4, with the corresponding input signal by the mathematical model of the human operator and the helm model with the selected gain between the two parts of the transfer function of the human operator.

Accepted designations:

1 - the generator-generator of the set positions of the wheel;

2 - adder;

3 - the director's device (DP);

4 - mathematical model of the self-inertia of the human operator (prototype);

5 - vector-column of gain factors (in the general case of variables);

6 - mathematical model of estimating the state variables of the dynamic generator-generator model, corresponding, for example, to the Laplace transform of the time function of the given steering wheel positions;

7 - complete mathematical model of the human operator;

8 - mathematical model of the wheel;

9 - model of the handwheel deflection sensor X_w;

x_z - time function of the preset positions (deviations) of the wheel (output of block 1);

x_w= x_R - steering wheel deflection (output of block 8);

e - steering wheel deflection error (e = x_z-x_w) (output of adder 2);

e_P - the output of the mathematical model of the self-inertia of the human operator (block 4);

x is the vector of state variables of the assumed or real dynamic model of the generator-generator of the given steering wheel positions;

x (0) is a vector of initial values ​​of state variables of the dynamic generator-generator model;

x_m - a vector of estimating the state variables of the mathematical model of the generator-generator in the mathematical model of the human operator;

x_zm - an estimation of the position of the handwheel assigned by the operator-operator model (output of block 6);

A - feedback matrix of the dynamic generator-generator model;

H is the matrix-row of the formation of a given time function x3 from the components of the vector x;

K is the vector gain in the mathematical model of the human operator in the general case, time-variable (block 5);

W_P(s) = e^-τs (T₁s + 1) / (T₂s + 1) is the transfer function of the operator's own inertia (prototype model) (block 4);

W_w(s) is the transfer function of the helm model (block 8).

Sequence of actions by method.

Form a mathematical model of estimating the state variables of the dynamic generator-generator model of the given steering wheel positions on the basis of the assumed dynamic model of the generator-generator, for example, in the form of linear vector differential and algebraic equations

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where x is the n-dimensional vector of the state variables of the generator of the given positions of the wheel with the initial condition x (0), A is the matrix (nxn), and H is the row matrix (nx1). These equations and their parameters, if they are stationary, must correspond to the Laplace transform of the time function of the given positions of the handwheel. For some problems, a system of the type (1), (2) can be nonstationary and nonlinear.

In accordance with the proposed solution, the mathematical model of the vector of estimates of the state variables of the generator-generator and the position of the handwheel set by the operator-operator model is written in the form of equations

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Here the output of the model of the self-inertia of the human operator (prototype) e_P corrects, as required in the observing device, the state variables of the model (Kuzovkov NT Modal control and observing devices .- M .: Mechanical Engineering, 1976. - 184 s).

Equations (3), (4) represent the proposed addition to the mathematical model of the prototype.

Consider the examples of obtaining a complete mathematical model of the human operator.

Example 1. Let the given positions of the wheel represent a function in the form of alternating constant values ​​equal in magnitude to the value 2.5. Then, for example, in the region of positive x_z= 2.5 the Laplace transform will be equal to 2.5 / s, and the equations of the dynamic generator-generator model will have the form

dx / dt = 0,

x_z= x,

x (0) = 2.5.

Accordingly, the proposed addition to the mathematical model of the self-inertia of the human operator will be determined by equations

dx_m/ dt = ke_P,

x_zm= x_m.

As a result, the complete mathematical model of the human operator corresponds to the transfer function

W_P(s) = e^-τs k (T₁s + 1) / ((T₂s + 1) s),

where the proposed addition to the prototype model is an integrating link k / s.

The concrete values ​​of all the constants τ, k, T₁, T₂ can be determined by the results of a bench experiment for a particular person who participated in the experiment.

In Fig. 2 shows a fragment (from the 30th to the 34th second) of the tracking by a specific human operator of the specified stepped position of the handwheel in the physical (bench) experiment, where the specified positions x_z= x_from and the resulting deviation of the steering wheel x_w= x_R, as well as the magnitude of the deviation error e (t). Here x_z= x_w= 2.5 for t &lt;30 s and x_z= -2.5 for t&gt; 30 s, and the initial error is e = 0 for t &lt;30 s and e = 5 for t&gt; 30 s. As a result, the error is reset after 1.5 seconds.

In Fig. 3 shows a similar fragment of mathematical simulation on a PC for the same set positions of the wheel with the selected suitable values ​​of all parameters of the mathematical model of a particular human operator τ = 0.3, k = 1.23, T₁= 0.27, T₂= 0.15. The transfer function of the wheel had the form

W_w(s) = 200 / (s²+ 23s + 200).

As you can see, simulation simulation with the complete mathematical model of the human operator is a good repetition of the bench model.

Example 2. Let the given position of the hand wheel represent the alternating segments of the exponential functions of time x_z= c_ie^-0.2t, where c_i varies from 2.5 to 4.5 and can have different signs. Then, for example, in the region of positive value c_i= 2.5, the Laplace transform will be 2.5 / (s + 0.2), and the equations of the dynamic generator-generator model will have the form

dx / dt = -0.2x,

x_z= x,

x (0) = 2.5.

Accordingly, the proposed addition to the mathematical model of the self-inertia of the human operator will be determined by equations

dx_m/ dt = -0.2x_m+ kе_P,

x_zm= x_m.

As a result, the complete mathematical model of the human operator corresponds to the transfer function

W_P(s) = e^-τs k (T₁s + 1) / ((T₂s + 1) (s + 0.2)),

where the proposed addition to the prototype model is an aperiodic link with a transfer function k / (s + 0.2).

The specific values ​​of all the constants τ, k, T₁, T₂ can be determined by the results of a bench experiment for a particular person who participated in the experiment.

In Fig. 4 shows a fragment (from the 20th to the 30th second) of the tracking of the given exponential functions of the handwheel positions in the bench experiment, where the specified positions x_z= 4,4 e^-0.2t and the resulting deviation of the steering wheel x_p(t), as well as the magnitude of the deviation error e (t) = x_z(t) -x_p(t). Here x_z= x_R= -0.6 for t &lt;20 s and x_z= 4.4 for t&gt; 20 s, and the initial error is e = 0 for t &lt;20 s and e = 5 for t&gt; 20 s. As a result, the error is reset after 1.5 seconds.

In Fig. 5 shows a similar fragment of mathematical simulation on the PC of the same processes as in Fig. 4, with the chosen values ​​of the parameters τ = 0.3, k = 1.08, T₁= 0.18, T₂= 0.15.

As you can see, simulation simulation with the complete mathematical model of a particular human operator, as in example 1, is a good repetition of the bench model.

Examination of these and other examples of given positions of the wheel allows to draw a general conclusion that the added part of the mathematical model of the human operator corresponds to the dynamic model of the generator-generator.

The technical result of using the proposed method of forming a mathematical model of a human operator is to improve the accuracy of mathematical simulation on a PC and to analyze the processes of the director's management if it is based on the operator's tracking system of the specified steering wheel positions, as recommended in the work (Eliseev V.D. ., Klyuev ED, Petrin KV, Teryaev ED Improving the quality of directorate management of a dynamic object .-- M., Problems of Management, 2012, № 4. - P. 69-74).

The novelty of the proposed invention is confirmed by the distinctive part of the claims that has not been known so far, namely, to the known mathematical model of the operator's own inertia for the accuracy increase, the observing device is added in the form of a mathematical model for estimating the state variables of the dynamic generator-generator dynamic model preset positions of the steering wheel.