Vibration fault-tolerant control method for main drive system of rolling mill under fixed time and predetermined performance

Abstract

The present invention discloses a vibration fault-tolerant control method for the main drive system of a rolling mill under fixed-time predetermined performance, which relates to the technical field of torsional vibration control of the main drive system of a rolling mill in the strip rolling process, and includes the following steps: Step S1, collect the electromechanical physical quantity parameters of the main drive system of the rolling mill; Step S2, according to Lagrange's theorem, considering the actuator fault factor, establish an electromechanical coupling nonlinear model of the main drive system of the rolling mill according to the torsional vibration dynamics principle of the main drive system of the rolling mill; Step S3, determine the target of suppressing torsional vibration of the rolling mill according to the actual working conditions; Step S4, combine the electromechanical coupling nonlinear model of the main drive system of the rolling mill and the target of suppressing the vibration of the rolling mill, and design a vibration fault-tolerant controller for the main drive system of the rolling mill with fixed-time predetermined performance. The present invention realizes the rapid and active suppression of torsional vibration in the main drive system with actuator faults during the strip rolling process, and ensures the stability of the strip rolling process.

Description

Technical Field

[0001] The present invention relates to the technical field of torsional vibration control of the main drive system of a rolling mill during the strip rolling process, and in particular to a vibration fault-tolerant control method for the main drive system of a rolling mill under fixed-time prescribed performance. Background Art

[0002] During the rolling process of a rolling mill, due to large and frequent load impacts, the balance between the driving torque and the load torque is lost, resulting in torsional vibration problems in the main drive system of the rolling mill. The torsional vibration of the main drive system of the rolling mill not only reduces the quality accuracy of strip products, but also easily causes fatigue damage to the shafting and reduces the service life of the equipment. Seriously, it may even lead to damage or fracture of the unit shafting, affecting the safe and reliable operation of the unit. Therefore, it is particularly important to control the torsional vibration of the rolling mill.

[0003] Traditional means for controlling the torsional vibration of a rolling mill mainly include mechanical, technological, and electrical methods. These methods can only take control measures after the rolling mill vibrates to eliminate the harmful effects of vibration, and cannot achieve the effect of actively suppressing the vibration of the rolling mill. With the development of control theory, advanced control algorithms have gradually been applied to torsional vibration control. Considering that the state variables in the actual main drive system of a rolling mill need to meet certain performance requirements and equipment safety conditions, the motor torque, load speed, and motor speed are restricted. Therefore, Hua Changchun et al. applied prescribed performance control to the suppression of torsional vibration of a rolling mill. However, this method can only meet the system performance requirements when the time approaches infinity. Therefore, incorporating the idea of fixed-time prescribed performance to achieve vibration suppression under fixed time has better effects. In addition, as a mechanical system, the main drive system of a rolling mill inevitably has actuator faults during operation, and the torsional vibration suppression control strategies proposed by Chen Shuzong et al. are all designed based on the backstepping method, with relatively high computational complexity. Therefore, further considering the torsional vibration suppression control of a rolling mill with actuator faults and reducing the complexity of controller design is of practical significance. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a vibration fault-tolerant control method for the main drive system of a rolling mill under fixed-time prescribed performance. Aiming at the torsional vibration problem existing in the main drive of the rolling mill during the rolling process, the present invention first establishes a more realistic vertical vibration nonlinear model of the rolling mill. Then, based on this model, by considering the limitation of the fixed-time prescribed performance on the torsional vibration displacement of the roll, a vibration fault-tolerant control strategy for the main drive system of the rolling mill with fixed-time prescribed performance is designed to achieve rapid and active suppression of torsional vibration with actuator faults in the main drive system during the strip rolling process, ensuring the stability of the strip rolling process.

[0005] To solve the above technical problems, the technical solution adopted by the present invention is: a vibration fault-tolerant control method for the main drive system of a rolling mill under fixed-time predetermined performance, including the following steps:

[0006] Step S1, collect the electromechanical physical quantity parameters of the main drive system of the rolling mill;

[0007] Step S2, according to Lagrange's theorem, considering the actuator fault factor, based on the torsional vibration dynamics principle of the main drive system of the rolling mill, establish an electromechanical coupling nonlinear model of the main drive system of the rolling mill;

[0008] Step S3, determine the target of suppressing torsional vibration of the rolling mill according to the actual working conditions;

[0009] Step S4, combining the electromechanical coupling nonlinear model of the main drive system of the rolling mill and the target of suppressing the vibration of the rolling mill, design a vibration fault-tolerant controller for the main drive system of the rolling mill with fixed-time predetermined performance.

