Dispensing system servo control method based on self-adaptive finite time control

Abstract

The invention discloses a glue dispensing system servo control method based on self-adaptive finite time control. The glue dispensing system servo control method specifically comprises the following steps that 1, a mathematical model of a glue dispensing system servo motor is established; and 2, designing a speed ring self-adaptive finite time controller of the servo motor according to the mathematical model of the servo motor and a finite time control theory, and realizing high-dynamic control on the servo motor of the dispensing system. By the adoption of the method, the problem that the dispensing speed of the dispensing system is decreased due to the fact that the control gain is small when the error state variable of the dispensing system based on finite time control is large is solved, and it is guaranteed that the dispensing system can achieve high-dynamic and high-speed dispensing in different error convergence states.

Description

Technical Field

[0001] The invention belongs to the technical field of servo motor control of a high-performance dispensing system, and relates to a servo control method for a dispensing system with adaptive finite time control. Background Art

[0002] The rapid development of science and technology has promoted the development of electronic products towards miniaturization, high precision and full intelligence. At present, the demand and market size of curved surfaces in the field of electronic products, represented by laptops, smart phones, flat-panel displays, etc., are growing rapidly. In this context, high-bandwidth, high-dynamic dispensing system servo control technology has become one of the key technologies to improve the packaging efficiency of electronic products and save production costs. With the rapid development of electronic products such as computers, communications, and consumer electronics, the miniaturization and complexity of precision electronic devices have placed higher and higher requirements on dispensing systems. As the demand for dispensing system applications gradually increases, traditional dispensing servo motor systems have already met the demand for high-dynamic control. Therefore, it has become an urgent need to study a high-dynamic control strategy for servo motors suitable for dispensing systems.

[0003] The traditional servo control method of the dispensing system is usually a vector control strategy based on the proportional differential controller. As a linear controller, the proportional differential controller can only achieve the effect of infinite time convergence when the error converges, while the finite time control starts from the perspective of the optimal convergence time of the system error state, so that the closed-loop system converges to the equilibrium point within a finite time. Due to the introduction of exponential power in the finite time controller, compared with the traditional linear controller, the finite time control can ensure that the system has a faster convergence speed. In addition, because the traditional linear controller can only achieve exponential convergence, that is, the system state can converge to zero when the time approaches infinity, the finite time control can prove that the system state converges to zero within a finite time in its non-smooth form. In addition, compared with the linear controller, the finite time control has better anti-disturbance and improves the robustness of the system. Compared with the discontinuous sliding mode controller, there is no chattering problem. Based on the above advantages, the finite time control technology is widely used in high-precision fields such as spacecraft attitude coordination control, missile terminal guidance control and dispensing servo control.

[0004] However, the traditional finite time control has a small control gain when the error input is large, which affects the dynamic performance of the dispensing system and causes the dispensing rate of the dispensing system to decrease. Based on this, an adaptive finite time control strategy is proposed. It can provide a large gain to the controller when the error input is large, so that it can converge quickly, and restore its error convergence characteristics under small gain. The gain size is adaptive according to the error size, which ensures that the system can achieve high dynamic dispensing under different error convergence states, making up for the problem that the dispensing system based on finite time control has low dynamic performance when the input error is large, resulting in a decrease in dispensing speed. Summary of the invention

[0005] The purpose of the present invention is to provide a servo control method for a dispensing system based on adaptive finite time control, which solves the problem that the dispensing speed of the dispensing system based on finite time control decreases when the error state variable is large.

[0006] The technical solution adopted by the present invention is a servo control method for a dispensing system with adaptive finite time control, which specifically includes the following steps:

[0007] Step 1, establish a mathematical model of the servo motor of the dispensing system;

[0008] Step 2: Design a speed loop adaptive finite time controller for the servo motor based on the servo motor mathematical model and finite time control theory to achieve high dynamic control of the servo motor of the dispensing system.

