WO2022232977A1 - 基于快速积分终端滑模及干扰估计的永磁同步电机有限时间调速控制方法 - Google Patents
基于快速积分终端滑模及干扰估计的永磁同步电机有限时间调速控制方法 Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
- H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
- H02P25/022—Synchronous motors
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
- H02P21/0007—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode control
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
- H02P21/001—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using fuzzy control
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
- H02P21/18—Estimation of position or speed
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
- H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation
Definitions
- the invention belongs to the technical field of permanent magnet synchronous motor speed regulation control, and more particularly relates to a permanent magnet synchronous motor limited time speed regulation control technology based on fast integral terminal sliding mode and interference estimation, which can realize the limited time tracking of the motor speed , and can effectively overcome the influence of internal and external disturbances including system parameter uncertainty and unknown load torque fluctuation.
- Permanent magnet synchronous motor is a type of motor that uses permanent magnets as rotors. It provides an excitation magnetic field through permanent magnets, eliminating the need for excitation coils, thereby simplifying the motor structure, reducing the quality and volume of the motor, and effectively improving the efficiency of the motor. power density and reliability. Due to the above-mentioned advantages, permanent magnet synchronous motors have been widely used in many fields such as electric vehicles, industrial production, and aerospace.
- PI control algorithm occupies a major position because of its simple structure and convenient adjustment.
- the influence of interference caused by various factors such as parameter uncertainty and load fluctuation is inevitable in the motor control system.
- the PI algorithm does not have strong robustness and excellent anti-interference ability, and its control performance will be greatly reduced in the face of system interference, which cannot meet the requirements of modern industrial applications for permanent magnet synchronous motors with high precision and strong anti-interference ability. requirements of speed control technology.
- sliding mode control is one of the most popular control algorithms. Its main idea is to design a sliding mode surface that is independent of system parameters and disturbances, and "force" the system state to move along the designed sliding mode surface through the sliding mode controller. , so that the control system has strong anti-interference ability. It should be pointed out that there are certain defects in the sliding mode control, that is, when the system state reaches the sliding mode surface, it is difficult to strictly slide along the sliding mode surface to the equilibrium point, but approach the equilibrium point back and forth on both sides of the sliding mode surface. , resulting in chattering, which is one of the main obstacles to the practical application of sliding mode control.
- the speed tracking ability of the permanent magnet synchronous motor is also an important indicator to test the pros and cons of the speed regulation algorithm, because faster regulation speed and better tracking accuracy mean higher work efficiency , while the traditional sliding mode control method can only achieve asymptotic convergence, that is, when the time tends to infinity, the motor speed tracks to the target value, but it cannot be guaranteed to converge in a limited time.
- the traditional sliding mode control method can only achieve asymptotic convergence, that is, when the time tends to infinity, the motor speed tracks to the target value, but it cannot be guaranteed to converge in a limited time.
- the present invention provides a permanent magnet synchronous motor limited time speed control technology based on fast integral terminal sliding mode and disturbance estimation.
- the method ensures that the motor speed tracking error converges to zero within a limited time, improves the speed of the permanent magnet synchronous motor speed control system, and uses an adaptive fuzzy algorithm at the same time. Online estimation and real-time compensation for the internal and external disturbances of the system further enhance the robustness and anti-interference ability of the speed control system, and effectively reduce the switching gain of the sliding mode control term, thereby weakening the chattering phenomenon.
- a finite-time speed control method of permanent magnet synchronous motor based on fast integral terminal sliding mode and disturbance estimation The method: First, determine the speed loop mathematics of permanent magnet synchronous motor under the influence of system parameter uncertainty and unknown load torque Model. Secondly, based on the idea of terminal sliding mode control, an improved fast integral terminal sliding mode surface is designed, which can improve the convergence time of the traditional integral terminal sliding mode surface and ensure that the motor speed tracking error can be located in the sliding mode surface within a limited time. converges to zero. Then, a disturbance estimation method based on adaptive fuzzy system is proposed for the disturbance existing in the permanent magnet synchronous motor system. This estimation method does not need to perform offline calculation, and can realize real-time estimation of system disturbance through online adaptive adjustment of fuzzy network weights.
