CN108390597A - Permanent magnet synchronous motor nonlinear predictive controller design with disturbance observer - Google Patents
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Abstract
The invention discloses a kind of designs of the permanent magnet synchronous motor nonlinear predictive controller with disturbance observer, belong to the technical field of high performance motor driving control system.Exist firstdqAll model errors and external disturbance are considered under coordinate system, build the nonlinear mathematical model of PMSM;Secondly, on the basis of this model, the Design of Predictive of outer shroud speed ring and inner ring electric current loop is carried out respectively, and the design of disturbance observer is carried out when there are control device limitation.The present invention is designed by the Nonlinear Model Predictive Control device design of cascade structure and the disturbance observer with anti-saturation, the shortcomings that electrical parameter of motor being highly dependent in terms of overcoming the limitation existing for system to handled variable and limitation electric current, and disturbance will be considered and be compensated in predictive controller, to enhance the robustness of control system for permanent-magnet synchronous motor.The present invention can make system output more accurately track reference track by experimental verification this method, while in view of current limit can keep higher robustness in Errors and load variation.
Description
Technical Field
The invention relates to a design of a nonlinear predictive controller of a permanent magnet synchronous motor with a disturbance observer, belonging to the technical field of high-performance motor drive control.
Background
The permanent magnet synchronous motor has the characteristics of high efficiency and high power density, so that the permanent magnet synchronous motor occupies a very important position in practical industrial application; however, its multivariable, non-linear, parametric time-varying, and its fast dynamics of the model make it very complex to control; although various advanced control methods for the permanent magnet synchronous motor driving system are proposed based on the modern control theory at present, such as adaptive control, self-correcting control, intelligent control and the like, the problem of robustness of the system is still to be further solved due to the complex algorithm, large calculation amount, poor adaptability to unmodeled dynamics and disturbance, and limited application range.
The main challenge of our research task is to devise a control method for a permanent magnet synchronous motor that has better continuous trajectory tracking performance, disturbance rejection performance, stability and robustness, and at the same time, preserves the strong non-linear characteristics of the system when the parameters are uncertain and the physical constraints and computation time are considered.
Under the framework, model prediction control is proposed as an ideal solution; however, the proposed discrete time model based nonlinear predictive controller requires a long computation time, which limits the nonlinear system to industrial applications with slow dynamic processes, such as metallurgy, oil refining, chemical industry and paper making, due to the long computation time required for the optimization of the nonlinear problem, especially if constraint effects are considered; due to the reason, in most cases, researchers carry out linearization processing on the prediction behavior of the nonlinear system on a working point, so that the nonlinear constraint optimization problem is avoided being solved, the online calculation amount is reduced, and the approximation and constraint nonlinear problems caused by the nonlinear constraint optimization problem are not fully considered; with the development of a new nonlinear predictive control technology based on a continuous time model, the calculation time of the system is greatly reduced; in the new technologies, a prediction model based on a continuous time model is designed by applying Taylor series expansion, and then the obtained controller is analyzed and modeled on a digital signal processor to obtain a better effect; however, this control strategy is known to be less robust when considering external disturbances and inaccuracies in the model built; to this end, we propose to add a disturbance observer capable of estimating all the disturbances affecting the output regulation. The nonlinear predictive control and disturbance observation are combined, so that the system can still keep higher robustness under the influence of motor parameter change and external disturbance. On the other hand, variables we handle are generally limited by the saturation module. In practical applications, an anti-saturation module is usually added to the control loop when designing the disturbance observer.
Disclosure of Invention
The invention provides a design method of a permanent magnet synchronous motor nonlinear predictive controller with a disturbance observer aiming at the situation that a permanent magnet synchronous motor is required to have a rapid dynamic response process, high-precision stable rotating speed tracking performance and stronger robustness in a high-performance motor drive control occasion, and the method is established on the basis of a permanent magnet synchronous motor nonlinear model considering all model errors and external disturbance, and is based on a generalized predictive control theory, the nonlinear model predictive control and the disturbance observer design are tightly combined, and an established optimization control strategy of a rolling time domain is provided; the control strategy can enable the system output to more accurately track the reference track, meanwhile, the influence of current limitation is considered, and high robustness can be kept when the model parameter error and the load change.
The method of the invention comprises the following steps:
the method comprises the following steps: in thatdqConstructing a nonlinear mathematical model of the PMSM by considering all model errors and external disturbance under a coordinate system
(25)
In the formula,、andrepresenting model errors and external load disturbances.
