CN110943649B - Input quantization control method and system of dual-motor servo system - Google Patents
Input quantization control method and system of dual-motor servo system Download PDFInfo
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Abstract
According to the input control method and system of the dual-motor servo system, the control input of the dual-motor servo system is obtained by adopting the state model of the dual-motor servo system. After the control input of the dual-motor servo system is obtained, it is further necessary to determine whether there is a backlash in the dual-motor servo system. And if the backlash exists, determining the time-varying bias torque of the motor according to the rotation angle difference between the motor and the load and the maximum value of the motor bias torque, and further determining the input of each motor according to the time-varying bias torque and the obtained control input. If the double-motor servo system does not have tooth gaps, the average value of control input is directly used as the input of each motor to realize synchronous drive of the two motors, different motor input constraint conditions are selected according to the existence of the tooth gaps, and the output of the double-motor drive servo system can be accurately controlled while the problem of uncontrollable load in the tooth gap stage is solved.
Description
Technical Field
The invention relates to the technical field of electromechanical control, in particular to an input quantization control method and system of a dual-motor servo system.
Background
With the rapid development of modern science and technology and industry, the practical requirements of the fields of military, industry and agriculture and the like on large-inertia high-power systems are increasing day by day. Due to the limitation of technology, cost and other factors, the power of a single motor is difficult to be made large enough, so that the driving capability of the motor to a large inertia load is insufficient. Aiming at the problem, the driving capability of the servo system can be improved by adopting a mode that a plurality of low-power motors drive a large inertia load together. Compared with a single-motor servo system, the multi-motor servo system not only improves the driving capability of the system, but also reduces the design difficulty and cost of a single motor. However, the multi-motor servo system needs a gear transmission link to realize the common driving of a plurality of motors to a load, and inevitably introduces nonlinearity such as backlash, friction and the like. The traditional PID control method has certain disturbance rejection capability on a general low-order system, but the defect of the error dynamic behavior is obvious, and particularly when unmodeled dynamic and dead zone nonlinearity and other factors exist in the system, the defect of the error dynamic behavior is more obvious. Therefore, how to design a suitable controller to specify the transition process of the tracking error of the multi-motor servo system while ensuring the tracking accuracy of the multi-motor servo system has become a research hotspot in motor control.
The classic method for tracking control of a motor servo system comprises the following steps: sliding mode variable structure control, backstepping control, dynamic surface control and the like. The sliding mode variable structure control has the advantages of high response speed, strong anti-interference capability and simple realization, and has the defect that the high-frequency buffeting phenomenon exists when the tracking error of the system is close to a zero steady state. The advantage of the backstepping control is that the programmed design steps are adopted, the single-step design idea is simpler, and the defects are two points: firstly, the nonlinear system structure is required to be in a strict negative feedback form, and secondly, the differential explosion phenomenon of a high-order system is difficult to process. Swaroop et al introduce a first-order filter to design dynamic surface control on the basis of a back-stepping method, so that the design of a controller is greatly simplified. Aiming at parameter uncertainty and internal disturbance of a system, a controller designed by Wu et al in combination with a disturbance observer and dynamic surface control ensures the boundedness of tracking errors. Aiming at a servo system containing unknown nonlinearity and an undetectable state, Zhang et al designs a dynamic surface control method based on a parameterized observer, so that the convergence of a system tracking error is ensured.
However, most of the above methods do not restrict the transient behavior of the tracking error. While the design of the predetermined performance control based on the error transformation is complex, the Ilchmann et al designs a control method with performance index constraint in a simple form, and simultaneously realizes the approximate tracking of the system output to the reference signal, and the transient state of the system tracking error does not exceed a constraint area with the performance index. Recently, such control with performance index constraints has been successfully applied to two-mass systems, robot systems, turntable servo systems, and the like. Hackl et al, on the assumption that the tracking error and its derivative can be used directly for feedback, implement control with performance index constraints for a system of relative order 2, which guarantees the predetermined performance of the system tracking error and its derivative at the same time.
In addition, in practice, a digital processor is mostly adopted in a control cabinet of a motor servo system, and calculation and transmission of control quantity are also digital, so that how to design quantization input of a motor end when system input is quantized is considered is also a problem which is concerned by many researchers. For a nonlinear system with uncertain parameters, Zhou et al design a self-adaptive quantization input controller based on a back-stepping method, realize accurate tracking of a given reference signal, and provide a unified calculation formula of upper bounds of quantization errors under different quantizers.
When both backlash nonlinearity and input quantization are present in the servo system, it is difficult for the above control method to simultaneously constrain the transient and steady-state behavior of the system tracking error. Therefore, in the prior art, the output of the dual-motor drive servo system cannot be accurately controlled.
Disclosure of Invention
The invention aims to provide an input quantization control method and system of a dual-motor servo system, so as to achieve the purpose of accurately controlling the output of the dual-motor drive servo system.