- ⁇ is the motor speed
- i q is the q-axis stator current
- K t is the torque constant
- J is the moment of inertia
- B is the viscous friction coefficient
- T L is the load torque.
- the deviation of ; i q * represents the reference value of the q-axis stator current, that is, the speed controller of the permanent magnet synchronous motor to be designed.
- d(t) represents the lumped interference term, and the expression is Since both the torque constant K t and the nominal value J n of the moment of inertia are known, a is a known constant coefficient;
- the sliding mode surface of the fast integration terminal is designed as: Among them, ⁇ , ⁇ >0, which are constant coefficients; 0 ⁇ q/p ⁇ 1, and q and p are positive odd numbers.
- the fuzzy system is used to estimate the lumped interference term d(t) defined in step S1. According to the universal approximation theory of fuzzy systems, there is an optimal fuzzy system makes:
- r is the number of fuzzy rules
- ⁇ represents the estimation error, which satisfies
- x [x 1 , x 2 ,...,x n ] T is the input vector of the fuzzy system, and n is the number of fuzzy inputs; in the technical scheme of the present invention, the fast integral terminal sliding mode is selected
- the online adaptive weight adjustment rate of the fuzzy system can be designed as:
- ⁇ R r ⁇ r is a positive definite symmetric matrix
- s represents the fast integration terminal sliding mode surface constructed in step S2.
- k 1 and k 2 are positive adjustable control gains, and k 2 >l+ ⁇ , l>0 is the upper bound of and represents the weight estimation error vector; sign(s) represents the sign function.
- the speed tracking error can be converged to the sliding mode surface within the time t o , and t o satisfies the following relational formula:
- s(0) represents the value of the fast integration terminal sliding mode surface s constructed in step S2 when the time is 0.
- the motor speed ⁇ is measured in real time by the sensor installed in the permanent magnet synchronous motor. After obtaining the motor speed signal ⁇ , make the difference with the motor target speed ⁇ d to obtain the speed tracking error e; after obtaining e, The value of the sliding mode surface s of the fast integration terminal can be further obtained, and at the same time, the estimated value of the interference output by the adaptive fuzzy system can also be obtained based on step S3
- the velocity tracking error e, the fast integration terminal sliding mode surface s and the estimated interference value are calculated as Substitute the permanent magnet synchronous motor speed controller given in step S4, and use this controller as the speed loop controller under the permanent magnet synchronous motor vector control framework to generate the reference value i q * of the q-axis stator current.
- the classic PI controller is used, the voltage in the d-q coordinate system is obtained according to the input stator current reference value, and the voltage signal in the static coordinate system is obtained through the inverse Park transformation, and then the corresponding voltage signal is generated by the SVPWM algorithm.
- the duty cycle is obtained, the switching signal of the three-phase inverter is obtained, and the three-phase stator voltage of the permanent magnet synchronous motor is output through the three-phase inverter, and then the motor speed is controlled to track the target speed to realize the entire motor speed regulation process.
- the time used in the entire motor speed regulation process is limited, and the limited time tracking of the motor speed can be realized, and the time taken for the motor speed tracking error obtained in step S2 to converge to zero on the designed fast integral terminal sliding mode surface t s and the time t o for the motor speed tracking error obtained in step S4 to converge to the sliding mode surface, it can be obtained that the motor speed tracking error converges from the initial state to zero, that is, the time t r for the motor to reach the target speed, satisfies:
- Finite time control In the prior art, most control methods can only ensure that the motor speed tracking error converges asymptotically, that is, when the time tends to infinity, the speed tracking error converges to zero, but cannot guarantee finite time convergence.
- the terminal sliding mode control can realize the finite time convergence of the system state by introducing a nonlinear term into the sliding mode surface.
- the present invention designs a new type of fast integral terminal sliding mode surface, which solves the problem of the traditional integral terminal The slow convergence speed of the sliding mode surface further shortens the time for the speed tracking error to converge to zero.
- the traditional terminal sliding mode control can only ensure that the time of the sliding mode motion phase of the system is limited, and the convergence time of the approaching phase is not analyzed in detail.
- the rigorous theoretical analysis process proves the proposed method. It can ensure the time limit of the whole motor speed regulation process, that is, the time used by the system state in the approach stage and the sliding mode movement stage is limited, which effectively improves the speed of the permanent magnet synchronous motor speed regulation system.