Step two: on the basis of the established disturbance model, respectively designing a prediction controller of an outer ring speed ring and an inner ring current ring, selecting a cost function according to a generalized prediction control theory, and searching an optimal control rate in a rolling time domain in a minimized way, so that the output of the system in the prediction time can track a given reference track to achieve the purpose of prediction control; meanwhile, the design of a disturbance observer is considered when the limitation of a control device exists, so that the system can keep high robustness when the model parameter error and the load change exist.
Firstly, designing an outer ring speed ring prediction controller;
state space model of permanent magnet synchronous motor speed ring in rotating speedAs state variables, quadrature-axis current componentsFor input, rotational speedIs the output. The purpose of the nonlinear model predictive control is to find a suitable quadrature-axis current componentSo that the selected cost functionAnd minimum.
Applying a taylor series expansion to represent the prediction of the output and the prediction of the output reference value, and such that:if so, the minimum value of the quadrature axis current component which minimizes the cost function is finally obtained as:
(26)
wherein,(27)。
the disturbance signal, usually as an unknown variable, must be estimated and replaced in the controller to ensure the accuracy of disturbance rejection and reference signal continuity; therefore, the control rate (26) can be rewritten as:
(28)
wherein,representing the estimated perturbation.
Secondly, designing a speed loop disturbance observer when quadrature axis current component limitation exists;
in order to limit quadrature axis current components, a saturation module is introduced into the outer ring of the control loop; the disturbance observer can be written as:
(29)
wherein,,and is andis a parameter that is adjusted by the observer,
in view of (25), we obtain:
(30)
will be provided withAndexpanding and jointly substituting (28) into (29) to obtain:
(31)
wherein,。
now, if we substitute (31) into the controller (28), the quadrature axis current reference value that ensures speed regulation is written in the following relation:
(32)
wherein,
(33)
(34)。
thirdly, designing an inner loop current loop controller;
the design of the inner loop current loop aims at designing a robust prediction type regulator when the parameters of the motor are changed; dynamic equations in the form of current loop non-linearities toAndin order to be a state variable, the state variable,andin order to be an input, the user can select,andis an output; the goal of generalized predictive control is to find the controller variables that minimize the cost function:
(35)
predicting the output and future reference values by Taylor series expansion, and controlling the cost function pairThe rate is differentiated and the optimal control rate minimizes the cost function, i.e. satisfiesAnd finally obtaining:
(36)
wherein,;;;
;
in a real system, the disturbance is observed and compensated for, so equation (36) can be rewritten as:
(37)。
finally, an inner loop disturbance observer is designed when there are control device limitations
As with the disturbance observer design in the outer loop, the initial observer allowing for disturbance estimation is of the form:
(38)
wherein,,and is andis a constant coefficient matrix;
the error between the regulator output and the saturation block output can be integrated when the observer is designed:
(39)
thus:
(40)
finally, we get the disturbance observer with the limiting device module as:
(41)
as before, the observer in the controller is replaced by that defined by (37) to obtain
(42)
Wherein,
(43)
(44)。
the invention has the advantages that: first, the main disadvantage of the controller compared to the traditional control mode is the lack of robustness to model errors and load disturbance variations; the invention fully considers the influence of model error and load change when establishing the nonlinear model of the motor, and considers the model error and the load change as unknown and unmeasurable disturbance in limited time, thereby designing a function based on a new designThe disturbance observer of (1), the disturbance will be considered and compensated in the predictive controller; secondly, compared with the model prediction control of a direct structure, the limit and current limit of the direct structure mode on the processed variable are very dependent on the electric parameters of the motor; the invention constructs a control strategy of a cascade structure, the outer ring of the system ensures speed regulation by applying predictive control, and the inner ring forms multivariable predictive control for current regulation; the current is limited directly by the saturation module, and since the outer loop contains the integration and saturation modules, the speed response will inevitably overshoot each time the limiting device is active; in order to eliminate the influence of the limiting device, an anti-saturation module is introduced into the control loop; through the control strategy implemented by the invention, the output can more accurately track the reference track, and meanwhile, the robustness is kept when the model parameter error and the load change.
Drawings
Fig. 1 is a structural diagram of a permanent magnet synchronous motor cascade nonlinear model predictive control system of the present invention.