[0010] A further improvement of the technical solution of the present invention is that: the electromechanical physical quantity parameters of the main drive system of the rolling mill in step S1 include: roll angular velocity θ 1 , motor angular velocity θ 2 , current i, load torque T during stable rolling L1 , interference torque T LD , motor electromagnetic torque constant C m , moment of inertia J of the motor and the load m , J L , armature winding resistance R, resonance frequency w 1 , slow-varying frequency w 2 , equivalent stiffness K of the transmission shaft 0 .

[0011] A further improvement of the technical solution of the present invention is that: the electromechanical coupling nonlinear model of the main drive system of the rolling mill in step S2:

[0012]

[0013] where, x 1 is the roll angular velocity, x 2 is the angle difference between the roll and the motor, x 3 is the motor angular velocity, x 4 is the current, T L is the load torque, T L = T L1 + T LD , where, T L1 is the load torque under steady state; T LD is the load torque under environmental interference, C m is the motor electromagnetic torque constant, C e is the electromotive force constant, Jm , J L represent the moments of inertia of the motor and the load respectively, and L m is the inductance, and c 1 , c 2 , c 3 , c 4 is the damping coefficient, R is the armature winding resistance, u = β(t)u a + u f (t) is the true control input of the system, β(t) is the actuator failure coefficient, and u f (t) is the unknown additive fault, and K(t) = K 0 (1 + h 1 cos(ω 1 t) + h 2 cos(ω 2 t)) is the non - linear stiffness of the transmission shaft, and K 0 is the equivalent stiffness, ω 1 is the resonance frequency, ω 2 is the slowly - varying frequency, and h 1 , h 2 is the amplitude of the variation of the transmission - shaft stiffness.

[0014] A further improvement of the technical solution of the present invention lies in that: the goal of suppressing torsional vibration of the rolling mill in step S3 is that all state variables of the main drive system of the rolling mill can be strictly limited within asymmetric upper and lower bounds within a fixed time, realizing vibration control of the main drive system of the rolling mill in the presence of actuator faults.

[0015] A further improvement of the technical solution of the present invention lies in that: the goal of the torsional vibration of the rolling mill is expressed by the following formula:

[0016]

[0017] where z i represents the error variable introduced by the main drive system of the rolling mill, z 1 = x 1 - x d , z 2 = x 2 - α 1 , z 3 = x 3 - α 2 , h 0 = h(0) > h p , x d represents the load speed during stable rolling, and α 1 represents the virtual control law 1; α 2 represents the virtual control law 2; α 3 represents the virtual control law 3; tσ is the set time, λ and τ are designed positive real numbers; h(t) is the introduced fixed-time predefined performance function; h 0 = h(0) represents the value of the introduced fixed-time predefined performance function h(t) at time t = 0; h p is the set bound that converges when time t ≥ t σ ; δ and are both given positive real numbers;

[0018] To convert the asymmetric constraint into a symmetric constraint, the following conversion is given:

[0019]

[0020] e i = z i + q i

[0021] Convert formula (2) to

[0022] - p i <e i <p i

[0023] where

[0024] The dynamic equation of the error variable of the main drive system of the rolling mill is expressed as:

[0025]

[0026]

[0027]

[0028]

[0029] where

[0030] A further improvement of the technical solution of the present invention lies in: The design process of the vibration fault-tolerant controller of the main drive system of the rolling mill with fixed-time predefined performance in step S4 is as follows:

[0031] S41. To ensure that the error satisfies |e i | < p i , the error conversion function is constructed as

[0032]

[0033] S42. The virtual controller is

[0034] α i = -λi ξ i (i = 1, 2, 3);

[0035] where α i (i = 1, 2, 3) represents a virtual controller, and λ i (i = 1, 2, 3) represents a designed positive parameter;

[0036] S43. The actual controller is

[0037] u a = -λ 4 ξ 4 ;

[0038] where u a represents the control input, and λ 4 represents a designed positive parameter.

