Adaptive finite time control method for dispensing system servo control

Abstract

The application discloses a dispensing system servo control method based on adaptive finite time control, and specifically comprises the following steps: step 1, establishing a mathematical model of a dispensing system servo motor; step 2, designing a speed loop 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 of the dispensing system servo motor. The method solves the problem that the control gain is small when the error state variable of the dispensing system based on the finite time control is large, the dispensing speed of the dispensing system is reduced, and high dynamic and high speed dispensing of the dispensing system in different error convergence states is ensured.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of high-performance dispensing system servo motor control, and relates to a dispensing system servo control method based on adaptive finite time control. BACKGROUND

[0002] The rapid development of science and technology promotes electronic products to develop in the direction of micro-volumization, high precision and full intelligence. At present, the demand and market size of curved surfaces represented by notebook computers, smart phones and tablet displays in the electronic product field are growing rapidly. Under this background, high-bandwidth and 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 computer, communication, consumer electronics and other electronic products, the miniaturization and complexity of precision electronic devices have increasingly high requirements for dispensing systems. As the demand for dispensing system applications gradually increases, the traditional dispensing servo motor system has been unable to meet the high dynamic control requirements. Therefore, it is an urgent need to study a high dynamic control strategy for dispensing system servo motors.

[0003] The traditional dispensing system servo control method is usually a vector control strategy based on a proportional-derivative controller. As a linear controller, the proportional-derivative controller can only achieve infinite time convergence when the error converges, while the finite time control starts from the optimal error state convergence time of the system, so that the closed-loop system converges to the equilibrium point in 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 faster convergence of the system. Because the traditional linear controller can only achieve exponential convergence, i.e. the system state converges to zero when the time approaches infinity, the finite time control can prove that the system state converges to zero in a finite time due to its non-smooth form. In addition, the finite time control has better disturbance rejection than the linear controller, which improves the robustness of the system, and there is no chattering problem compared with the non-continuous sliding mode controller. 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 small control gain when the error input is large, which affects the dynamic performance of the dispensing system and leads to a decrease in the dispensing rate of the dispensing system. Based on this, an adaptive finite time control strategy is proposed. The controller can provide large gain to achieve fast convergence in the state of large error input, and restore its error convergence characteristics under small gain. The gain size is adapted according to the error size, which ensures that the system can achieve high dynamic dispensing under different error convergence states, and makes up for the problem that the dispensing speed decreases due to the small dynamic performance of the dispensing system based on finite time control when the input error is large. SUMMARY

[0005] The object of the present application is to provide a point glue system servo control method of adaptive finite time control, which solves the problem of point glue system speed drop when the error state variable is large based on finite time control.

[0006] The technical scheme adopted by the present application is a point glue system servo control method of adaptive finite time control, which specifically comprises the following steps:

[0007] Step 1, establishing a mathematical model of the point glue system servo motor;

[0008] Step 2, designing a speed loop adaptive finite time controller of the servo motor according to the servo motor mathematical model and the finite time control theory, and realizing high dynamic control of the point glue system servo motor.

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

[0010] The specific process of step 1 is:

[0011] Assuming that the magnetic field of the servo motor is sinusoidal distribution, the magnetic circuit is not saturated, and the mechanical equation of the servo motor is shown in the following formula:

[0012]

[0013] Where, 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 in the following formula:

[0014] T1=n p ψ f i q (2)

[0015] Where, n p is the number of pole pairs, ψ f is the permanent magnet flux linkage, i q is the q-axis current;

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

[0017]

[0018] Where, 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 \(g_0 = n\) p ψ f0 / J0, \(g_0\) is the rated current coefficient, ψ f0 is the nominal value of the permanent magnet flux linkage, \(J_0\) is the nominal value of the moment of inertia; \(g_1 = n\) p ψ f1 / J1, \(g_1\) is the parameter variation of the current coefficient, Ψ f1 is the parameter variation of the permanent magnet flux linkage, \(J_0\) 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] \(d = d_1 + d_2 + d_3 + d_4\) (5)

[0024] where \(d_1\) is the parameter variation disturbance, \(d_2 = -T_1 / J\), \(d_2\) is the load disturbance, \(d_3\) is the q-axis current loop tracking error disturbance, \(d_4 = -Bω\) r / J, \(d_4\) 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] ​​​​​​​​​​​​​​​​​​​​​​ x is an input variable.

