CN114453431A - Fault-tolerant anti-interference control method for vertical pressing system of rolling mill under typical working condition - Google Patents
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Abstract
The invention discloses a fault-tolerant anti-interference control method for a vertical pressing system of a rolling mill under typical working conditions, which belongs to the technical field of rolling mill control and comprises the following steps of 1, establishing a two-degree-of-freedom nonlinear vertical pressing system model; step2, considering system model parameter unknown and servo valve execution direction fault characteristics to design an adaptive controller, estimating unknown parameter perturbation and external disturbance by using an adaptive method, adding a Nussbaum function into the controller to counteract the influence of the controller fault, and obtaining a control scheme of the adaptive disturbance-resistant fault-tolerant controller; and 3, verifying the effectiveness of the control scheme through computer simulation. The method can effectively inhibit the disturbance of load mutation in the rolling process to a rolling mill screw-down system while ensuring the stability of the closed loop of the system, and has important significance for the high-precision rolling of the plate strip.
Description
Technical Field
The invention relates to the technical field of rolling mill control, in particular to a fault-tolerant anti-interference control method for a vertical pressing system of a rolling mill under a typical working condition.
Background
The invention aims at a cold-rolled strip rolling mill system, and the problem that the input direction of a controller is opposite to the input direction of a controller due to the fact that feedback control cannot follow and resist disturbance quickly because load disturbance possibly fluctuates violently in the rolling process occurs. Such problems can be regarded as the faults that the direction of the controller is unknown, if the faults can not be reasonably avoided, the fluctuation oscillation of the roller can be caused when the problems occur in the production, the quality of outlet steel is seriously influenced, and even the structure of the continuous rolling unit can be damaged to cause safety accidents. In order to solve such a problem, it is necessary to design an anti-interference controller capable of resisting the failure of unknown direction of the controller.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a fault-tolerant disturbance-rejection control method for a vertical pressing system of a rolling mill under a typical working condition, fully consider the rigidity nonlinearity of a hydraulic cylinder and the unknown control direction fault of an electro-hydraulic servo valve, establish a rolling mill system model aiming at the characteristics of the rolling mill in the control process, obtain a disturbance-tolerant back-step self-adaptive control method, ensure the closed-loop stability of the system, effectively inhibit the disturbance caused by load mutation in the rolling process to the pressing system of the rolling mill, and have important significance for the high-precision rolling of plate strips.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a fault-tolerant disturbance rejection control method for a vertical pressing system of a rolling mill under typical working conditions comprises the following steps:
step1, establishing a two-degree-of-freedom nonlinear vertical pressing system model;
step2, considering system model parameter unknown and servo valve execution direction fault characteristics to design a self-adaptive controller, estimating unknown parameter perturbation and external disturbance by using a self-adaptive method, adding a Nussbaum function into the controller to counteract the influence of controller faults, and obtaining a control scheme of the self-adaptive disturbance-resistant fault-tolerant controller;
and 3, verifying the validity of the control scheme through computer simulation.
The technical scheme of the invention is further improved as follows: in the step1, the specific process of establishing the two-degree-of-freedom nonlinear rolling mill vertical reduction system model is as follows:
1.1, establishing a dynamic differential equation model of a rolling mill vertical reduction system:
in the formula, m1,m2Respectively the mass of the working roll, the equivalent mass of the supporting roll and the piston of the hydraulic cylinder; fvarThe disturbance rolling force of the working roll; k is a radical of1,k2The equivalent rigidity of the working roll and the supporting roll and the equivalent rigidity between the supporting roll and the upper frame and between the hydraulic cylinder and the upper frame are respectively; c. ClDamping between the equivalent mass block of the hydraulic cylinder of the supporting roller and the upper frame; z is a radical of1,z2Respectively the vibration displacement of the two mass blocks; c. C0The third damping coefficient; u is the control pressure output by the hydraulic cylinder; b is that the control coefficient is unknown and is +1 or-1; k is a radical of1,k2In operation there is a perturbation of the parameters, order