- the permanent magnet synchronous motor system inevitably has interference effects caused by changes in system parameters and unknown load fluctuations. How to suppress the interference effects is the focus of the design of the permanent magnet synchronous motor control system. difficulty.
- the invention utilizes the universal approximation theorem of fuzzy systems to propose an adaptive fuzzy interference estimation method, which can perform online estimation and real-time compensation for interference without making too many theoretical assumptions about interference in advance like other interference estimation methods.
- the uncertainty existing in the system can be greatly reduced, which means that the gain of the sliding mode term in the controller does not need to be selected too large, thus effectively weakening the system chattering.
- the permanent magnet synchronous motor speed regulation control technology proposed by the present invention can realize the limited time convergence of the speed tracking error, that is, the motor can reach the target speed within a limited time, and the permanent magnet synchronous motor can be improved.
- the rapidity of the motor speed control system can simultaneously estimate the system disturbance online and compensate in real time, effectively overcoming the influence of internal and external disturbances in the permanent magnet synchronous motor system.
- the system state signals used in the technical solution of the present invention are all measurable signals, that is, they have strong achievability, which means that they have good practical application prospects.
- Figure 1 shows the vector control framework of the permanent magnet synchronous motor speed control system
- Fig. 2 is the control frame of the permanent magnet synchronous motor speed regulation system proposed by the present invention
- Figure 3 shows the vector control framework of the permanent magnet synchronous motor speed control system based on the PI algorithm commonly used in the industry
- Figure 4 is a comparison diagram of the speed curve under ideal conditions using the proposed method and using the PI algorithm control
- Figure 5 is the i q * response curve under ideal conditions using the proposed method and using the PI algorithm control;
- Figure 6 is a comparison diagram of the speed curve using the proposed method under the influence of disturbance and using the PI algorithm control
- Figure 7 shows the i q * response curves under the influence of disturbance using the proposed method and using the PI algorithm control.
- the present embodiment discloses a finite-time speed control technology of permanent magnet synchronous motor based on fast integral terminal sliding mode and interference estimation.
- the specific implementation is as follows:
- the cascade control structure of the current loop is added, that is, the output of the speed loop controller is the reference current input of the current loop.
- the present invention mainly designs and improves the speed loop in the vector control frame shown in Figure 1, and builds the control frame of the permanent magnet synchronous motor speed control system shown in Figure 2. The design process is described in detail below:
- ⁇ is the motor speed
- i q is the q-axis stator current
- K t is the torque constant
- J is the moment of inertia
- B is the viscous friction coefficient
- TL is the load torque.
- Deviation; i q * represents the reference value of the q-axis stator current, that is, the permanent magnet synchronous motor speed controller to be designed.
- the present invention selects the integral terminal sliding mode surface as the sliding mode.
- the expression of the traditional integral terminal sliding surface is as follows:
- ⁇ 1 >0 is a constant coefficient
- 0 ⁇ q 1 /p 1 ⁇ 1 is positive odd numbers.
- the present invention proposes the following form of fast integral terminal sliding mode surface:
- ⁇ , ⁇ >0 which are constant coefficients; 0 ⁇ q/p ⁇ 1, and q and p are positive odd numbers.
- the convergence speed provided by it can be guaranteed to be proportional to the distance between the motor speed tracking error and the balance point, so when the speed tracking error is far from the balance point, ie
- the e q/p term provides a small convergence rate, but the - ⁇ e term will provide a large convergence rate.
- the - ⁇ e term provides a small convergence speed, but because 0 ⁇ q/p ⁇ 1, the - ⁇ e q/p term will provide a relatively small convergence speed.
- the sliding mode surface of the fast integration terminal designed by the present invention can ensure that as long as the motor speed tracking error is located on the sliding mode surface, it will have a fast convergence speed.
- the present invention uses a fuzzy system to estimate the lumped interference term d(t) defined in step S1. According to the universal approximation theory of fuzzy systems, there is an optimal fuzzy system makes:
- ⁇ represents the estimation error, which satisfies
- the online adaptive weight adjustment rate of the fuzzy system can be designed as:
- ⁇ R r ⁇ r is a positive definite symmetric matrix
- s represents the fast integral terminal sliding mode surface (9) constructed in step S2.