[0035] In step 2, the finite-time disturbance observer is used to compensate the disturbance and ensure that the speed loop of the servo system converges in finite time, therefore, the adaptive finite-time disturbance observer is designed as shown in formula (10):

[0036]

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

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

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

[0040]

[0041] 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 finite time when tracking the speed, and the adaptive finite-time disturbance observer formula (10) ensures that the dispensing system can estimate the disturbance and compensate in finite time when disturbed; the adaptive finite-time controller of the dispensing servo system speed loop obtained from formula (10) and formula (11) is shown in formula (12):

[0042]

[0043] The beneficial effects of the present application are that, compared with the conventional dispensing system servo control method based on finite-time control, the adaptive finite-time control strategy of the present application can ensure large gain convergence of the controller in the state of large error input, and ensure that the system can realize high dynamic and high bandwidth control in different error convergence states, thereby making up for the problem that the dynamic performance of the dispensing system based on finite-time control is limited when the input error is large. BRIEF DESCRIPTION OF DRAWINGS

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

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

[0046] Figure 3 This is a block diagram of the adaptive finite-time disturbance observer in the servo control method of the dispensing system of the present invention. Detailed Implementation

[0047] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0048] Example 1

[0049] This invention relates to an adaptive finite-time control method for a dispensing system servo control, employing a servo motor based on adaptive finite-time control. The block diagram of the vector control system used is shown below. Figure 1 As shown, the control system employs an adaptive finite-time controller in the speed loop, forming a closed-loop AC speed regulation system for speed control. A PI controller is used in the current loop, forming a dual-loop control system for both speed and current. The stator current i of the dispensing servo motor in the three-phase stationary coordinate system is detected by a Hall effect current sensor. a i b i c The detected three-phase stator current i a i b i c The current value i is transformed into a two-phase stationary coordinate system through the abc / αβ transformation. α i β i α i β The current value i is transformed into a two-phase synchronous rotating coordinate system through the αβ / dq transformation. d i q Feedback of actual rotor electrical angular velocity ω r With a given electric angular velocity The difference is passed through an adaptive finite-time controller to obtain the current in a two-phase rotating coordinate system. Feedback current i d i q With a given current The difference is used by a PI regulator to obtain the output voltage of the two-phase rotating coordinates. After passing through dq / αβ, it is converted into a two-phase voltage u in a two-phase stationary coordinate system. α u β After modulation by the SVPWM generator module, the generated PWM wave is applied to the dispensing servo motor through the three-phase inverter bridge.

[0050] Example 2

[0051] The point glue system servo control method of adaptive finite time control of the application is implemented according to the following steps:

[0052] Step 1, a mathematical model of the point glue system servo motor is established;

[0053] Step 2, according to the servo motor mathematical model and the finite time control theory, a speed loop adaptive finite time controller of the servo motor is designed to realize high dynamic control of the point glue system servo motor.

[0054] Example 3

[0055] The specific process of step 1 is as follows:

[0056] Assuming that the magnetic field of the servo motor is sinusoidal distribution and the magnetic circuit is not saturated, the mechanical equation of the servo motor is expressed as shown in the following formula:

[0057]

[0058] Where, 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 in the following formula:

[0059] T1=n p ψ f i q (2)

[0060] Where, n p is the number of pole pairs, ψ f is the permanent magnet flux linkage, and i q is the q-axis current.

[0061] According to formula (1) and formula (2), the servo system speed loop dynamics equation can be expressed as shown in the following formula:

[0062]

[0063] Where, 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 f0J0, 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.

[0068] Embodiment 5

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

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

[0071] wherein, 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.

[0072] Embodiment 6

[0073] The design speed error ε is the error state variable, is the given speed, then ε is expressed as follows:

[0074]

[0075] The derivative of ε is obtained:

[0076]

[0077] Since d1 and d2 are the main disturbances, they are 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 adaptive finite-time feedback control law of the servo motor can be designed as follows:

[0080]

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

[0082] As shown in equation (9), the values of disturbances d1 and d2 are needed in the feedback control law, which are usually not directly available in the actual system. Servo motors are often subject to various disturbances, and the designed adaptive finite-time feedback control law can only make the error converge to a region, not a point, when subject to disturbances. Since the finite-time disturbance observer can compensate for disturbances and ensure the speed loop of the servo system to converge in finite time. Therefore, the adaptive finite-time disturbance observer is designed as shown in equation (10), and the structure diagram is shown in Fig. 2. Figure 3

[0083]

[0084] wherein ε1 is the estimation error; is an adaptive finite-time function; η2, η3 are gain coefficients, η2>0, η3>0; ε 1max is the maximum value of the estimation error; b1, 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 estimation value ζ2 converges to the actual total disturbance d, which can complete the estimation of the actual disturbance.