[0039] Due to the adoption of the above technical solution, the technical progress achieved by the present invention is:

[0040] 1. The present invention provides a vibration fault-tolerant control method for the main drive system of a rolling mill under fixed-time prescribed performance. Aiming at the torsional vibration problem existing in the main drive of the rolling mill during the rolling process, the present invention first establishes a more realistic vertical vibration nonlinear model of the rolling mill. Then, based on this model, by considering the limitation of the fixed-time prescribed performance on the torsional vibration displacement of the roll, a vibration fault-tolerant control strategy for the main drive system of the rolling mill with fixed-time prescribed performance is designed to achieve rapid active suppression of the torsional vibration in the case of actuator faults in the main drive system during the strip rolling process, ensuring the stability of the strip rolling process;

[0041] 2. The present invention establishes a more realistic torsional vibration nonlinear model, considers the actuator faults existing in the system and realizes the suppression of the torsional vibration of the rolling mill within a fixed time, designs a low-complexity rolling mill torsional vibration suppressor that does not rely on a large amount of calculations, and realizes rapid active suppression of the torsional vibration occurring during the high-speed rolling process, ensuring the stability of the high-speed strip rolling process. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 Flowchart of the vibration fault-tolerant control method for the main drive system of the rolling mill under fixed-time prescribed performance of the present invention;

[0043] Figure 2 Comparison chart of the response curves of the system error variable z 1 with and without fixed-time performance constraints;

[0044] Figure 3 Comparison chart of the response curves of the system error variable z 2 with and without fixed-time performance constraints;

[0045] Figure 4 System error variable z under fixed-time performance constraints 3 Response curve comparison diagram;

[0046] Figure 5 System error variable z under fixed-time performance constraints 4 Response curve comparison diagram. Specific implementation mode

[0047] The present invention will be further described in detail below in conjunction with embodiments:

[0048] The vibration fault-tolerant control method for the main drive system of a rolling mill under fixed-time predetermined performance, as Figure 1 shown, includes the following steps:

[0049] Step S1: Collect the electromechanical physical quantity parameters of the main drive system of the rolling mill: Specifically include: roll angular velocity θ 1 , motor angular velocity θ 2 , current i, load torque T during stable rolling L1 , interference torque T LD , motor electromagnetic torque constant C m , moment of inertia J of the motor and the load m , J L , armature winding resistance R, resonance frequency w 1 , slow-varying frequency w 2 , equivalent stiffness K of the transmission shaft 0 .

[0050] Step S2: According to Lagrange's theorem, considering the actuator fault factor, based on the torsional vibration dynamics principle of the main drive system of the rolling mill, establish an electromechanical coupling nonlinear model of the main drive system of the rolling mill:

[0051]

[0052] Among them, x 1 is the roll angular velocity, x 2 is the angle difference between the roll and the motor, x 3 is the motor angular velocity, x 4 is the current, T L is the load torque, T L = T L1 + T LD , where, T L1 is the load torque under steady state; T LD is the load torque under environmental interference, C m is the motor electromagnetic torque constant, C e is the electromotive force constant, J m , J L respectively represent the moments of inertia of the motor and the load, Lm is an inductor, c 1 , c 2 , c 3 , c 4 is the damping coefficient, R is the armature winding resistance, u = β(t)u a + u f (t) is the true control input of the system, β(t) is the actuator failure coefficient, u f (t) is the unknown additive fault, K(t) = K 0 (1 + h 1 cos(w 1 t) + h 2 cos(w 2 t)) is the non - linear stiffness of the transmission shaft, K 0 is the equivalent stiffness, w 1 is the resonance frequency, w 2 is the slowly - varying frequency, h 1 , h 2 is the amplitude of the variation of the transmission shaft stiffness.

[0053] Step S3: Determine the goal of suppressing the torsional vibration of the rolling mill according to the actual working conditions. Since the excessive difference between the roll speed and the desired speed is the main cause of the torsional vibration of the rolling mill, the goal is to suppress the torsional vibration of the rolling mill. Considering that the state variables in the main drive system of the rolling mill need to meet certain performance requirements and equipment safety conditions, the system state variables such as roll speed, the angle difference between the roll and the motor, and motor speed will satisfy certain limitations. That is to say, the goal of suppressing the torsional vibration of the rolling mill is that all state variables of the main drive system of the rolling mill can be strictly limited within the asymmetric upper and lower bounds within a fixed time, realizing the vibration control of the main drive system of the rolling mill under the actuator fault.