- k 1 and k 2 are positive adjustable control gains, and k 2 >l+ ⁇ , where l>0 is the upper bound of and represents the weight estimation error vector, and the boundedness of this signal will be proved later; sign(s) represents the sign function.
- l>0 is a normal number.
- the velocity tracking error can converge to the sliding mode surface in a finite time, that is, the time for s to converge to zero is limited.
- s(0) represents the value of the fast integration terminal sliding mode surface s constructed in step S2 when the time is 0.
- step S2 Further combined with the time t s that the motor speed tracking error obtained in step S2 converges to zero on the designed fast integral terminal sliding mode surface, it can be obtained that the motor speed tracking error converges from the initial state to zero, that is, the time t r that the motor takes to reach the target speed ,Satisfy:
- the control framework of the permanent magnet synchronous motor speed regulation system as shown in Figure 2 can be built, and its specific implementation is described in detail here.
- the motor speed ⁇ is measured in real time by the sensor installed in the permanent magnet synchronous motor. After the motor speed signal ⁇ is obtained, it is made to differ from the motor target speed ⁇ d to obtain the speed tracking error e. After obtaining e, the speed tracking error e can be obtained. The value of the sliding mode surface s of the fast integration terminal is further obtained. At the same time, based on step S3, the estimated value of the interference output by the adaptive fuzzy system can also be obtained.
- the velocity tracking error e, the fast integral terminal sliding surface s, and the estimated disturbance Substitute the permanent magnet synchronous motor speed controller (17) given in step S4, and use this controller as the speed loop controller under the permanent magnet synchronous motor vector control framework to generate the reference value i of the q-axis stator current q * .
- the classic PI controller is used, the voltage in the dq coordinate system is obtained according to the input stator current reference value, and the voltage signal in the static coordinate system is obtained through inverse Park transformation, and then the corresponding duty cycle is generated by the SVPWM algorithm. ratio, obtain the switching signal of the three-phase inverter, and output the three-phase stator voltage of the permanent magnet synchronous motor through the three-phase inverter, and then control the motor speed to track the target speed to realize the entire motor speed regulation process.
- the present invention compares its control performance with the most commonly used control framework in the industry—“the vector control framework of permanent magnet synchronous motor speed regulation system based on PI algorithm” through simulation.
- the vector control framework of the permanent magnet synchronous motor speed control system based on the PI algorithm is shown in Figure 3, which is referred to as the "PI algorithm” in the subsequent description, because the PI algorithm is used in both the speed loop and the current loop, and this control scheme has the ability to adjust It is convenient and easy to realize, so it is most widely used in the industrial field.
- simulation 2 comprehensively considers the influence of internal and external disturbances such as system parameter uncertainty and external load torque changes, and adjusts the motor rotational inertia as in simulation 1.
- Figure 6 is a comparison chart of the speed curve under the control of the proposed method and the PI algorithm
- Figure 7 is the response curve of i q * when two different schemes are used.
- the method proposed in the present invention can eliminate the influence of interference more quickly, so that the motor speed can return to the target value stably in a short time.
- the results of simulation 2 show that compared with the PI algorithm, the method proposed in the present invention has a very obvious advantage in anti-interference performance, which can effectively overcome the influence of internal and external interference in the system, and at the same time ensure the control accuracy and rapidity of the motor speed control system.
- simulation 1 and simulation 2 show that compared with the PI algorithm control scheme commonly used in the industry, the technical scheme proposed by the present invention has faster response speed and higher control accuracy, and can make the The motor speed is precisely adjusted to the given value.
- the proposed technical solution has more advantages in anti-interference ability, and can effectively overcome the influence of system parameter uncertainty and unknown load torque interference, which means that the present invention is more practical and suitable for application in practical systems. middle.