[0009] The present invention is also characterized in that:

[0010] The specific process of step 1 is:

[0011] Assuming that the servo motor magnetic field is sinusoidally distributed and the magnetic circuit is unsaturated, the servo motor mechanical equation is as follows:

[0012]

[0013] Among them, ω r is the rotor speed, J is the moment of inertia, is the time derivative of the rotor speed, T1 is the electromagnetic torque, T2 is the load torque, B is the damping coefficient, and the electromagnetic torque T1 can be expressed as shown below:

[0014] T1=n p ψ f i q (2)

[0015] Among them, n p is the pole pair number, ψ f is the permanent magnet flux, i q is the q-axis current;

[0016] According to equations (1) and (2), the servo system speed loop dynamic equation is as follows:

[0017]

[0018] in, is the q-axis reference current, g is the current coefficient, and d is the total disturbance of the speed loop.

[0019] In step 1, the current coefficient g is expressed as shown in the following formula:

[0020] g=g0+g1=n pψ f / J (4)

[0021] where g0 = n p ψ f0 / J0, g0 is the rated current coefficient, ψ f0 is the nominal value of the permanent magnet flux linkage, J0 is the nominal value of the moment of inertia; g1 = n p ψ f1 / J1, g1 is the parameter variation of the current coefficient, Ψ f1 is the parameter variation of the permanent magnet flux linkage, J0 is the parameter variation of the moment of inertia.

[0022] In step 1, the total loop disturbance d is expressed by the following formula:

[0023] d = d1 + d2 + d3 + d4 (5)

[0024] where d1 is the parameter variation disturbance, d2 = -T1 / J, d2 is the load disturbance, d3 is the q-axis current loop tracking error disturbance, d4 = -Bω r / J, d4 is the damping disturbance.

[0025] The specific process of step 2 is as follows:

[0026] Design the speed error ε as the error state variable, is the given speed, then ε is expressed by the following formula:

[0027]

[0028] Taking the derivative of ε gives:

[0029]

[0030] Ignoring the q-axis current loop tracking error disturbance d3 and the damping disturbance d4, equation (7) is rewritten as:

[0031]

[0032] According to formula (8) and the adaptive finite-time feedback law The adaptive finite-time feedback control law of the servo motor can be designed as shown in the following formula (9):

[0033]

[0034] where is the adaptive finite-time function, η1 is the control gain, η1 > 0; ε max is the maximum value of the error; a is the exponential power, 0 < a < 1; sign() is the sign function, specifically expressed as x is the input variable.

[0035] In step 2, a finite-time disturbance observer is used to compensate for the disturbance and ensure the convergence of the speed loop of the servo system within a finite time. Therefore, an adaptive finite-time disturbance observer is designed as shown in Equation (10):

[0036]

[0037] where ε1 is the estimation error; is the adaptive finite-time function; η2 and η3 are gain coefficients, η2 > 0, η3 > 0; ε 1max is the maximum value of the estimation error; b1 and b2 are exponential powers, 0 < b1, b2 < 1, ζ1 is the estimated value of the speed, and ζ2 is the estimated value of the disturbance.

[0038] In step 2, when the adaptive finite-time disturbance observer converges, the disturbance estimated value ζ2 converges to the actual total disturbance d, and the estimation of the actual disturbance is completed.