1.2, establishing a rolling mill vertical pressing system state space model:
order to
The state space expression is established as follows:
the technical scheme of the invention is further improved as follows: in the step2, the control target is to make the vibration speed and the displacement of the working roll as small as possible under disturbance, and the ideal reference track is considered to be 0; the backstepping method is used for designing the controller, the backstepping method is used, errors of each recursion step are solved, the electro-hydraulic servo valve is used for controlling input current, and the specific design steps are as follows:
step1, introducing control error
e1＝x1-x1d (3)
e2＝x2-x2d (4)
Wherein x is1d、x2dAre respectively x1、x2Is calculated for equation (3) as a differential:
selecting Lyapunov function
Design x2dThe following were used:
x2d＝-c1e1 (7)
wherein, c1Is any constant greater than 0, as differentiated by formula (6):
V.1＝-c1e1 2+e1e2 (8)
e in formula (8)2From x2-x2dIt is decided, therefore, to design x in the next step2dTo counteract e2The influence of (a);
step2, introducing control error
e3＝x3-x3d (9)
Differentiating the formula (4):
defining Lyapunov functions
Order to
Is obvious to
|e2|＜ε+e2sg(e2,ε)
The inequality is scaled and substituted into (11), and order
D ═ max | D (t) |; to pair
And (5) obtaining a derivative:
get
Is an estimate of the value of D,
is composed of
The reference trajectory is designed as follows:
order to
Substituting into (12) to obtain:
wherein
Wherein,
designing Lyapunov function for any constant larger than 0 by considering estimation error
Wherein, theta, cdFor positive constants and for ensuring negative determination of the Lyapunov function, an adaptive law is designed:
substituting (14) to obtain:
step3, taking a third Lyapunov function:
and (5) obtaining a derivative:
to sum up design x4Reference track of
Wherein, c3,Θ2Is any normal number; because of the fact that
May be 0 during the estimation process, in order to prevent
Unbounded, with the addition of a constant ε greater than 00The reference trajectory is expressed as follows:
differentiation by substitution of Lyapunov function
Step4, order
Are each k1,k2Taking into account estimation errors
State Lyapunov function for closed-loop systems
Deriving (19) as:
the controller parameters were designed as follows:
the definition of N (x) will be given later, and the control law is substituted into (20)
Considering the bounding property of N (χ) and χ (τ), the global Lyapunov function is expressed as:
n (χ) is chosen here as follows:
wherein i 1,2, N, α and β are positive constants;
Ni(χ) is an odd function, order
Is apparent Gi(χ) is an even function, obtained by direct integration:
for any χi＞0，
Considering only χiIn the case of > 0, for χiThe case analysis procedure is similar for < 0; for clarity of expression, make
When sign (b)i) When 1 is associated with sign (b)i) Is-1, apparently
Thus by selecting the value of alpha so that
The interval of (a) exists, and the interval is
Wherein M is 1/beta, and N is a positive integer; the bounding property can then be analyzed (22):
consider the following two cases:
in case one, V is available at χ → ∞, t → ∞4(t) → - ∞ contradicts the hypothesis, so V4(t) Is bounded;
case two, χ bounded, apparent V4(t) bounded;
to sum up V4(t) must be bounded; the individual signals of the closed loop system are bounded.
The technical scheme of the invention is further improved as follows: in the step3, the self-adaptive fault-tolerant disturbance rejection controller is verified through numerical simulation, the disturbance of the rolling mill screw-down system caused by load mutation in the rolling process can be effectively inhibited while the stability of the system closed loop is ensured, and the oscillation divergence condition under the fault condition does not occur.
Due to the adoption of the technical scheme, the invention has the technical progress that:
1. the invention fully considers the rigidity nonlinearity of the rolling mill, establishes nonlinear rolling mill models before and after the rolling mill is controlled, designs an active rolling mill nonlinear self-adaptive controller considering input faults, enables the system to reach a stable state under the conditions that structural parameters are unknown and an actuator has faults, and finally verifies the correctness of the proposed model and the validity of the proposed controller through simulation, thereby meeting the control performance of the rolling mill system and achieving the purpose of improving the quality and the precision of plates by a rolling mill control system.
2. The invention provides an anti-disturbance fault-tolerant back-stepping self-adaptive control method aiming at typical nonlinearity of a rolling mill system, fully considering the rigidity nonlinearity of a hydraulic cylinder and the unknown control direction fault of an electro-hydraulic servo valve, establishing a rolling mill system model aiming at the characteristics of a rolling mill in the control process, and verifying the self-adaptive fault-tolerant back-stepping self-adaptive control method through computer simulation.