In order to achieve the purpose, the invention provides the following scheme:
an input quantization control method of a dual-motor servo system comprises the following steps:
acquiring structural parameters of a dual-motor servo system; the structural parameters include: the position and speed of the motor, the rotational inertia of the motor, the viscous friction coefficient of the motor, the position and speed of the load, the rotational inertia of the load, the viscous friction coefficient of the load and the transmission torque between the motor and the load;
according to the structural parameters, constructing a state model of the dual-motor servo system;
acquiring control parameters of the dual-motor servo system; the control parameters include: velocity tracking error, position tracking error, assist error, and equivalent viscous friction coefficient;
obtaining the control input of the dual-motor servo system according to the control parameters and the state model;
judging whether the double-motor servo system has a tooth gap or not;
if the double-motor servo system has a tooth gap, acquiring the rotation angle difference between the motor and the load and the maximum value of the motor offset torque;
determining the time-varying bias torque of the motor according to the rotation angle difference between the motor and the load and the maximum value of the motor bias torque;
determining the input of each motor according to the time-varying bias moment and the control input so as to realize the driving of the two motors to the load;
and if the double-motor servo system does not have a backlash, the average value of the control input is used as the input of each motor so as to realize the synchronous driving of the two motors to the load.
Optionally, the determining the input of each motor according to the time-varying bias torque and the control input to implement synchronous driving of the two motors specifically includes:
quantizing the control input by adopting a uniform quantizer to obtain quantized control input;
and determining the input of each motor according to the quantized control input and the time-varying bias torque so as to realize the driving of the two motors to the load.
Optionally, the quantizing the control input by using a uniform quantizer to obtain a quantized control input includes:
determining a minimum value of an upper bound of quantization errors of the uniform quantizer according to the parameter of the uniform quantizer;
according to the minimum value of the upper bound of the quantization error and the control input, compensating the quantization error and determining the quantization input;
and taking the determined quantized input as the input of the uniform quantizer to obtain a quantized control input.
Optionally, the obtaining of the control input of the dual-motor servo system according to the control parameter and the state model specifically includes:
judging whether the viscous friction coefficients of the load and the double motors can be obtained or not;
if the viscous friction coefficients of the load and the double motors can be obtained, obtaining the control input of the double-motor servo system according to the speed tracking error, the position tracking error, the auxiliary error, the equivalent viscous friction coefficient and the state model;
and otherwise, obtaining the control input of the dual-motor servo system according to the speed tracking error, the position tracking error, the auxiliary error and the state model.
Optionally, when the viscous friction coefficients of the load and the dual motors can be obtained, the control inputs of the dual-motor servo system are as follows:
when the viscous friction coefficients of the load and the double motors cannot be obtained, the control input of the double-motor servo system is as follows:
wherein, Jl+2JmTo equivalent moment of inertia, JlIs moment of inertia of the load, JmIs the rotational inertia of the motor, delta is a comprehensive factor,
for velocity tracking error, es(t) is the virtual tracking error, bl+2bmIs the equivalent viscous friction coefficient between load and double motors, blViscous coefficient of friction for load, bmIs the coefficient of viscous friction of the motor,
is an acceleration, x2For system state variables, F (t) is a constraint function that assists error steady state and process, F (t) is A.e-at+b，e-atFor the exponential decay term of the constraint function, t is the system runtime, A, a and b are both parameters of the performance indicator constraint boundary, and A, a and b are both constants greater than zero.
Optionally, the state model is:
wherein, thetamiThe position of motor i, i 1,2,
is the speed of the motor i and,
is the acceleration, θ, of motor ilIn order to be the position of the load,
is the speed of the load and is,
as the speed of the load, JmIs the moment of inertia of the motor, JlIs the moment of inertia of the load, bmiIs the viscous friction coefficient of the motor, blViscous coefficient of friction for load, umi(t) is the input to motor i, τi(t) is the transfer torque between the motor and the load,
Δθi(t) is the difference between the angle of rotation of the motor and the load, Δ θi(t)＝θmi(t)-miθl(t)，θmi(t) is the rotation angle of the motor, thetal(t) is the rotation angle of the load, alpha is the tooth gap width between the motor and the load, alpha is more than or equal to 0, kiIs the stiffness coefficient of motor i in contact with the load gear, ciThe damping coefficient for the torque transmitted by the motor i,
is the rate of change of the difference between the rotation angles of the motor and the load, miThe gear ratio between the motor i and the load is shown, m represents the motor, and l represents the load.
An input quantization control system of a dual motor servo system, comprising:
the structural parameter acquisition module is used for acquiring structural parameters of the dual-motor servo system; the structural parameters include: the position and speed of the motor, the rotational inertia of the motor, the viscous friction coefficient of the motor, the input of the motor, the position and speed of the load, the rotational inertia of the load, the viscous friction coefficient of the load and the transmission torque between the motor and the load;
the state model building module is used for building a state model of the dual-motor servo system according to the structural parameters;
the control parameter acquisition module is used for acquiring control parameters of the dual-motor servo system; the control parameters include: velocity tracking error, position tracking error, assist error, and equivalent viscous friction coefficient;
the control input determining module is used for obtaining the control input of the dual-motor servo system according to the control parameters and the state model;
the gear backlash judging module is used for judging whether the double-motor servo system has gear backlash or not;
if the double-motor servo system has a tooth gap, acquiring the rotation angle difference between the motor and the load and the maximum value of the motor offset torque;
determining the time-varying bias torque of the motor according to the rotation angle difference between the motor and the load and the maximum value of the motor bias torque;
and determining the input of each motor according to the time-varying offset moment and the average value of the control input so as to realize the driving of the two motors to the load.
And if the double-motor servo system does not have a backlash, the average value of the control input is used as the input of each motor so as to realize the synchronous driving of the two motors to the load.