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Abstract
一种基于快速积分终端滑模及干扰估计的永磁同步电机有限时间调速控制方法,首先,确定受***参数不确定性以及未知负载转矩影响下的永磁同步电机速度环数学模型。其次,基于终端滑模控制的思想设计改进型快速积分终端滑模面。然后,针对永磁同步电机***中存在的干扰,提出基于自适应模糊***的干扰估计方法;在此基础上设计永磁同步电机速度控制器。最后,完成整个技术方案的具体实现。本发明通过设计快速积分终端滑模面及滑模控制律,保证电机速度跟踪误差在有限时间内收敛到零,提高永磁同步电机调速***的快速性,同时使用自适应模糊算法对***内、外干扰进行在线估计并实时补偿,增强调速***的鲁棒性和抗干扰能力,且有效降低滑模控制项切换增益,进而削弱抖振现象。
Description
本发明属于永磁同步电机调速控制技术领域,更具体地,涉及一种基于快速积分终端滑模及干扰估计的永磁同步电机有限时间调速控制技术,其能够实现电机速度的有限时间跟踪,并能有效克服包含***参数不确定性以及未知负载转矩波动等在内的***内、外干扰的影响。
永磁同步电机是一类使用永磁体作为转子的电机,其通过永磁体提供励磁磁场,省去了励磁线圈,因而简化了电机结构,降低了电机质量和体积,同时有效提高了电机的效率、功率密度以及可靠性。因具备上述多种优点,永磁同步电机在电动汽车、工业生产、航空航天等众多领域得到了广泛应用。
在传统永磁同步电机调速控制技术领域,PI控制算法因具备结构简单、调节方便的优点而占据主要地位。但是,电机控制***里无可避免地存在因参数不确定性、负载波动等多种因素所带来的干扰的影响。而PI算法不具备强鲁棒性以及出色的抗干扰能力,其在面对***干扰时控制性能将大幅度下降,无法满足现代工业应用对具有高精度、强抗干扰能力的永磁同步电机调速控制技术的要求。
为提高永磁同步电机调速控制***的抗干扰能力,众多学者开始致力于强鲁棒性控制算法的研究。滑模控制是其中最受青睐的控制算法之一,其主要思想是设计与***参数及干扰无关的滑模面,并通过滑模控制器“迫使”***状态沿设计好的滑模面进行运动,从而使控制***具备强的抗干扰能力。需要指出的是,滑模控制存在一定缺陷,即当***状态到达滑模面后,其难以严格地沿着滑模面向平衡点滑动,而是在滑模面两侧来回穿越地趋***衡点,从而产生抖振,这是滑模控制在实际应用中的最主要障碍之一。同时,除强抗干扰能力之外,永磁同步电机的速度跟踪能力也是检验调速算法优劣的一个重要指标,因为更快的调节速度、更佳的跟踪精度,意味着更高的工作效率,而传统滑模控制方法只能实现渐近收敛,即当时间趋于无穷大时电机转速跟踪到目标值,而无法保证其在有限时间内收敛,例如在论文“谢涛,高桂革,王杰.基于滑模控制器的PMSM的矢量控制***研究[J].电机与控制应用,2018.”中,作者提出了一种基于滑模控制的永磁同步电机调速控制方法,但其在理论上仅能得到渐近收敛的控制效果,无法确定电机转速跟踪到目标值所用时间,也即无法保证电机转速可以在有限时间内跟踪到目标值。
此外,在现有技术中,存在部分技术方案在进行控制器设计时为达到目标控制效果,使用电机加速度、加加速度等在实际中难以获得的信号,例如论文“童灵华.永磁同步电机快速高阶终端滑模控制[J].电机与控制应用,2016.”在控制器设计时用到了电机的加速度信号,但 加速度信号很难通过传感器进行测量,这意味着此类技术方案是无法直接实际应用的,而技术方案的可实现性是工业应用的决定要素。
总结而言,包括PI控制和滑模控制在内的已有技术无法同时满足现代永磁同步电机调速控制***在快速性、准确性以及抗干扰能力等方面的需求,故急需新的高性能控制方法的提出。
发明内容