[0039] In step 2, with the speed error ε as the input, the following equation is obtained from Equation (9) and Equation (5):

[0040]

[0041] Combining Equation (11) with the adaptive finite-time disturbance observer formula (10), the adaptive finite-time feedback control law formula (9) ensures that the servo motor can converge to the convergence point within a finite time during speed tracking, and the adaptive finite-time disturbance observer formula (10) ensures that the dispensing system can estimate and compensate for the disturbance within a finite time when受到扰动; the adaptive finite-time controller of the speed loop of the dispensing servo system is obtained from Equation (10) and Equation (11) as shown in Equation (12):

[0042]

[0043] The beneficial effect of the present invention is that, compared with the traditional servo control method of the dispensing system based on finite-time control, the adaptive finite-time control strategy of the present invention enables it to ensure the large-gain convergence of the controller under the state of large error input, ensuring that the system can achieve high-dynamic and high-bandwidth control under different error convergence states, and making up for the problem of limited dynamic performance of the dispensing system based on finite-time control when the input error is large. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is the system block diagram of the vector control method of the servo motor of the dispensing system for the servo control method of the dispensing system with adaptive finite-time control of the present invention.

[0045] Figure 2It is a structural block diagram of the adaptive finite time feedback control law in the servo control method of the dispensing system of the adaptive finite time control of the present invention;

[0046] Figure 3 It is a structural block diagram of an adaptive finite-time disturbance observer in a servo control method for a dispensing system with adaptive finite-time control according to the present invention. DETAILED DESCRIPTION

[0047] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0048] Example 1

[0049] The servo control method of the dispensing system with adaptive finite time control of the present invention adopts a servo motor of the dispensing system based on adaptive finite time control, wherein the block diagram of the vector control system adopted is as follows Figure 1 As shown in the figure, the control system uses an adaptive finite time controller in the speed loop to form a closed-loop AC speed control system for speed control, and a PI regulator is used in the current loop to form a dual-loop control of the speed loop and the current loop. The stator current i of the dispensing servo motor in the three-phase stationary coordinate system is detected by the current Hall sensor. a 、i b 、i c ; Detected three-phase stator current i a 、i b 、i c Through the abc / αβ transformation, the current value i is converted to the two-phase stationary coordinate system α 、i β ;i α 、i β Through αβ / dq transformation, the current value i is converted to the two-phase synchronous rotating coordinate system d 、i q ; Feedback actual rotor electrical angular velocity ω r With a given electrical angular velocity After the difference is passed through the adaptive finite time controller, the current in the two-phase rotating coordinate system is obtained. Feedback current i d 、i q With given current The difference is passed through the PI regulator to obtain the output voltage of the two-phase rotating coordinates After dq / αβ, it is converted into the two-phase voltage u in the two-phase stationary coordinate system α 、u β After modulation by the SVPWM generation module, the PWM wave is generated and applied to the dispensing servo motor through the three-phase inverter bridge.

[0050] Example 2

[0051] The servo control method of the dispensing system with adaptive finite time control of the present invention is specifically implemented according to the following steps:

[0052] Step 1, establish a mathematical model of the servo motor of the dispensing system;

[0053] Step 2: Design a speed loop adaptive finite time controller for the servo motor based on the servo motor mathematical model and finite time control theory to achieve high dynamic control of the servo motor of the dispensing system.

[0054] Example 3

[0055] The specific process of step 1 is:

[0056] Assume that the servo motor magnetic field is sinusoidally distributed and the magnetic circuit is unsaturated. The servo motor mechanical equation is expressed as shown in the following formula:

[0057]

[0058] Among them, ω r is the rotor speed, J is the moment of inertia, is the time derivative of the rotor speed, T1 is the electromagnetic torque, T2 is the load torque, and B is the damping coefficient. The electromagnetic torque T1 can be expressed as shown below:

[0059] T1=n p ψ f i q (2)

[0060] Among them, n p is the pole pair number, ψ f is the permanent magnet flux, i q is the q-axis current.

[0061] According to equations (1) and (2), the servo system speed loop dynamic equation can be expressed as follows:

[0062]

[0063] in, is the q-axis reference current, g is the current coefficient, and d is the total disturbance of the speed loop.