Optionally, the backlash judging module specifically includes:
a quantization control input determination unit for quantizing the control input using a uniform quantizer to obtain a quantized control input;
and the motor input determining unit is used for determining the input of each motor according to the quantized control input and the time-varying bias moment so as to realize the driving of the two motors to the load.
Optionally, the quantization control input determining unit specifically includes:
a quantization error determination subunit configured to determine, according to the parameter of the uniform quantizer, a minimum value of an upper bound of quantization errors of the uniform quantizer;
a quantization input determination subunit, configured to determine a quantization input according to the minimum value of the upper bound of the quantization error and the control input;
and the quantization control input determining subunit is used for taking the quantization input as the input of the uniform quantizer to obtain the quantized control input.
Optionally, the control input determining module specifically includes:
a viscous friction judging unit for judging whether the viscous friction coefficients of the load and the double motors can be obtained;
if the viscous friction coefficients of the load and the double motors can be obtained, obtaining the control input of the double-motor servo system according to the speed tracking error, the position tracking error, the auxiliary error, the equivalent viscous friction coefficient and the state model;
and otherwise, obtaining the control input of the dual-motor servo system according to the speed tracking error, the position tracking error, the auxiliary error and the state model.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects: according to the input quantization control method and system of the dual-motor servo system, the control input of the dual-motor servo system is obtained by adopting the state model of the dual-motor servo system. After the control input of the dual-motor servo system is obtained, it is further necessary to determine whether there is a backlash in the dual-motor servo system. If the backlash exists, the time-varying bias torque of the motor is determined according to the rotation angle difference between the motor and the load and the maximum value of the motor bias torque, and then the input of each motor is determined according to the time-varying bias torque and the obtained control input, so that the two motors drive the load. If the double-motor servo system does not have a backlash, the average value of the control input is directly used as the input of each motor so as to realize the synchronous driving of the two motors to the load. Namely, according to the input quantization control method and system of the dual-motor servo system provided by the invention, two different motor input constraint conditions are designed for the dual-motor system with or without the backlash, so that the problem of uncontrollable load at the backlash stage is solved, and meanwhile, the output of the dual-motor drive servo system can be accurately controlled.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a block diagram of an input quantization tracking control of a dual-motor servo system according to an embodiment of the present invention;
FIG. 2 is a flowchart illustrating an input quantization control method of a dual-motor servo system according to an embodiment of the present invention;
FIGS. 3a and 3b are graphs of performance index constraint control errors in an embodiment of the invention;
FIGS. 4a and 4b are graphs of performance index constrained control errors with unknown coefficients of friction in an embodiment of the present invention;
FIGS. 5a and 5b are graphs of performance index constrained control errors with bias torque in an embodiment of the present invention;
FIGS. 6a and 6b are graphs of performance index constrained control errors with bias torque and unknown friction coefficient in an embodiment of the present invention;
FIGS. 7a and 7b are graphs of performance index constraint quantization control errors with bias torque in an embodiment of the present invention;
FIGS. 8a and 8b are graphs of performance index constrained quantization control errors with bias torque and unknown friction coefficient in an embodiment of the present invention;
fig. 9 is a schematic structural diagram of an input quantization control system of a dual-motor servo system according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide an input quantization control method and system of a dual-motor servo system, so as to achieve the purpose of accurately controlling the output of the dual-motor drive servo system.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
The input quantization control method provided by the invention mainly depends on a control method formed by a dual-motor servo system comprising a quantization controller. As shown in fig. 1, the main purpose of the input quantization control method disclosed in the present invention is to perform quantization error compensation on the output (input of quantizer) u (t) of the controller, so as to accurately control the output of the system.
The following describes in detail a specific technical solution of the input quantization control method and the technical effects achieved thereby.
Fig. 2 is a flowchart of an input control method of a dual-motor servo system according to an embodiment of the present invention, and as shown in fig. 2, the input control method of the dual-motor servo system includes:
and S0, acquiring the structural parameters of the dual-motor servo system. The structural parameters include: position and speed of the motor, moment of inertia of the motor, viscous coefficient of friction of the motor, position and speed of the load, moment of inertia of the load, viscous coefficient of friction of the load, and transfer torque between the motor and the load.
And S1, constructing a state model of the dual-motor servo system according to the structural parameters.
And S2, acquiring the control parameters of the dual-motor servo system. The control parameters include: velocity tracking error, position tracking error, assist error, and equivalent viscous friction coefficient.
And S3, obtaining the control input of the dual-motor servo system according to the control parameters and the state model.
And S4, judging whether the double-motor servo system has a backlash or not.
And S40, if the double-motor servo system has a backlash, acquiring the rotation angle difference between the motor and the load and the maximum value of the motor offset torque.
S41, determining the time-varying bias torque of the motor according to the rotation angle difference between the motor and the load and the maximum value of the motor bias torque.
And S42, determining the input of each motor according to the time-varying bias torque and the control input so as to realize the driving of the two motors to the load.
And S43, if the dual-motor servo system does not have backlash, the average value of the control input is used as the input of each motor, so that the two motors can synchronously drive the load.