致力于解决现有技术中永磁同步电机调速控制方法所存在的缺陷与不足,本发明提供了一种基于快速积分终端滑模及干扰估计的永磁同步电机有限时间调速控制技术。所述方法通过设计快速积分终端滑模面及滑模控制律,保证了电机速度跟踪误差在有限时间内收敛到零,提高了永磁同步电机调速***的快速性,同时使用自适应模糊算法对***内、外干扰进行在线估计并实时补偿,进一步增强了调速***的鲁棒性和抗干扰能力,且有效降低了滑模控制项切换增益,进而削弱了抖振现象。
为了达到上述目的,本发明的技术方案:
一种基于快速积分终端滑模及干扰估计的永磁同步电机有限时间调速控制方法,该方法:首先,确定受***参数不确定性以及未知负载转矩影响下的永磁同步电机速度环数学模型。其次,基于终端滑模控制的思想,设计一种改进型快速积分终端滑模面,其可以提高传统积分终端滑模面的收敛时间,保证电机速度跟踪误差位于此滑模面时能够在有限时间内收敛到零。然后,针对永磁同步电机***中存在的干扰,提出一种基于自适应模糊***的干扰估计方法,此估计方法无需进行离线计算,可通过在线自适应调节模糊网络权值实现***干扰的实时估计;在此基础上,进一步设计基于快速积分终端滑模以及自适应模糊干扰估计的永磁同步电机速度控制器,并通过严谨的理论分析证明所提方法可以在有限时间内实现电机转速的快速调节,同时有效抑制***干扰的影响。最后,完成整个技术方案的具体实现。具体包括以下步骤:
S1.确定受***参数不确定性以及未知负载转矩影响下的永磁同步电机速度环数学模型:
在d-q坐标系下,隐极式永磁同步电机的速度环数学模型为:
式中,ω为电机转速;i
q表示q轴定子电流;K
t为转矩常数;J表示转动惯量;且B为粘性摩擦系数;T
L表示负载转矩。
进一步考虑***参数不确定性、未知负载转矩以及电流环追踪误差影响,可将永磁同步电机速度环数学模型改写为:
式中,B
o和J
n分别表示粘性摩擦系数以及转动惯量的标称值;ΔB=B-B
o和ΔJ=J-J
n则分别指的是粘性摩擦系数和转动惯量的真实值与其标称值之间的偏差;i
q
*表示q轴定子电流的参考值,也即需设计的永磁同步电机速度控制器。
将上述考虑***干扰的永磁同步电机速度环数学模型做进一步处理,得到:
S2.构造快速积分终端滑模面:
首先定义速度跟踪误差:e=ω-ω
d,其中,ω
d表示电机目标转速。
求解上述方程,可得出电机速度跟踪误差从到达滑模面开始收敛至零的时间为:
S3.基于自适应模糊***对集总干扰项进行干扰估计:
式中,
为最佳逼近时的权值向量,r为模糊规则个数;ε表示估计误差,其满足|ε|<ρ,而ρ>0为正常数,且ε的值可以通过增加模糊规则个数来无限缩小;x=[x
1,x
2,...,x
n]
T为模糊***的输入向量,n为模糊输入的个数;在本发明所提技术方案中,选用快速积分终端滑模面以及速度跟踪误差作为模糊***输入,即x=[s,e]
T,而H(x)=[h
1(x),h
2(x),...,h
r((x))]
T表示模糊基函数向量,且:
其中,Γ∈R
r×r为正定对称矩阵;s表示步骤S2构造的快速积分终端滑模面。
S4.设计永磁同步电机速度控制器:
基于步骤S2和S3,设计如下形式的永磁同步电机速度控制器:
采用本发明所设计永磁同步电机速度控制器,可以使转速跟踪误差在时间t
o内收敛至滑模面,t
o满足如下关系式:
式中,λ=k
2-ρ-l,表示常值系数;s(0)表示步骤S2中构造的快速积分终端滑模面s在时间为0时的值。
S5.技术方案具体实现:
5.1)首先,通过安装在永磁同步电机内的传感器对电机转速ω进行实时测量,在得到电机转速信号ω之后,使其与电机目标转速ω
d作差得到速度跟踪误差e;得到e之后,可进一步得到快速积分终端滑模面s的值,同时,基于步骤S3还可以得到自适应模糊***所输出的干扰估计值
5.2)其次,将速度跟踪误差e、快速积分终端滑模面s以及干扰估计值
代入步骤S4中所给出的永磁同步电机速度控制器,并以此控制器作为永磁同步电机矢量控制框架下的速度环控制器,用来生成q轴定子电流的参考值i