[0054] Controlling the roll speed, the angle difference between the roll and the motor, and the motor speed of the rolling mill within the set range, the goal of suppressing the vibration of the rolling mill can be expressed as:

[0055]

[0056] where, z i represents the error variable introduced by the main drive system of the rolling mill, z 1 = x 1 - x d , z 2 = x 2 - α 1 , z 3 = x 3 - α 2 , h 0 = h(0) > h p , x dDenoted as the load speed during stable rolling, α 1 Denotes the virtual control law 1; α 2 Denotes the virtual control law 2; α 3 Denotes the virtual control law 3; t σ Is the set time, λ and τ are designed positive real numbers; h(t) is the introduced fixed-time prescribed performance function; h 0 = h(0) represents the value of the introduced fixed-time prescribed performance function h(t) at t = 0; h p Is the set bound that converges when t ≥ t σ ; δ And Are both given positive real numbers.

[0057] To realize the conversion of asymmetric constraints into symmetric constraints, the following conversion is given:

[0058]

[0059] e i = z i + q i

[0060] Convert formula (2) to

[0061] - p i <e i <p i

[0062] Where

[0063] The dynamic equation of the main drive system error variable of the rolling mill is expressed as:

[0064]

[0065]

[0066]

[0067]

[0068] Where

[0069] Step S4. Combining the electromechanical coupling nonlinear model of the rolling mill main drive system and the goal of suppressing rolling mill vibration, design a vibration fault-tolerant controller for the rolling mill main drive system with fixed-time prescribed performance, which specifically includes the following steps:

[0070] S41. To ensure that the error satisfies |e i | < p i , the error transformation function is constructed as

[0071]

[0072] S42. The virtual controller is

[0073] α i = -λ i ξ i (i = 1, 2, 3);

[0074] where, α i (i = 1, 2, 3) represents the virtual controller, and λ i (i = 1, 2, 3) represents the designed positive parameter;

[0075] S43. The actual controller is

[0076] u a = -λ 4 ξ 4 ;

[0077] where, u a represents the control input, and λ 4 represents the designed positive parameter.

[0078] Embodiment 1

[0079] Collect the electromechanical parameters of the main drive system of the rolling mill, as shown in Table 1. And the form of the controller is given as follows: p 1 = h 1 (t), p 2 = h 2 (t), p 3 = h 3 (t), p 4 = h 4 (t), The failure coefficient β of the controller is 0.5, and the additive fault value is 1.

[0080] Table 1 Electromechanical parameters of the main drive system of the rolling mill

[0081] parameter numerical value parameter numerical value <![CDATA[J m > <![CDATA[1552 kg·m 2 > <![CDATA[J L > <![CDATA[1542kg·m 2 > <![CDATA[K 0 > <![CDATA[5.9*10 6 N·m / rad]]> <![CDATA[h 1 > 0.01 <![CDATA[w 1 > 25Hz <![CDATA[T L1 > 14500 N·m <![CDATA[T LD > 2190*sin(πt) N·m i 1720A <![CDATA[C e > 29π / 30 N·m / A <![CDATA[L m > 0.0003H <![CDATA[c 1 > 0.2 <![CDATA[c 3 > 0.1 <![CDATA[c 2 > 0.1 <![CDATA[c 4 > 0.2 <![CDATA[h 2 > 0.04 <![CDATA[w 2 > 0.01Hz <![CDATA[C m > <![CDATA[2*10 5 N / (m / s)]]> R 0.4m

[0082] According to the parameters given in Table 1 and combined with the control laws α i and u a , the simulation results can be obtained. To show the effectiveness of the method proposed in this patent, the simulation results of the control effects with and without fixed-time performance constraints are compared as Figure 2-5 shown. It can be seen from Figure 2-5 that, under the method without performance constraint control, the error variable z of the main drive system of the rolling mill iIt will exceed the specified range, while under the action of the patented method, the error variables of the system can be well limited within the specified bounds. Moreover, the vibration attenuation rate, steady-state error, and overshoot of the rolling mill system are also improved compared with traditional control methods.