The state model constructed in S1 is:
the state model is:
wherein, thetamiThe position of motor i, i 1,2,
is the speed of the motor i and,
is electricityAcceleration of machine i, θlIn order to be the position of the load,
is the speed of the load and is,
as the speed of the load, JmIs the moment of inertia of the motor, JlIs the moment of inertia of the load, bmiIs the viscous friction coefficient of the motor, blViscous coefficient of friction for load, umi(t) is the input to motor i, τi(t) is the transfer torque between the motor and the load,
(2)，Δθi(t) is the difference between the angle of rotation of the motor and the load, Δ θi(t)＝θmi(t)-miθl(t)，θmi(t) is the rotation angle of the motor, thetal(t) is the rotation angle of the load, alpha is the tooth gap width between the motor and the load, alpha is more than or equal to 0, kiIs the stiffness coefficient of motor i in contact with the load gear, ciThe damping coefficient for the torque transmitted by the motor i,
is the rate of change of the difference between the rotation angles of the motor and the load, miThe gear ratio between the motor i and the load is shown, m represents the motor, and l represents the load.
For the above state model, the control design with performance index constraints when the system has no backlash is as follows:
for the motor subsystem in the state model
Reselect new subsystem state
The state equation for the motor subsystem can be expressed as:
assuming that the model numbers and the structural parameters of the two driving motors in the state model are the same, namely Jm＝Jm1＝Jm2And bm＝bm1＝bm2. The state model can be written as follows:
when the dual-motor servo system has no backlash (namely the width alpha of the backlash is 0), the two motors can always synchronously drive the load to operate. With a gear ratio of 1, the speed of the motor subsystem is
In conjunction with equation (4), the state model can be further rewritten as:
further, an equivalent second-order system of the state model when the two motors synchronously drive the load can be obtained:
wherein the content of the first and second substances,
representing control inputs to the motor subsystem, Jl+2JmTo equivalent moment of inertia, bl+2bmIs the equivalent viscous coefficient of friction.
Selecting the state of the second order system (6) as
The state model can be represented as:
assuming a tracking reference signal of a dual-motor servo system as an expected position y of a loaddAnd desired speed of the load
And desired acceleration
Is continuously bounded. The problem of the design study in this step is: the controller u (t) with performance index constraints is designed for equation (7) so that the system output y tracks the desired reference signal yrAnd simultaneously ensuring the position tracking error e (t) y (t) -y by setting the boundary of the auxiliary errorrAre within a certain range.
When it is determined in S4 that the dual servo system has no backlash, the design process for the controller output (control input) specifically includes:
based on the position tracking error e (t) y (t) -yrAnd reference signal speed
And acceleration
Continuously bounded condition defining a velocity tracking error of
Design system aiding error es(t)：
Wherein the content of the first and second substances,
the constant delta > 0 is the integral factor of the velocity tracking error. It is worth noting that when the integration factor δ is small, there is a small normal number e, so that
By taking the derivative of equation (8) in conjunction with equation (7), one can obtain:
the Lyapunov function was chosen as:
taking its derivative and considering equation (9), one can obtain:
the following general control inputs can be designed for the motor subsystem:
wherein, v (t) is a virtual control quantity, and is designed into a control form with performance index constraint:
wherein F (t) is A.e-at+ b is the steady state and transient process constraints of the auxiliary error (the boundary of the auxiliary error), and the initial auxiliary error satisfies es(0) < F (0). Constant b > 0 is the steady-state margin of the aiding error, F (t) is A.e-at+ b constrains the range of variation of the system aiding error. By the gain term 1/(F (t) - | e) in the virtual control amount (13)s(t) |) it can be known that at any time when t is more than or equal to 0, when the auxiliary error es(t) approaching the set boundary F (t) where A.e is equal-at+ b, the gain 1/(F (t) - | e) in equation (13)s(t) |) becomes a larger value, and the auxiliary error e can be made by combining the negative feedback design in the formula (12)s(t) away from the boundary, thereby ensuring that the assist error is always within the set boundary.
Then, it is judged whether or not the viscous friction coefficient between the load and the two motors can be obtained.
And if the viscous friction coefficients of the load and the double motors can be obtained, obtaining the control input of the double-motor servo system according to the speed tracking error, the position tracking error, the auxiliary error, the equivalent viscous friction coefficient and the state model.
The control input of the double-motor servo system is as follows:
and otherwise, obtaining the control input of the dual-motor servo system according to the speed tracking error, the position tracking error, the auxiliary error and the state model. The control inputs are:
wherein, Jl+2JmTo equivalent moment of inertia, JlIs moment of inertia of the load, JmIs the rotational inertia of the motor, delta is a comprehensive factor,
for velocity tracking error, es(t) is the position tracking error, bl+2bmIs the equivalent viscous friction coefficient between load and double motors, blViscous coefficient of friction for load, bmIs the coefficient of viscous friction of the motor,
is an acceleration, x2For the system state variable (load speed), f (t) is a constraint function that assists error steady state and process, f (t) a · e-at+b，e-atFor the exponential decay term of the constraint function, t is the system runtime, A, a and b are both parameters of the performance indicator constraint boundary, and A, a and b are both constants greater than zero.
Finally, the control input is evenly divided into the input ends of the two motors (namely, the evenly divided value of the control input is used as the input of each motor), so that the synchronous driving of the double motors to the load can be realized when no tooth gap exists.
When it is determined in S4 that there is backlash in the dual servo system, the design process for the controller output (control input) specifically includes:
when the system has a backlash (alpha is more than 0), the phase of the load driven by the two motors together is similar to the phase of the load driven by the two motors together when the backlash is not generated, so that the tracking performance of the system in the non-backlash stage and the backlash stage can be ensured simultaneously only by properly designing on the basis of the formula (14) and the formula (15).