q
*。
5.3)在电流环中,采用经典的PI控制器,根据输入的定子电流参考值得到d-q坐标系下 的电压,并经过反Park变换得到静止坐标系下的电压信号,然后由SVPWM算法生成相应的占空比,得到三相逆变器的开关信号,并通过三相逆变器输出永磁同步电机三相定子电压,进而控制电机转速跟踪到目标转速,实现整个的电机调速过程。
采用本发明方法,整个电机调速过程所用时间是有限的,即可实现电机转速的有限时间跟踪,结合步骤S2得到的电机转速跟踪误差在所设计快速积分终端滑模面上收敛至零所用时间t
s以及步骤S4得到的电机转速跟踪误差收敛至滑模面所用时间t
o,可得到电机转速跟踪误差由初始状态收敛至零,即电机到达目标转速所用时间t
r,满足:
相对于现有技术,本发明的有益效果如下:
(1)有限时间控制:现有技术中,大多数控制方法只能保证电机转速跟踪误差渐近收敛,即当时间趋于无穷大时,速度跟踪误差收敛于零,而无法保证有限时间收敛。终端滑模控制通过在滑模面引入非线性项可以实现***状态的有限时间收敛,本发明基于终端滑模控制的思想,设计了一种新型的快速积分终端滑模面,解决了传统积分终端滑模面存在的收敛速度慢的问题,进一步缩短了速度跟踪误差收敛于零的时间。同时,传统终端滑模控制仅能保证***滑模运动阶段的时间是有限的,对趋近阶段的收敛时间并未做详细分析,而在本发明中,严谨的理论分析过程证明了所提方法可以保证整个电机调速过程的时间有限性,即***状态在趋近阶段以及滑模运动阶段所用时间都是有限的,这有效提高了永磁同步电机调速***的快速性。
(2)干扰估计及抑制:永磁同步电机***里不可避免地存在因***参数变化以及未知负载波动等原因所带来的干扰影响,如何抑制干扰影响是永磁同步电机控制***设计的重点及难点。本发明利用模糊***的万能逼近定理,提出了一种自适应模糊干扰估计的方法,能够对干扰进行在线估计及实时补偿,且无需像其它干扰估计方法一样事先对干扰做过多理论假设。同时,通过对***干扰进行补偿,可以大幅降低***中所存在的不确定性,这意味着控制器里的滑模项增益不需要过大选取,因而有效削弱了***抖振。
(3)方案可实现性:现有技术中,存在部分技术方案在进行控制器设计时为达到目标控制效果,使用电机加速度、加加速度等在实际中难以获得的信号,这意味着此类技术方案是无法直接实际应用的。而在本发明所提方法中,所用到的***状态信号均可通过相应传感器直接获得,即所有信号皆为有效信号,这保证了所提技术方案的可实现性,说明其能够被直接应用于实际工业生产之中。
总结而言,本发明所提出的永磁同步电机调速控制技术相比于现有技术,能够实现速度 跟踪误差的有限时间收敛,即保证电机在有限时间内到达目标转速,提高了永磁同步电机调速***的快速性,同时可以对***干扰进行在线估计并实时补偿,有效克服永磁同步电机***中存在的内、外干扰影响。尤为关键的是,本发明所提技术方案中使用的***状态信号均为可测信号,即具有很强的可实现性,这意味着其拥有良好的现实应用前景。
图1为永磁同步电机调速***矢量控制框架;
图2为本发明所提永磁同步电机调速***控制框架;
图3为工业常用的基于PI算法的永磁同步电机调速***矢量控制框架;
图4为理想条件下使用所提方法与使用PI算法控制下的速度曲线对比图;
图5为理想条件下使用所提方法与使用PI算法控制下的i
q
*响应曲线;
图6为干扰影响下使用所提方法与使用PI算法控制下的速度曲线对比图;
图7为干扰影响下使用所提方法与使用PI算法控制下的i
q
*响应曲线。
下面结合附图及具体实施例,对本发明所提技术方案做进一步详细说明。
本实施例公开了一种基于快速积分终端滑模及干扰估计的永磁同步电机有限时间调速控制技术,具体实施方式如下:
本发明针对隐极式永磁同步电机的调速控制展开设计,并基于如图1所示的i