Drawings
FIG. 1 is a flow chart of a research route of the present invention;
FIG. 2 is a schematic view of the vertical rolling system of the rolling mill according to the present invention;
FIG. 3 is a displacement diagram of a working roll in a steel biting condition according to the invention;
FIG. 4 is a displacement diagram of a support roller under a steel biting condition in the invention;
FIG. 5 is a graph showing the displacement of the work rolls in the case of fluctuation in the thickness of the steel sheet in the present invention;
FIG. 6 is a graph showing the displacement of the support rollers when the thickness of the steel sheet fluctuates in the present invention.
Detailed Description
The invention is described in further detail below with reference to the following figures and examples:
when a rolling mill vertically presses down a system, due to severe load change in the rolling process, the output of an electro-hydraulic servo valve and a hydraulic cylinder of a controller in feedback control cannot follow up to resist disturbance, the output direction of the controller is opposite to the expected control direction, and the system oscillates at the moment. Meanwhile, due to the conditions of installation position deviation, individual difference of mechanical structures and the like, the structural rigidity of the system actually has a perturbation condition to a certain degree. The above reasons make the anti-disturbance control strategy of the rolling mill vertical reduction system in the rolling process a very complicated problem.
In a vertical pressing system of a rolling mill, certain structural parameters are not accurately obtained, the center of mass of a roller is changed due to eccentricity generated in the rotation process of the roller, so that the structural parameters of the roller and rigidity damping between the rollers are actually unknown when the roller and the roller are different from static in work, and the challenge is brought to high-precision steel rolling; the electro-hydraulic servo valve is widely applied to a cold continuous rolling mill control system as an efficient actuator, but due to the defects of feedback control, in the disturbance process facing severe change, a controller can not quickly follow the disturbance change and act, and the result that the input direction of the controller is opposite to the expected direction appears.
As shown in fig. 1 and 2, a fault-tolerant disturbance rejection control method for a vertical rolling reduction system of a rolling mill under typical conditions comprises the following steps:
step1, establishing a two-degree-of-freedom nonlinear vertical pressing system model;
1.1, establishing a dynamic differential equation model of a rolling mill vertical reduction system:
wherein m is1,m2Respectively the mass of the working roll, the equivalent mass of the supporting roll and the hydraulic cylinder piston, FvarFor the disturbing rolling forces to which the work rolls are subjected, k1,k2Equivalent stiffness between the work roll and the back-up roll, between the back-up roll and the hydraulic cylinder and the upper frame, respectively, clDamping between equivalent mass block of hydraulic cylinder of support roll and upper frame, z1,z2Respectively, the vibration displacement of the two masses, c0The damping coefficient is a tertiary damping coefficient, u is the control pressure output by the hydraulic cylinder, and b is the unknown control coefficient which is +1 or-1; k is a radical of1,k2In operation there is a perturbation of the parameters, order
1.2, establishing a rolling mill vertical pressing system state space model:
order to
The state space expression is established as follows:
step2, considering system model parameter unknown and servo valve execution direction fault characteristics to design a self-adaptive controller, estimating unknown parameter perturbation and external disturbance by using a self-adaptive method, adding a Nussbaum function into the controller to counteract the influence of controller faults, and obtaining a control scheme of the self-adaptive disturbance-resistant fault-tolerant controller;
because the control target is to make the vibration speed and the displacement of the working roll as small as possible under disturbance, the ideal reference track is considered to be 0; the backstepping method is used for designing the controller, the backstepping method is used, errors of each recursion step are solved, the electro-hydraulic servo valve is used for controlling input current, and the specific design steps are as follows:
step1 introduction of control error
e1＝x1-x1d (3)
e2＝x2-x2d (4)
Wherein x is1d、x2dAre respectively x1、x2The ideal reference trajectory, as derived from the differentiation of equation (3):
selecting Lyapunov function
Design x2dThe following were used:
x2d＝-c1e1 (7)
wherein, c1Is any constant greater than 0, as differentiated by equation (6):
e in formula (8)2From x2-x2dIt is decided, therefore, to design x in the next step2dTo counteract e2The influence of (a);
step2 introduction of control error