If the two motors drive the load synchronously all the time, when the system enters a backlash mode, the two motors are not in contact with the load, so that the load is uncontrollable, and the control performance of the system is seriously influenced. The common solution is to apply a pair of constant offset torques with equal magnitude and opposite direction at the input ends of the two motors at the same time, so that the two motors are asynchronous to some extent when driving the load together, and ensure that one motor continues to restrict the driving load according to the performance index, and the other motor rapidly passes through the backlash (commutation) under the action of the offset torque. In order to solve the problem that the constant offset torque cannot give consideration to both small energy consumption and rapid tooth clearance passing, the following time-varying offset torque needs to be designed:
wherein, tau w0 is the maximum value of the bias moment, kwGreater constant > 0, Δ θi(t) is the difference between the angle of rotation of the motor and the load, Δ θi(t)＝θmi(t)-miθl(t)，θmi(t) is the rotation angle of the motor, thetalAnd (t) is the rotation angle of the load.
When the system enters the backlash, the load is in a low speed operation phase. From equation (16) for the time-varying bias torque, the first motor is biased at the bias torque
Continues to drive the load (forward) and maintains the | Δ θ1The | -alpha > 0 is smaller, so that the bias moment uw1＜＜τw. While the second motor is at the bias torque
Over the tooth space (reverse) under the action of (1) | delta theta2The | - α < 0 undergoes a first increase and then decrease process, so that the biasing moment uw2Is rapidly increased to τwAnd then reduced (shock reduced). Therefore, the offset torque in equation (16) not only enables the system to quickly bridge the backlash, but also reduces the system energy consumption due to the offset torque (compared with a constant offset torque). The process of the first motor passing through the backlash is similar.
In combination with equation (16) of the time-varying bias torque, the control inputs of each motor under the existence of backlash in the design system on the basis of equation (14) are as follows:
when the load and the viscous friction coefficients of the dual motors are unknown or bounded time varying, the overall control input in equation (15) is combined to obtain the same form of individual motor control input as equation (17).
Considering that the control cabinet of the dual-motor servo system is digitized in practice, it is particularly necessary to compensate the quantization error of the control input in S41 to ensure the tracking performance of the backlash-containing system. The process of quantization control comprises:
and compensating the quantization error of the control input according to the parameters of the consistent quantizer to obtain the input of the quantizer.
And determining the input of each motor according to the input of the quantizer and the time-varying bias torque so as to realize the driving of the two motors to the load.
Wherein the mathematical model of the uniform quantizer is described as:
in the formula, constant u0＞0，u1＝u0+h/2，uj＝uj-1+ h, (j ═ 2.. times, N), with a constant h > 0 being the length of the quantization interval. It can be seen that the quantization control set is U ═ 0, ± UjControl quantity U (t) after passing through the uniform quantizer q (U) in the set U ═ 0, ± UjIn. As defined by the uniform quantizer, the quantization error has a definite upper bound, i.e., | Q (u (t)) -u (t) | ≦ umin＝max{u0,h}。
For this quantization control error, the quantization input of equation (14) at uniform quantization is:
uQ＝u(t)-umintanh(umines(t)/λ) (19)。
where u (t) is the control input in equation (14) and the constant λ > 0 is the parameter to be designed.
The actual inputs to each motor at this time are:
as can be seen from equations (18) and (19):
since phi is less than or equal to 0.2785 lambda, the constant M in the above formula1＝0.2785λ。
Selecting a Lyapunov function
The derivative thereof is obtained by considering equation (14) and equation (21):
further, a small upper bound on the assistance error of the system at steady state can be obtained. When the auxiliary error esOutside this limit (transient), the controller is designed to continue to reduce the system assist error until the assist error e is reachedsEnter this limit and remain there (steady state). Also, this quantization control process is also applicable to equation (15).
The invention adopts another embodiment of the disclosed input quantization control method to control the dual-motor servo system, which specifically comprises the following steps:
step one, designing control input with performance index constraint when the system has no backlash:
when two motors drive a load simultaneously, the angular speed at the motor end is converted to the load end to obtain a second-order system:
selecting the state of the system as
Equation (1) can be expressed as:
given a reference signal of ydAnd is and
is continuously bounded. According to the tracking error e (t) yrDesign system aiding error
The control inputs with performance index constraints are designed as:
setting the appropriate F (t) ═ A.e-at+ b, so that the initial value of the auxiliary error satisfies the inequality es(0) F (0) is smaller, and the steady-state error is smaller.
The control inputs with performance index constraints under unknown or bounded variations in the design load and the viscous friction coefficients of the dual motors are:
second, designing the offset moment when the system has backlash
When the system is operating in the backlash mode, a time-varying bias torque is used, with one motor continuing to drive the load and the other motor rapidly passing through the backlash under the action of the bias torque.
The time-varying bias torque is designed as:
selecting a suitable τw＞0，kw＞0。
The control inputs to each motor are:
and 3, step 3: designing a quantized control input with bias torque and performance index constraints
The uniform quantizer may be represented as:
given u0> 0 and h > 0, calculate u1＝u0+h/2，uj＝uj-1+ h, (j 2.. times.n), giving the quantization control set U ═ 0, ± UjCalculating the upper limit | Q (u (t)) -u (t)) | ≦ u (t)) of the quantization errormin＝max{u0,h}。
Given λ < 1 > and 0.1, the quantization control is:
uQ＝u(t)-umintanh(umines(t)/λ)。
where u (t) is the control input in equation (13) or equation (14).