[0064] Example 4

[0065] In step 1, the current coefficient g is expressed as shown in the following formula:

[0066] g=g0+g1=n p ψ f / J(4)

[0067] Where g0 = n p ψ f0 / J0, where g0 is the rated current coefficient, ψ f0 is the nominal value of the permanent magnet flux linkage, and J0 is the nominal value of the moment of inertia; g1 = n p ψ f1 / J1, where g1 is the parameter variation of the current coefficient, Ψ f1 is the parameter variation of the permanent magnet flux linkage, and J0 is the parameter variation of the moment of inertia.

[0068] Example 5

[0069] In step 1, the total loop disturbance d in equation (3) is expressed as the following formula:

[0070] d = d1 + d2 + d3 + d4 (5)

[0071] where d1 is the parameter variation disturbance, d2 = -T1 / J, and d2 is the load disturbance, d3 is the q-axis current loop tracking error disturbance, d4 = -Bω r / J, and d4 is the damping disturbance.

[0072] Example 6

[0073] The designed speed error ε is the error state variable, is the given speed, then ε is expressed as the following formula:

[0074]

[0075] Taking the derivative of ε gives:

[0076]

[0077] Since d1 and d2 are the main disturbances and account for the main factors in the total loop disturbance. Therefore, ignoring the q-axis current loop tracking error disturbance d3 and the damping disturbance d4, equation (7) can be rewritten as

[0078]

[0079] From equation (8) and the adaptive finite-time feedback law The servo motor adaptive finite-time feedback control law can be designed as shown in the following equation (9):

[0080]

[0081] where is the adaptive finite-time function, η1 is the control gain, η1 > 0; ε max is the maximum error, usually set to be consistent with the input error limit amplitude; a is the exponential power, 0 < a < 1; sign() is the sign function, specifically expressed as x is the input variable. The structural block diagram of the finite-time feedback control law is as Figure 2 shown.

[0082] As can be seen from Equation (9), the values of the disturbances d1 and d2 need to be obtained in the feedback control law, which usually cannot be directly obtained in an actual system. The servo motor is often subject to various disturbances. The designed adaptive finite-time feedback control law can only make the error converge to a region but not to a point when disturbed. Since the finite-time disturbance observer can compensate for the disturbance and ensure the convergence of the speed loop of the servo system within a finite time. Therefore, an adaptive finite-time disturbance observer is designed as shown in Equation (10), and the structural block diagram is as Figure 3 shown.

[0083]

[0084] where ε1 is the estimation error; is the adaptive finite-time function; η2 and η3 are gain coefficients, η2>0, η3>0; ε 1max is the maximum value of the estimation error; b1 and b2 are exponential powers, 0 < b1, b2 < 1; ζ1 is the estimated value of the speed, and ζ2 is the estimated value of the disturbance. When the adaptive finite-time disturbance observer converges, the disturbance estimated value ζ2 converges to the actual total disturbance d to complete the estimation of the actual disturbance.

[0085] Taking the speed error ε as the input, the following equation can be obtained from Equations (9) and (5):

[0086]

[0087] Combining Equation (11) with the adaptive finite-time disturbance observer as shown in Equation (10). The adaptive finite-time feedback control law (9) ensures that the servo motor can converge to the convergence point within a finite time during speed tracking, and the adaptive finite-time disturbance observer (10) ensures that the dispensing system can estimate and compensate for the disturbance within a finite time when disturbed.

[0088] From (10) and (11), the adaptive finite-time controller of the speed loop of the dispensing servo system can be obtained as shown in Equation (12).

[0089]

Claims

1. The servo control method of the dispensing system with adaptive finite time control is characterized by: The specific steps include: Step 1, establish a mathematical model of the servo motor of the dispensing system; Step 2: Design a speed loop adaptive finite time controller for the servo motor based on the servo motor mathematical model and finite time control theory to achieve high dynamic control of the servo motor of the dispensing system.