FIG. 2 is a graph of the speed and speed error of the cascade architecture system of the present invention: without anti-saturation and with a given signal having fast dynamics.
FIG. 3 is a graph of the speed and speed error of the cascade architecture system of the present invention: the band is anti-saturating and the given signal has fast dynamics.
FIG. 4 is a graph of speed and speed error for a cascade architecture system of the present invention: the electrical parameter changes at T = 0.5 s.
FIG. 5 is a cross-axis and direct-axis current curve of the cascade structure system of the present invention: the electrical parameter changes at T = 0.5 s.
FIG. 6 is a graph of speed and speed error for a cascade architecture system of the present invention: load mutations at T = 0.5 s.
FIG. 7 is a cross-axis and direct-axis current curve of the cascade structure system of the present invention: load mutations at T = 0.5 s.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings and the detailed description;
FIG. 1 is a general block diagram of a motor control system required by the present invention, as shown in FIG. 1, a rotor position signal of a permanent magnet synchronous motor control systemObtained by means of a photoelectric encoder.
Firstly, obtaining the stator three-phase current of the permanent magnet synchronous motor by using a current sensor for sampling、Andthen, the two phases are converted into a two-phase rotating coordinate system through Clark conversion (3 s/2 s) and Park conversion (2 s/2 r)dShaft currentAndqshaft current(ii) a In thatConsidering all model errors and external disturbances under a coordinate system, the nonlinear mathematical model of the PMSM is constructed by:
(45)
in the formula,、andrepresenting model errors and external load disturbances, and defining:
(46)
when the dynamics of the various uncertainties are unknown, we assume that they change very slowly compared to the dynamics of the system time constant, and therefore, there are:
;;(47)。
and secondly, respectively designing a predictive controller of an outer ring speed ring and a predictive controller of an inner ring current ring on the basis of the established nonlinear disturbance model of the permanent magnet synchronous motor, and simultaneously considering the design of a disturbance observer when the control device limits, so that the system can keep higher robustness when the model parameter error and the load change.
(1) Design of outer ring speed ring controller
The state space model of the permanent magnet synchronous motor is as follows:
(48)
wherein,;;;
thus:(49)
the output is controllable:
(50)
the processed variable is represented by quadrature axis current components; therefore, direct application of saturation is limiting; the purpose of the generalized predictive control is to find a suitable quadrature axis current component to minimize the selected cost function; here, a cost function is chosen:
(51)
applying a taylor series expansion to represent the prediction of the output and the prediction of the output reference value:
;(52)
substituting (52) into (51) yields:
(53)
this equation is equivalent to:
(54)
wherein,
(55)
on the other hand, the differential of the velocity is:
(56)
thus, the differentiation of the quadrature axis current component by the cost function can result in:
(57)
the essential condition is that:
(58)
from equation (57), we can derive the quadrature current minimum that minimizes the cost function, i.e.:
(59)
wherein,
(60)
substituting (59) into (56), the dynamic error is:
(61)
since the prediction time is positive, the dynamics of the continuous system are stable;
the disturbance is considered an unknown variable and therefore it must be estimated and replaced in the controller to ensure disturbance rejection and accurate amplitude of the reference signal continuity; therefore, the control rate is rewritten as follows:
(62)
wherein,representing the estimated perturbation.
(2) Design of disturbance observer when quadrature axis current component limitation is present
In order to limit quadrature axis current components, a saturation module is introduced into the outer ring of the control loop; the disturbance observer can be estimated as follows:
(63)
wherein,
(64)
(65)
wherein,is a parameter adjusted by an observer
Unfolding (64) and (65) to obtain:
(66)
in view of (48), we obtain:
(67)
substituting (67) into (63) and considering the derivative of the disturbance as zero, we get the error equation of the disturbance observer:
(68)
this equation is stable when the following equation is established:
(69)
note that the initial observations defined at (63) can be written in the form:
(70)
wherein,
(71)
substituting (62) and (66) into (70), we get:
(72)
wherein,
(73) 。
now, if we substitute (72) into the controller (62), the quadrature axis current reference value that ensures speed regulation is written in the following relation:
(74)
wherein,
(75)
(76)
the limit on the amplitude of the phase current can be translated into a limit on the amplitude of the quadrature current component as follows:
(77)
wherein,the term acts as an anti-saturation compensation, which can compensate for the adverse effects of the current limiting device.