The actual inputs to the two motors are:
the technical scheme disclosed by the invention is subjected to simulation verification, and the method specifically comprises the following steps:
the control method designed by the invention is applied to carry out simulation research on the dual-motor servo system containing the tooth gap nonlinearity, and under the two conditions of known and unknown viscous friction coefficients, different performance indexes are used for restricting control input, so that the load-to-sine signal y can be obtainedd2sin (tt) and tracking error. It can be seen from the simulations that the designed bias torque is used whether the load and motor viscous friction in the system is known or unknownThe performance index constraint control and the quantitative control can meet the requirements of the tracking error transient state and the steady state which are preset.
In a simulation experiment of tracking control of a dual-motor servo system with a tooth gap, the load parameters are as follows: moment of inertia J of loadl＝0.0113kg·m2Coefficient of loaded viscous friction bm0.02Nm · s/rad. Motor parameter Jmi＝0.0026kg·m2，bmi0.015 Nm.s/rad, stiffness factor ki1Nm/rad and a damping coefficient c of 0.2Nm s/rad. The gap width α between the motor and the load is 0.1 rad. Parameters of performance index constraint boundaries: a is 2, b is 0.05, and a is 3. The controller parameters are as follows: δ is 0.03. Quantizer parameters: u. of00.06, h 0.1, quantization controller parameter: λ is 0.2. The deflection moment parameter: tau isw＝0.1Nm，kw＝50。
The simulation results of the control input with performance index constraints are shown in fig. 3 a-6 b, and the tracking error of the sinusoidal reference signal can be loaded in the graph and is always in the set performance index constraint area, which shows that the design of the control with performance index constraints in the text can meet the requirements for the steady-state and transient performance of the tracking error.
7 a-8 b are graphs of the trace curve and error evolution of the sinusoidal reference signal for performance indicator constrained quantization control input. It can be seen from the tracking error evolution diagram that the quantitative control method provided by the invention can still ensure the steady-state and transient-state performances of the system tracking error, and has good convergence rate, steady-state precision and robustness to the unknown viscous friction coefficient of the system.
Based on the above technical content, the input quantization control method disclosed by the present invention further has the following advantages:
1) most of the conventional tracking control methods for the servo system consider the accuracy when the tracking error reaches a steady state, and the transient behavior of the tracking error is rarely considered. The control method with performance index constraint designed by the invention can not only ensure that the steady-state tracking error of the dual-motor servo system is within a given range, but also ensure that the transient state of the system tracking error is within a preset performance index constraint area. The design of the steady-state and transient behaviors of the specified tracking error can not only meet the set steady-state tracking precision, but also limit the overshoot of the tracking error.
2) The error transform based predetermined performance control typically needs to be combined with either the classical sliding mode method or the dynamic surface method, whereas the design of the control with performance index constraints of the present invention does not. In addition, the control design form in the invention is simple, the parameters needing to be adjusted are less, and the robustness on the unknown viscous friction coefficient of the load and the motor end is stronger.
3) Most of the traditional servo system tracking control methods are designed with continuous control input, and the actual servo system adopts a digital control cabinet, so that errors of data processing are inevitably introduced. Therefore, on the premise of introducing a typical uniform quantizer, the invention carries out quantization design on the control input with performance index constraint, the control with performance index constraint after quantization can still ensure the transient and steady-state performance of the tracking error of the system, and the unknown viscous friction coefficient of the load and the motor end still has robustness.
In addition, aiming at the input control method of the dual-motor servo system provided by the present invention, an input control system of the dual-motor servo system is also correspondingly provided, as shown in fig. 9, the system includes: the system comprises a structural parameter acquisition module 1, a state model construction module 2, a control parameter acquisition module 3, a control input determination module 4 and a backlash judgment module 5.
The structural parameter acquiring module 1 is used for acquiring structural parameters of the dual-motor servo system, wherein the structural parameters comprise: position and speed of the motor, rotational inertia of the motor, viscous friction coefficient of the motor, input to the motor, position and speed of the load, rotational inertia of the load, viscous friction coefficient of the load, and transfer torque between the motor and the load.
And the state model building module 2 is used for building a state model of the dual-motor servo system according to the structural parameters.
The control parameter obtaining module 3 is configured to obtain control parameters of the dual-motor servo system, where the control parameters include: velocity tracking error, position tracking error, assist error, and equivalent viscous friction coefficient.
And the control input determining module 4 is used for obtaining the control input of the dual-motor servo system according to the control parameters and the state model.
And the backlash judgment module 5 is used for judging whether the dual-motor servo system has backlash.
And if the double-motor servo system has a backlash, acquiring the rotation angle difference between the motor and the load and the maximum value of the motor offset torque.
And determining the time-varying bias torque of the motor according to the rotation angle difference between the motor and the load and the maximum value of the motor bias torque.
And determining the input of each motor according to the time-varying offset moment and the average value of the control input so as to realize the driving of the two motors to the load.
And if the double-motor servo system does not have a backlash, the average value of the control input is used as the input of each motor so as to realize the synchronous driving of the two motors to the load.
The backlash judgment module 5 further specifically includes: a quantization control input determination unit and a motor input determination unit. The quantization control input determining unit is used for performing quantization error compensation on the control input according to the consistent quantizer parameters to obtain the control input after the quantization error compensation. And the input determining unit is used for determining the input of each motor according to the quantized control input and the time-varying bias moment so as to realize the driving of the two motors to the load.