2. The servo control method for a dispensing system with adaptive finite time control according to claim 1 is characterized in that: The specific process of step 1 is as follows: Assuming that the servo motor magnetic field is sinusoidally distributed and the magnetic circuit is unsaturated, the servo motor mechanical equation is as follows: Among them, ω r is the rotor speed, J is the moment of inertia, is the time derivative of the rotor speed, T1 is the electromagnetic torque, T2 is the load torque, B is the damping coefficient, and the electromagnetic torque T1 can be expressed as shown below: T1=n p ψ f one q (2) Among them, n p is the pole pair number, ψ f is the permanent magnet flux, i q is the q-axis current; According to equations (1) and (2), the servo system speed loop dynamic equation is as follows: in, is the q-axis reference current, g is the current coefficient, and d is the total disturbance of the speed loop.

3. The servo control method for a dispensing system with adaptive finite time control according to claim 2 is characterized in that: In step 1, the current coefficient g is expressed as shown in the following formula: g=g0+g1=n p ψ f / J (4) Where g0 = n p ψ f0 / J0, g0 is the rated current coefficient, ψ f0 is the nominal value of permanent magnet flux, J0 is the nominal value of moment of inertia; g1 = n p ψ f1 / J1, g1 is the parameter change of the current coefficient, Ψ f1 is the parameter change of the permanent magnet flux, and J0 is the parameter change of the moment of inertia.

4. The servo control method for a dispensing system with adaptive finite time control according to claim 3 is characterized in that: In step 1, the total loop disturbance d is expressed as shown in the following formula: d=d1+d2+d3+d4 (5) in, d1 is the parameter change disturbance, d2 = -T1 / J, d2 is the load disturbance, d3 is the q-axis current loop tracking error disturbance, d4=-Bω r / J, d4 is the damped disturbance.

5. The servo control method for a dispensing system with adaptive finite time control according to claim 4 is characterized in that: The specific process of step 2 is: The design speed error ε is the error state variable, For a given speed, ε is expressed as follows: Taking the derivative of ε, we get: Ignoring the q-axis current loop tracking error disturbance d3 and damping disturbance d4, equation (7) is rewritten as: According to formula (8) and the adaptive finite-time feedback law The servo motor adaptive finite-time feedback control law can be designed as shown in the following equation (9): Among them, is an adaptive finite-time function, η1 is a control gain, η1 > 0; ε max is the maximum value of the error; a is an exponential power, 0 < a < 1; sign() is a sign function, specifically expressed as where x is the input variable.

6. The servo control method for a dispensing system with adaptive finite time control according to claim 4 is characterized in that: In step 2, a finite-time disturbance observer is used to compensate for the disturbance and ensure that the servo system speed loop converges within a finite time. Therefore, an adaptive finite-time disturbance observer is designed as shown in formula (10): where ε1 is the estimation error; is the adaptive finite-time function; η2 and η3 are gain coefficients, η2 > 0, η3 > 0; ε 1max is the maximum value of the estimation error; b1 and b2 are exponential powers, 0 < b1, b2 < 1, ζ1 is the estimated value of the velocity, and ζ2 is the estimated value of the disturbance.

7. The servo control method for a dispensing system with adaptive finite time control according to claim 6 is characterized in that: In step 2, when the adaptive finite-time disturbance observer converges, the disturbance estimation value ζ2 converges to the actual total disturbance d, and the estimation of the actual disturbance is completed.

8. The servo control method for a dispensing system with adaptive finite time control according to claim 7 is characterized in that: In step 2, the speed error ε is used as input, and the following formula is obtained from formula (9) and formula (5): Combining formula (11) with the adaptive finite-time disturbance observer formula (10), the adaptive finite-time feedback control law formula (9) ensures that the servo motor can converge to the convergence point in a finite time during speed tracking, and the adaptive finite-time disturbance observer formula (10) ensures that the dispensing system can estimate the disturbance and compensate it in a finite time when it is disturbed. The adaptive finite-time controller of the speed loop of the dispensing servo system is obtained from formula (10) and formula (11) as shown in formula (12):

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