(3) Design of inner loop current loop controller
The goal of the inner loop current loop design is to design a robust predictive regulator when motor parameters change. The nonlinear form of the dynamic equation is:
(78)
wherein,;;;;;;
the controlled output is the quadrature-direct axis component of the current:
(79)
the goal of generalized predictive control is to find the controller variables that minimize the cost function:
(80)
wherein,
(81)
calculating the quadrature axis current reference value by the formula (74); to calculate the control rate, we use the same procedure as the outer loop;
(82)
the output is expanded by Taylor series:
(83)
similarly, future reference values are predicted by taylor series expansion:
(84)
substituting (83) and (84) into (80), we get:
(85)
wherein,(86)
wherein,is a two-dimensional unit matrix;
combining (82) and (85), the differential of the cost function versus the control rate can be written as:
(87)
the optimal control rate minimizes the cost function,
(88)
solve equation (88) to obtain
(89)
Wherein,;;;
;
in a real system, the disturbance is observed and compensated for, so equation (4.52) can be rewritten as:
(90)。
(4) design of disturbance observer when there is a control device limitation
As with the disturbance observer design in the outer loop, the initial observer allowing for disturbance estimation is of the form:
(91)
wherein,
(92)
(93)
wherein,is a constant coefficient matrix;
equation (78) is written as:(94)
this relationship is substituted into the expression (91) of the initial observer to obtain:
(95)
we note that the matrix is justWhen the characteristic value of the observer has a negative real part, the dynamic error of the observer is stable;
however, we know that:
(96)
therefore, to simplify the study of observer stability, a matrix is chosenComprises the following steps:
(97)
combining these equations, we can conclude that the stability of the observer is ensured by the following conditions:
;(98)
we note that:
(99)
the error between the regulator output and the saturation block output can be integrated when the observer is designed:
(100)
thus:
(101)
substituting (90), (96), and (99) into (101), we get the disturbance observer with the limiting device module as:
(102)
wherein,
(103)
as before, the observer in the controller is replaced by that defined by (90) to obtain
(104)
Wherein,
(105)
(106)
the limits on the variables processed are given by:
(107)。
the method is experimentally verified, and in order to verify the performance of the nonlinear predictive control system of the permanent magnet synchronous motor with the disturbance observer, a motor drive system experimental platform with an XMC4500 chip of the English flying company as a core is established, and the experimental platform mainly comprises a motor control system to be tested and a load system.
Has the advantages that: in order to verify the rotating speed tracking performance of the system, the experimental parameters of the nonlinear predictive controller with the cascade structure are as follows: model discrete timeSampling time of controllerInner loop prediction timeT=1.85ms, outer loop prediction timeT=18.5 ms. FIG. 2 is a graph of the speed and speed error of a cascade configuration system of the present invention without anti-saturation and with fast dynamics of a given signal. FIG. 3 is a graph of the speed and speed error of a cascade architecture system with anti-saturation and given fast dynamics of the signal according to the present invention. As can be seen from fig. 2 and 3, the predictive control system of the cascade structure reduces the static error due to the introduction of the disturbance observer. However, since the integration action is included in the estimator,the saturation module overshoots the speed response by about 50%. An anti-saturation module is introduced into the control strategy, so that the system can eliminate overshoot and improve the speed response time. FIG. 4 shows the present inventionTSpeed and speed error curves of the cascade structure system when the electrical parameter changes in the time of = 0.5 s. FIG. 5 shows the present inventionTAnd when the electrical parameter changes in the time of = 0.5s, the AC-DC axis current curve of the cascade structure system is obtained. From fig. 4 and 5, it can be seen that the influence of the variation of the motor parameter on the robustness of the controller will make the speed error quickly reduce to zero after adding the disturbance observer into the controller, even if the motor parameter is uncertain. This is because the estimator compensates for the uncertainty of all parameters and the effect of load disturbances. Also, we note that the direct-axis current component remains equal to the reference value at all times, despite all the parameters of the machine being varied. FIG. 6 shows the present invention at T = 0.5s (C:)) And when the load suddenly changes, the speed and the speed error curve of the cascade structure system are obtained. FIG. 7 shows that the present invention is performed at T = 0.5s (C:)) And when the load suddenly changes, the alternating current and direct current curves of the cascade structure system are obtained. As can be seen from fig. 6 and 7, when the load changes, the maximum speed error depends on the design of the disturbance observer, and the error is completely eliminated in a short time, and the system has good disturbance rejection capability.