Wherein, the quantization control input determination unit specifically includes: a quantization error determination subunit, a quantization input determination subunit, and a quantization control input determination subunit.
The quantization error determination subunit is configured to determine a minimum value of an upper bound of quantization errors of the uniform quantizer according to the parameter of the uniform quantizer.
The quantization input determination subunit is configured to determine a quantization input according to the minimum value of the upper bound of the quantization error and the control input.
The quantization control input determination subunit is configured to use the quantization input as an input of the uniform quantizer to obtain a quantized control input.
The control input determining module 4 specifically includes: and a viscous friction judging unit.
The viscous friction judging unit is used for judging whether the load and the viscous friction coefficient of the double motors can be obtained.
If the viscous friction coefficients of the load and the double motors can be obtained, the control input of the double-motor servo system is obtained according to the speed tracking error, the position tracking error, the auxiliary error, the equivalent viscous friction coefficient and the state model
And otherwise, obtaining the control input of the dual-motor servo system according to the speed tracking error, the position tracking error, the auxiliary error and the state model.
The input control method and the input control system of the dual-motor servo system provided by the invention consider the problem of dead zone type tooth gaps and load tracking control of input quantization in the dual-motor servo system. Based on the constructed auxiliary error and combined with the structural characteristics of a multi-motor system, the control method with performance index constraint has the advantages of simple design and disturbance resistance, the performance index constraint control input and the quantitative control input are designed for a dual-motor servo system, and the aim of meeting the preset performance index by the synchronization of the motor in the backlash-free system and the tracking of the load on the reference signal is fulfilled by equally dividing the control quantity. In order to enable a system containing the non-linearity of the backlash to be always driven by a motor, a time-varying bias torque is designed on the basis of the control. In addition, corresponding performance index constraint control and quantitative control are designed for the condition that the viscous friction coefficient of the system is unknown. The control input designed in the invention can not only ensure the steady-state and transient performance of the tracking error of the system, but also has certain robustness to the unknown viscous friction existing in the system.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (6)
1. An input quantization control method of a dual-motor servo system is characterized by comprising the following steps:
acquiring structural parameters of a dual-motor servo system; the structural parameters include: the position and speed of the motor, the rotational inertia of the motor, the viscous friction coefficient of the motor, the position and speed of the load, the rotational inertia of the load, the viscous friction coefficient of the load and the transmission torque between the motor and the load;
according to the structural parameters, constructing a state model of the dual-motor servo system;
acquiring control parameters of the dual-motor servo system; the control parameters include: velocity tracking error, position tracking error, assist error, and equivalent viscous friction coefficient;
obtaining the control input of the dual-motor servo system according to the control parameters and the state model;
judging whether the double-motor servo system has a tooth gap or not;
if the double-motor servo system has a tooth gap, acquiring the rotation angle difference between the motor and the load and the maximum value of the motor offset torque;
determining the time-varying bias torque of the motor according to the rotation angle difference between the motor and the load and the maximum value of the motor bias torque;
determining the input of each motor according to the time-varying bias moment and the control input so as to realize the driving of the two motors to the load;
if the double-motor servo system does not have a tooth gap, the average value of the control input is used as the input of each motor so as to realize the synchronous driving of the two motors to the load;
the obtaining of the control input of the dual-motor servo system according to the control parameters and the state model specifically includes:
judging whether the viscous friction coefficients of the load and the double motors can be obtained or not;
if the viscous friction coefficients of the load and the double motors can be obtained, obtaining the control input of the double-motor servo system according to the speed tracking error, the position tracking error, the auxiliary error, the equivalent viscous friction coefficient and the state model;
otherwise, obtaining the control input of the dual-motor servo system according to the speed tracking error, the position tracking error, the auxiliary error and the state model;
the state model is:
wherein, thetamiThe position of motor i, i 1,2,
is the speed of the motor i and,
is the acceleration, θ, of motor ilIn order to be the position of the load,
is the speed of the load and is,
as the speed of the load, JmIs the moment of inertia of the motor, JmiIs the moment of inertia of motor i, JlIs the moment of inertia of the load, bmiIs the viscous friction coefficient of the motor, blViscous coefficient of friction for load, umi(t) is the input to motor i, τi(t) is the transfer torque between the motor and the load,
Δθi(t) is the difference between the angle of rotation of the motor and the load, Δ θi(t)＝θmi(t)-miθl(t)，θmi(t) is the rotation angle of the motor, thetal(t) is the rotation angle of the load, alpha is the tooth gap width between the motor and the load, alpha is more than or equal to 0, kiIs the stiffness coefficient of motor i in contact with the load gear, ciThe damping coefficient for the torque transmitted by the motor i,
is the rate of change of the difference between the rotation angles of the motor and the load, miThe gear transmission ratio between the motor i and the load is shown, m represents the motor, and l represents the load;
the determining the input of each motor according to the time-varying bias torque and the control input to realize synchronous driving of the two motors specifically comprises:
quantizing the control input by adopting a uniform quantizer to obtain quantized control input;
determining the input of each motor according to the quantized control input and the time-varying bias moment so as to drive the two motors to the load;
the time-varying bias torque is:
wherein, tauw0 is the maximum value of the bias moment, kwGreater constant > 0, motor iA serial number.