e3＝x3-x3d (9)
Differentiating the formula (4):
defining Lyapunov functions
Order to
Is obvious to
|e2|＜ε+e2sg(e2,ε)
The inequality is scaled and substituted into (11), and order
D ═ max | D (t) |; to pair
The derivation can be:
get
Is an estimate of the value of D,
is composed of
The reference trajectory is designed as follows:
order to
Substituting into (12) to obtain:
wherein
Wherein
Designing Lyapunov function for any constant larger than 0 by considering estimation error
Wherein Θ, cdFor positive constants and for ensuring negative determination of the Lyapunov function, an adaptive law is designed:
substitution (14) can give:
step3, taking a third Lyapunov function,
derived by derivation
To sum up design x4Reference track of
Wherein c is3,Θ2Is any normal number; because of the fact that
May be 0 during the estimation process, in order to prevent
Unbounded, with the addition of a constant ε greater than 00The reference trajectory is expressed as follows:
differentiation by substitution of Lyapunov function
Step4, order
Are each k1,k2Taking into account estimation errors
State Lyapunov function for closed-loop systems
Derived from (19)
The controller parameters were designed as follows:
the definition of N (χ) will be given later;
substituting (20) the control law can obtain:
considering the bounding property of N (χ) and χ (τ), the global Lyapunov function is expressed as:
n (χ) is chosen here as follows:
where i 1,2, N, α and β are all positive constants.
N (χ) is an odd function, order
It is apparent that G (χ) is an even function, which can be obtained by direct integration
For any χi＞0，
Considering only the case of χ > 0, the analysis procedure is similar for the case of χ < 0.
Can be achieved by selecting the value of alpha
The interval of (a) exists, and the interval is
Wherein M is 1/beta, and N is a positive integer. The bounding property can then be analyzed (22):
consider the following two cases:
in case one, V is available at χ → ∞, t → ∞4(t) → -infinity and presuppositionConflict arises, so V4(t) bounded;
case two, χ bounded, apparent V4(t) bounded;
in conclusion V4And (t) is bound, and the closed loop of the system is stable.
Step3, verifying the validity of the control scheme through computer simulation; specifically, the parameter adjustment and simulation result comparison of the backstepping self-adaptive disturbance-resistant fault-tolerant controller designed in the step2 are carried out.
Through numerical simulation, the self-adaptive fault-tolerant disturbance rejection controller is verified, the closed loop stability of the system is guaranteed, meanwhile, the disturbance caused by load sudden change to a rolling mill pressing system in the rolling process can be effectively restrained, the oscillation divergence situation under the fault condition does not occur, and the method has important significance for high-precision rolling of plate strips.
Taking the following parameters of a vertical pressing system of a certain rolling mill:
m1＝1050kg,m2＝820kg,k1＝1.04×109N/m,
k2＝0.82×109N/m
cl＝4×106N·s/m,
c0＝1×102N·s/m3。
in a vertical pressing system of a rolling mill, the head of a rolled piece enters a roll gap to be in a steel biting working condition, and the disturbance of a working roll can be represented by step force; due to the deformation of the billet head caused by rolling and temperature unevenness, the thickness of the plate will fluctuate periodically, and the working roll disturbance in the working condition can be represented by a sinusoidal signal.
FIG. 3 is a displacement diagram of the working roll under the steel biting condition in the invention;
from FIG. 3, it can be seen that the maximum vertical displacement of the working roll is 0.148 μm, the maximum vertical displacement of the working roll after the adaptive disturbance rejection fault-tolerant controller designed by the present invention is 0.021 μm, and the amplitude is reduced by 85.81%;
FIG. 4 shows a displacement diagram of the support roller under the steel biting condition in the invention;
from fig. 4, it can be seen that the maximum displacement of the supporting roller is 0.152 μm, the maximum displacement of the supporting roller after the adaptive disturbance rejection fault-tolerant controller designed by the invention is used is 0.023 μm, and the amplitude is reduced by 84.69%.
Therefore, the system has remarkable control effect, and can still effectively realize the control target when the actuator fails.
FIG. 5 is a graph showing the displacement of the work rolls in the case of fluctuation in the thickness of the steel sheet in the present invention;
from FIG. 5, it can be seen that the maximum vertical displacement of the working roll is 0.382 μm, and after the adaptive disturbance rejection fault-tolerant controller designed by the invention is used, the maximum vertical displacement of the working roll is 0.112 μm, and the amplitude is reduced by 78.56%;
FIG. 6 is a graph showing the displacement of the support rollers when the thickness of the steel sheet fluctuates in the present invention.