[0085] Taking the speed error ε as the input, equation (9) and equation (5) can be used to obtain the following equation:

[0086]

[0087] Equation (11) is combined 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 a convergence point in finite time when tracking the speed, and the adaptive finite-time disturbance observer (10) ensures that the point dispensing system can estimate the disturbance and compensate in finite time when subject to disturbances.

[0088] The point dispensing servo system speed loop adaptive finite-time controller can be obtained from equation (10) and equation (11) as shown in equation (12).

[0089] ​​

Claims

1. A servo control method for an adaptive finite-time control dispensing system, characterized in that: Specifically, the steps include the following: Step 1: Establish a mathematical model of the servo motor of the dispensing system; The specific process of step 1 is as follows: Assuming the servo motor's magnetic field has a sinusoidal distribution and the magnetic circuit is unsaturated, the servo motor's mechanical equations are as follows: （1） in, ω r The rotor speed, J For rotational inertia, The time derivative of the rotor speed. T 1 represents electromagnetic torque. T 2 represents the load torque. B The damping coefficient and electromagnetic torque are given. T 1 can be represented as shown in the following formula: （2） in, n p For extreme logarithms, It is a permanent magnet flux chain. i q for q shaft current; Based on equations (1) and (2), the velocity loop dynamic equation of the servo system is as follows: （3） in, for q Shaft reference current, g For current coefficient, d For the total disturbance of the speed loop; In step 1, the current coefficient g This can be represented by the following formula: （4） in, , g 0 represents the rated current coefficient. This is the nominal value of the magnetic flux linkage of the permanent magnet. J 0 represents the nominal value of the moment of inertia; , g 1 represents the change in the current coefficient parameter. Ψ f1 This represents the parameter change of the permanent magnet flux linkage. J 1 represents the change in the parameter of the moment of inertia; In step 1, the total loop disturbance d The formula is shown below: （5） in, , d 1 represents parameter variation disturbance. , d 2 represents load disturbance. , d 3 is q Axis current loop tracking error disturbance , d 4 represents damped disturbance; Step 2: Design a speed loop adaptive finite time controller for the servo motor based on the mathematical model of the servo motor and the finite time control theory to achieve high dynamic control of the servo motor in the dispensing system. The specific process of step 2 is as follows: Design speed error ε For error state variables, For a given velocity, then ε The formula is shown below: （6） right ε Differentiating, we get: （7） neglect q Axis current loop tracking error disturbance d 3 and damping disturbance d 4. Equation (7) can be rewritten as: （8） Based on formula (8) and the adaptive finite-time feedback law The adaptive finite-time feedback control law for the servo motor can be designed as shown in equation (9): （9） in, For an adaptive finite-time function, η 1 represents the control gain. η 1>0; The maximum value of the error; a is the exponent, 0 < a < 1; sign() is the sign function, specifically expressed as , x For input variables.

2. The servo control method for an adaptive finite-time control dispensing system according to claim 1, characterized in that: In step 2, a finite-time perturbation observer is used to compensate for the disturbance and ensure that the servo system velocity loop converges within a finite time. Therefore, the adaptive finite-time perturbation observer is designed as shown in equation (10): （10） in, To estimate the error; , It is an adaptive finite-time function; η 2, η 3 represents the gain coefficient. η 2 > 0, η 3 > 0; This represents the maximum estimated error; b1 and b2 are exponents, where 0 < b1 and b2 < 1. It is an estimate of the speed. It is an estimate of the disturbance.

3. The servo control method for an adaptive finite-time control dispensing system according to claim 2, characterized in that: In step 2, when the adaptive finite-time perturbation observer converges, the perturbation estimate is... Converging to the actual total disturbance d That is, to complete the estimation of the actual disturbance.

4. The servo control method for an adaptive finite-time control dispensing system according to claim 3, characterized in that: In step 2, the speed error ε As input, the following equation is obtained from equations (9) and (5): （11） 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 converges to the convergence point in finite time during speed tracking, and the adaptive finite-time disturbance observer formula (10) ensures that the dispensing system can estimate and compensate for disturbances in finite time when subjected to disturbances. From equations (10) and (11), the adaptive finite-time controller of the speed loop of the dispensing servo system is obtained as shown in equation (12): （12）。

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