2. The input quantization control method of the dual-motor servo system according to claim 1, wherein the quantizing the control input by using the uniform quantizer to obtain a quantized control input specifically comprises:
determining a minimum value of an upper bound of quantization errors of the uniform quantizer according to the parameter of the uniform quantizer;
according to the minimum value of the upper bound of the quantization error and the control input, compensating the quantization error and determining the quantization input;
and taking the determined quantized input as the input of the uniform quantizer to obtain a quantized control input.
3. The input quantization control method of the dual-motor servo system as claimed in claim 1, wherein when the viscous friction coefficients of the load and the dual motors can be obtained, the control inputs of the dual-motor servo system are:
when the load and the viscous friction coefficient of the double motors cannot be obtained, the control input of the double-motor servo system is as follows:
wherein, Jl+2JmTo equivalent moment of inertia, JlIs moment of inertia of the load, JmIs the rotational inertia of the motor, delta is a comprehensive factor,
for velocity tracking error, es(t) is the virtual tracking error, bl+2bmFor equivalence between load and double motorsCoefficient of viscous friction, blViscous coefficient of friction for load, bmIs the coefficient of viscous friction of the motor,
is an acceleration, x2For system state variables, F (t) is a constraint function that assists error steady state and process, F (t) is A.e-at+b，e-atFor the exponential decay term of the constraint function, t is the system runtime, A, a and b are both parameters of the performance indicator constraint boundary, and A, a and b are both constants greater than zero.
4. An input quantization control system of a dual-motor servo system, comprising:
the structural parameter acquisition module is used for acquiring structural parameters of the dual-motor servo system; the structural parameters include: the position and speed of the motor, the rotational inertia of the motor, the viscous friction coefficient of the motor, the input of the motor, the position and speed of the load, the rotational inertia of the load, the viscous friction coefficient of the load and the transmission torque between the motor and the load;
the state model building module is used for building a state model of the dual-motor servo system according to the structural parameters;
the control parameter acquisition module is used for acquiring control parameters of the dual-motor servo system; the control parameters include: velocity tracking error, position tracking error, assist error, and equivalent viscous friction coefficient;
the control input determining module is used for obtaining the control input of the dual-motor servo system according to the control parameters and the state model; the state model is:
wherein, thetamiThe position of motor i, i 1,2,
is the speed of the motor i and,
is the acceleration, θ, of motor ilIn order to be the position of the load,
is the speed of the load and is,
as the speed of the load, JmIs the moment of inertia of the motor, JmiIs the moment of inertia of motor i, JlIs the moment of inertia of the load, bmiIs the viscous friction coefficient of the motor, blViscous coefficient of friction for load, umi(t) is the input to motor i, τi(t) is the transfer torque between the motor and the load,
Δθi(t) is the difference between the angle of rotation of the motor and the load, Δ θi(t)＝θmi(t)-miθl(t)，θmi(t) is the rotation angle of the motor, thetal(t) is the rotation angle of the load, alpha is the tooth gap width between the motor and the load, alpha is more than or equal to 0, kiIs the stiffness coefficient of motor i in contact with the load gear, ciThe damping coefficient for the torque transmitted by the motor i,
is the rate of change of the difference between the rotation angles of the motor and the load, miThe gear transmission ratio between the motor i and the load is shown, m represents the motor, and l represents the load;
the gear backlash judging module is used for judging whether the double-motor servo system has gear backlash or not;
if the double-motor servo system has a tooth gap, acquiring the rotation angle difference between the motor and the load and the maximum value of the motor offset torque;
determining the time-varying bias torque of the motor according to the rotation angle difference between the motor and the load and the maximum value of the motor bias torque;
determining the input of each motor according to the time-varying bias moment and the average value of the control input so as to realize the driving of the two motors to the load; the time-varying bias torque is:
wherein, tauw0 is the maximum value of the bias moment, kwThe constant is larger than 0, and i is the motor serial number;
if the double-motor servo system does not have a tooth gap, the average value of the control input is used as the input of each motor so as to realize the synchronous driving of the two motors to the load;
the control input determination module specifically includes:
a viscous friction judging unit for judging whether the viscous friction coefficients of the load and the double motors can be obtained;
if the viscous friction coefficients of the load and the double motors can be obtained, obtaining the control input of the double-motor servo system according to the speed tracking error, the position tracking error, the auxiliary error, the equivalent viscous friction coefficient and the state model;
and otherwise, obtaining the control input of the dual-motor servo system according to the speed tracking error, the position tracking error, the auxiliary error and the state model.
5. The input quantization control system of the dual-motor servo system as claimed in claim 4, wherein the backlash determining module specifically comprises:
a quantization control input determination unit for quantizing the control input using a uniform quantizer to obtain a quantized control input;
and the motor input determining unit is used for determining the input of each motor according to the quantized control input and the time-varying bias moment so as to realize the driving of the two motors to the load.
6. The input quantization control system of the dual-motor servo system of claim 5, wherein the quantization control input determination unit specifically comprises:
a quantization error determination subunit configured to determine, according to the parameter of the uniform quantizer, a minimum value of an upper bound of quantization errors of the uniform quantizer;
a quantization input determination subunit, configured to determine a quantization input according to the minimum value of the upper bound of the quantization error and the control input;
and the quantization control input determining subunit is used for taking the quantization input as the input of the uniform quantizer to obtain the quantized control input.
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