From FIG. 6, it can be seen that the maximum displacement of the supporting roller is 0.379 μm, the maximum displacement of the supporting roller after the adaptive disturbance rejection fault-tolerant controller designed by the invention is used is 0.120 μm, and the amplitude is reduced by 76.08%. Although the subsequent displacement of the supporting roller fluctuates, the control target can still be effectively realized when the actuator fault occurs, considering that the actual control target is the displacement of the working roller.
The present invention is capable of other embodiments and its several details are capable of modification and variation, and it is intended that all such modifications, equivalents, improvements and equivalents that fall within the spirit and scope of the present invention as defined by the appended claims be embraced thereby.
Claims (4)
1. A fault-tolerant disturbance rejection control method for a vertical pressing system of a rolling mill under typical working conditions is characterized by comprising the following steps: the method comprises the following steps:
step1, establishing a two-degree-of-freedom nonlinear vertical pressing system model;
step2, considering system model parameter unknown and servo valve execution direction fault characteristics to design a self-adaptive controller, estimating unknown parameter perturbation and external disturbance by using a self-adaptive method, adding a Nussbaum function into the controller to counteract the influence of controller faults, and obtaining a control scheme of the self-adaptive disturbance-resistant fault-tolerant controller;
and 3, verifying the validity of the control scheme through computer simulation.
2. The fault-tolerant disturbance rejection control method for the vertical screw-down system of the rolling mill under the typical working condition according to claim 1, characterized in that: in the step1, the specific process of establishing the two-degree-of-freedom nonlinear rolling mill vertical reduction system model is as follows:
1.1, establishing a dynamic differential equation model of a rolling mill vertical reduction system:
in the formula, m1,m2Respectively the mass of the working roll, the equivalent mass of the supporting roll and the piston of the hydraulic cylinder; fvarThe disturbance rolling force of the working roll; k is a radical of1,k2The equivalent rigidity of the working roll and the supporting roll and the equivalent rigidity between the supporting roll and the upper frame and between the hydraulic cylinder and the upper frame are respectively; c. ClDamping between the equivalent mass block of the hydraulic cylinder of the supporting roller and the upper frame; z is a radical of1,z2Respectively the vibration displacement of the two mass blocks; c. C0The third damping coefficient; u is the control pressure output by the hydraulic cylinder; b is that the control coefficient is unknown and is +1 or-1; k is a radical of1,k2In operation there is a perturbation of the parameters, order
1.2, establishing a rolling mill vertical pressing system state space model:
let x1＝z1,
x3＝z2,
The state space expression is established as follows:
3. the fault-tolerant disturbance rejection control method for the vertical screw-down system of the rolling mill under the typical working condition according to claim 1, characterized in that: in the step2, the control target is to make the vibration speed and the displacement of the working roll as small as possible under disturbance, and the ideal reference track is considered to be 0; the backstepping method is used for designing the controller, the backstepping method is used, errors of each recursion step are solved, the electro-hydraulic servo valve is used for controlling input current, and the specific design steps are as follows:
step1, introducing control error
e1＝x1-x1d (3)
e2＝x2-x2d (4)
Wherein x is1d、x2dAre respectively x1、x2Is calculated for equation (3) as a differential:
selecting Lyapunov function
Design x2dThe following were used:
x2d＝-c1e1 (7)
wherein, c1Is any constant greater than 0, as differentiated by formula (6):
e in formula (8)2From x2-x2dIt is decided, therefore, to design x in the next step2dTo counteract e2The influence of (a);
step2, introducing control error
e3＝x3-x3d (9)
Differentiating the formula (4):
defining Lyapunov functions
Order to
Is obvious to
|e2|＜ε+e2sg(e2,ε)
The inequality is scaled and substituted into (11), and order
D ═ max | D (t) |; for is to
And (5) obtaining a derivative:
get
Is an estimate of the value of D,
is composed of
The reference trajectory is designed as follows:
order to
Substituting into (12) to obtain:
wherein
Wherein,