Claims

1. Vibration fault-tolerant control method for the main drive system of a rolling mill under fixed-time preset performance, characterized in that: It includes the following steps: Step S1: Collect the electromechanical physical quantity parameters of the main drive system of the rolling mill; Step S2: According to Lagrange's theorem, considering the actuator fault factor, based on the torsional vibration dynamics principle of the main drive system of the rolling mill, establish an electromechanical coupling nonlinear model of the main drive system of the rolling mill; Step S3: Determine the goal of suppressing torsional vibration of the rolling mill according to the actual working conditions. The goal of suppressing torsional vibration of the rolling mill is that all state variables of the main drive system of the rolling mill can be strictly limited within the asymmetric upper and lower bounds within a fixed time, so as to realize the vibration control of the main drive system of the rolling mill under actuator faults; Step S4: Combine the electromechanical coupling nonlinear model of the main drive system of the rolling mill and the goal of suppressing the vibration of the rolling mill, and design a vibration fault-tolerant controller for the main drive system of the rolling mill with fixed-time preset performance.

2. The vibration fault-tolerant control method for the main drive system of a rolling mill under fixed-time preset performance according to claim 1, characterized in that: The electromechanical physical quantity parameters of the main drive system of the rolling mill in step S1 include: the angular velocity θ of the roll 1 , the angular velocity θ of the motor 2 , the current i, the load torque T during steady rolling L1 , the disturbance torque T LD , the motor electromagnetic torque constant C m , the moment of inertia J of the motor and the load m , J L , the armature winding resistance R, the resonance frequency w 1 , the slow-varying frequency w 2 , the equivalent stiffness K of the transmission shaft 0 .

3. The vibration fault-tolerant control method for the main drive system of a rolling mill under fixed-time preset performance according to claim 2, characterized in that: The electromechanical coupling nonlinear model of the main drive system of the rolling mill in step S2: Among them, x 1 is the angular velocity of the roll, x 2 is the angle difference between the roll and the motor, x 3 is the angular velocity of the motor, x 4 is the current, T L is the load torque, T L = T L1 + T LD , where T L1 is the load torque under steady state; T LD is the load torque under environmental interference, C m is the electromagnetic torque constant of the motor, C e is the electromotive force constant, J m , J L respectively represent the moments of inertia of the motor and the load, L m is the inductance, c 1 , c 2 , c 3 , c 4 is the damping coefficient, R is the resistance of the armature winding, u = β(t)u a + u f (t) is the true control input of the system, β(t) is the actuator failure coefficient, u f (t) is the unknown additive fault, K(t) = K 0 (1 + h 1 cos(w 1 t) + h 2 cos(w 2 t)) is the non-linear stiffness of the transmission shaft, K 0 is the equivalent stiffness, w 1 is the resonance frequency, w 2 is the slowly varying frequency, h 1 , h 2 is the amplitude of the variation of the transmission shaft stiffness.

4. The vibration fault-tolerant control method for the main drive system of a rolling mill under fixed-time preset performance according to claim 1, characterized in that: The goal of the rolling mill generating torsional vibration is expressed by the following formula: where, z i represents the error variable introduced by the main drive system of the rolling mill, and z 1 = x 1 - x d , z 2 = x 2 - α 1 , z 3 = x 3 - α 2 , z 4 = x 4 - α 3 , h 0 = h(0) > h p , x d represents the load speed during stable rolling, and α 1 represents the virtual control law 1; α 2 represents the virtual control law 2; α 3 represents the virtual control law 3; t σ is the set time, λ and τ are designed positive real numbers; h(t) is the introduced fixed-time predefined performance function; h 0 = h(0) represents the value of the introduced fixed-time predefined performance function h(t) at t = 0; h p is the set bound that converges after time t ≥ t σ ; δ and are both given positive real numbers; In order to realize the conversion of asymmetric limitation to symmetric limitation, the following conversion is given: e i = z i + q i Convert formula (2) to -p i <e i <p i Among them, The dynamic equation of the error variable of the main drive system of the rolling mill is expressed as: Among them, 5. The vibration fault-tolerant control method for the main drive system of a rolling mill under fixed-time preset performance according to claim 4, characterized in that: The design process of the vibration fault-tolerant controller for the main drive system of the rolling mill with fixed-time preset performance in step S4 is as follows: S41. To ensure that the error satisfies |e i | < p i , the error conversion function is constructed as S42: The virtual controller is α i = -λ i ξ i (i = 1, 2, 3); where α i (i = 1, 2, 3) represents a virtual controller, and λ i (i = 1, 2, 3) represents a designed positive parameter; S43: The actual controller is u a = -λ 4 ξ 4 ; where, u a represents the control input, and λ 4 represents a positive parameter of the design.

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