The design method of the nonlinear predictive controller of the permanent magnet synchronous motor cascade structure with the disturbance observer combines the rolling time domain optimization control strategy of nonlinear model predictive control and the design of the disturbance observer, and considers the influence of saturation limitation, thereby not only improving the tracking precision of the system, but also enhancing the robustness of the system. Experimental results show that the control strategy effectively enhances the dynamic control performance of the system when the model parameter error and the load change.
Claims (3)
1. The design of the nonlinear predictive controller of the permanent magnet synchronous motor with the disturbance observer is characterized by comprising the following two steps:
the method comprises the following steps: considering all model errors and external disturbance under a dq coordinate system, and constructing a nonlinear mathematical model of the PMSM;
step two: on the basis of the model, respectively designing a prediction controller of an outer ring speed ring and an inner ring current ring, selecting a cost function according to a generalized prediction control theory, and searching for an optimal control rate in a rolling time domain by minimizing the cost function, so that the output of the system in the prediction time can track a given reference track to achieve the purpose of prediction control; meanwhile, the design of a disturbance observer is considered when the limitation of a control device exists, so that the system can keep high robustness when the model parameter error and the load change exist.
2. The design of the nonlinear predictive controller of the permanent magnet synchronous motor with the disturbance observer according to claim 1, wherein the step one of considering all model errors and external disturbances in the dq coordinate system and constructing the nonlinear mathematical model of the PMSM comprises the following steps:
(1)
in the formula,、andrepresenting model errors and external load disturbances.
3. The design of the nonlinear predictive controller of the permanent magnet synchronous motor with the disturbance observer according to claim 1, wherein in the second step, on the basis of the constructed PMSM nonlinear disturbance model, the design of the predictive controller of an outer ring speed ring and an inner ring current ring is respectively carried out, and meanwhile, the design of the disturbance observer is considered when the limitation of a control device exists, so that the system can keep high robustness when the model parameter error and the load change exist, and the process is as follows:
(1) design of outer ring speed ring controller
The state space model of the permanent magnet synchronous motor speed ring is as follows:
(2)
wherein,;;;;;;;
the purpose of the nonlinear model predictive control is to find a suitable quadrature-axis current componentSo that the selected cost functionMinimum;
applying a taylor series expansion to represent the prediction of the output and the prediction of the output reference value, and such that:and if so, obtaining the minimum value of the quadrature axis current component which minimizes the cost function as follows:
(3)
wherein,
(4)
the disturbance signal, usually as an unknown variable, must be estimated and replaced in the controller to ensure the accuracy of disturbance rejection and reference signal continuity, so the control rate (3) can be rewritten as:
(5)
wherein,representing the estimated perturbation;
(2) design of disturbance observer when quadrature axis current component limitation is present
In order to limit the quadrature axis current component, a saturation module is introduced in the outer loop of the control loop, and the disturbance observer can estimate as follows:
(6)
wherein,,and is andis a parameter adjusted by the observer;
in view of (2), we obtain:
(7)
will be provided withAndexpanding, and jointly substituting into (6) with (5), obtaining:
(8)
wherein,;
now, if we substitute (8) into the controller (5), the quadrature axis current reference value that ensures speed regulation is written in the following relation:
(9)
wherein,
(10)
(11)
(3) design of inner loop current loop controller
The design of the inner loop current loop aims at designing a robust prediction type regulator when the parameters of the motor are changed; the nonlinear form of the dynamic equation is:
(12)
wherein,;;;;;;;
the goal of generalized predictive control is to find the controller variables that minimize the cost function:
(13)
the output and future reference values are predicted by taylor series expansion, and the derivative of the final cost function to the control rate can be written as:
(14)
the optimal control rate minimizes the cost function, i.e. satisfiesObtaining:
(15)
wherein;;;;
In a real system, the disturbance is observed and compensated for, so equation (15) can be rewritten as:
(16)
(4) design of disturbance observer when there is a control device limitation
As with the disturbance observer design in the outer loop, the initial observer allowing for disturbance estimation is of the form:
(17)
wherein,,and is andis a constant coefficient matrix;
the error between the regulator output and the saturation block output can be integrated when the observer is designed:
(18)
thus:
(19)
finally, we get the disturbance observer with the limiting device module as:
(20)
wherein,(21)
as before, the observer in the controller is replaced by that defined by (16) to obtain
(22)
Wherein,
(23)
(24)。
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