designing Lyapunov function for any constant larger than 0 by considering estimation error
Wherein, theta, cdFor positive constants and for ensuring negative definite of Lyapunov function, an adaptive law is designed:
substituting (14) to obtain:
step3, taking a third Lyapunov function:
and (5) obtaining a derivative:
to sum up design x4Reference track of
Wherein, c3,Θ2Is any normal number; because of the fact that
May be 0 during the estimation process, in order to prevent
Unbounded, with the addition of a constant ε greater than 00The reference trajectory is expressed as follows:
differentiation by substitution of Lyapunov function
Step4, order
Are each k1,k2Taking into account estimation errors
State Lyapunov function for closed-loop systems
Deriving (19) as:
the controller parameters were designed as follows:
the definition of N (x) will be given later, and the control law is substituted into (20)
Considering the bounding property of N (χ) and χ (τ), the global Lyapunov function is expressed as:
n (χ) is chosen here as follows:
wherein i 1,2, N, α and β are positive constants;
Ni(χ) is an odd function, let
Is apparent Gi(χ) is an even function, obtained by direct integration:
for any χi＞0，
Considering only χiIn the case of > 0, for χiThe case analysis procedure is similar for < 0; for clarity of expression, make
When sign (b)i) When 1 is associated with sign (b)i) Is-1, apparently
Thus by selecting the value of alpha so that
The interval of (a) exists, and the interval is
Wherein M is 1/beta, and N is a positive integer; the bounding property can then be analyzed (22):
consider the following two cases:
in case one, V is available at χ → ∞, t → ∞4(t) → - ∞ contradicts the hypothesis, so V4(t) bounded;
case two, χ bounded, apparent V4(t) bounded;
to sum up V4(t) must be bounded; the individual signals of the closed loop system are bounded.
4. The fault-tolerant disturbance rejection control method for the vertical screw-down system of the rolling mill under the typical working condition according to claim 1, characterized in that: in the step3, the self-adaptive fault-tolerant disturbance rejection controller is verified through numerical simulation, the disturbance of the rolling mill screw-down system caused by load mutation in the rolling process can be effectively inhibited while the stability of the system closed loop is ensured, and the oscillation divergence condition under the fault condition does not occur.
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210039021.9A CN114453431B (en) | 2022-01-13 | 2022-01-13 | Fault-tolerant anti-interference control method for vertical pressing system of rolling mill under typical working condition |
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210039021.9A CN114453431B (en) | 2022-01-13 | 2022-01-13 | Fault-tolerant anti-interference control method for vertical pressing system of rolling mill under typical working condition |
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| Publication Number | Publication Date |
|---|---|
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Citations (4)
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|---|---|---|---|---|
| US20070068210A1 (en) * | 2005-09-29 | 2007-03-29 | University Of Pittsburgh - Of The Commonwealth System Of Higher Education | System for controlling a rolling mill and method of controlling a rolling mill |
| CN110096750A (en) * | 2019-04-02 | 2019-08-06 | 燕山大学 | Consider the adaptive dynamic surface control method of non-linear Active suspension actuator |
| CN111723442A (en) * | 2020-06-08 | 2020-09-29 | 燕山大学 | Design method of rolling mill vertical vibration suppression controller based on self-adaptive fuzzy backstepping |
| CN112742878A (en) * | 2021-02-01 | 2021-05-04 | 燕山大学 | Anti-disturbance control method for vertical pressing system of rolling mill under typical working condition |
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| US20070068210A1 (en) * | 2005-09-29 | 2007-03-29 | University Of Pittsburgh - Of The Commonwealth System Of Higher Education | System for controlling a rolling mill and method of controlling a rolling mill |
| CN110096750A (en) * | 2019-04-02 | 2019-08-06 | 燕山大学 | Consider the adaptive dynamic surface control method of non-linear Active suspension actuator |
| CN111723442A (en) * | 2020-06-08 | 2020-09-29 | 燕山大学 | Design method of rolling mill vertical vibration suppression controller based on self-adaptive fuzzy backstepping |
| CN112742878A (en) * | 2021-02-01 | 2021-05-04 | 燕山大学 | Anti-disturbance control method for vertical pressing system of rolling mill under typical working condition |
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| 张瑞成等: "具有不确定性参数的轧机主传动***自抗扰控制器设计", 《电工技术学报》 * |
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