d=0永磁同步电机调速***矢量控制框架,为方便控制器设计,其采用速度环加电流环的级联控制结构,即速度环控制器的输出为电流环的参考电流输入。本发明主要对图1所示矢量控制框架中的速度环进行设计及改进,搭建如图2所示的永磁同步电机调速***控制框架,下面详细介绍其设计过程:
S1:确定受***参数不确定性以及未知负载转矩影响下的永磁同步电机速度环数学模型:
以转子坐标系(d-q坐标系)为参考坐标系,隐极式永磁同步电机的速度环数学模型为
式中,ω为电机转速;i
q表示q轴定子电流;K
t为转矩常数;J表示转动惯量;而B为粘性摩擦系数;T
L表示负载转矩。
进一步考虑***参数不确定性、未知负载转矩以及电流环追踪误差影响,可将永磁同步电机数学模型改写为
其中,B
o和J
n分别表示粘性摩擦系数以及转动惯量的标称值;ΔB=B-B
o和ΔJ=J-J
n则分别指的是粘性摩擦系数和转动惯量的真实值与其标称值之间的偏差;i
q
*表示q轴定子电流的参考值,也即需设计的永磁同步电机速度控制器。
将上述考虑***干扰的永磁同步电机速度环数学模型做进一步处理,得到:
S2:构造快速积分终端滑模面
定义速度跟踪误差:e=ω-ω
d (5)式中,ω
d表示电机目标转速。
因滑模控制具有强鲁棒性和抗干扰能力的优点,其在永磁同步电机速度控制领域得到了广泛的应用。然而,传统滑模控制只能实现渐近收敛的控制效果,无法保证电机转速在有限时间内追踪到其目标值。终端滑模控制通过将非线性项引入到滑模面,采用非线性超平面作为滑模面,可以使位于滑模面上的***状态在有限时间内收敛至平衡点。同时,为保证所提技术方案中用到的信号皆为可直接获取信号,并提高永磁同步电机调速***的稳态追踪性能,本发明选用积分终端滑模面作为滑动模态。传统积分终端滑模面的表达式如下:
其中,β
1>0为常值系数;0<q
1/p
1<1,且q
1和p
1为正奇数。
因0<q
1/p
1<1,所以当速度跟踪误差远离平衡点,即|e|>>1时,此时
的值将被大幅度削减,也就是说此时速度跟踪误差e的收敛速度会明显降低,且低于传统的线性滑模面,这是传统积分终端滑模面的缺点。
其中,α,β>0,其都为常值系数;0<q/p<1,且q和p为正奇数。
因存在-αe项,其提供的收敛速度可以保证跟电机速度跟踪误差与平衡点之间的距离成正比关系,所以当速度跟踪误差远离平衡点,即|e|>>1时,尽管-β
e
q/p项提供的收敛速度较小,但-αe项将会提供很大的收敛速度。而当速度跟踪误差靠***衡点,即|e|<<1时,此时-αe项提供的收敛速度较小,但因0<q/p<1,故-βe
q/p项会提供较大的收敛速度。综上所述,本发明所设计的快速积分终端滑模面可以保证只要电机速度跟踪误差位于滑模面,都将具有很快的收敛速度。
S3:基于自适应模糊***的干扰估计方法
通过乘积推理、加权平均和单点模糊化,模糊***的输出可以表示为:y(x)=Φ
TH(x)(13);式中,y表示模糊***的输出;x=[x
1,x
2,...,x
n]
T为模糊***的输入向量,n为模糊输入的个数,在本发明所提技术方案中,选用快速积分终端滑模面以及速度跟踪误差作为模糊***输入,即x=[s,e]
T;Φ
T=[φ
1,φ
2,...,φ
r]
T为可调权值向量,r为模糊规则个数;而H(x)=[h
1(x),h
2(x),...,h
r((x))]
T表示模糊基函数向量,且:
S4:设计永磁同步电机速度控制器
在步骤S2、S3的基础上,设计如下形式的永磁同步电机速度控制器:
下面,根据李雅普诺夫方法,对闭环***稳定性进行分析,证明本发明所提技术方案可以控制电机转速在有限时间内到达其给定值,并能有效克服***干扰的影响。
对李雅普诺夫函数求导,结合式(16)和(20)可得:
根据式(21)和(22),可以得知V(t)有界,即:V∈ζ
∞ (23)
其中,l>0为正常数。
接下来,证明速度跟踪误差可以在有限时间内收敛至滑模面,也即s收敛于零的时间是有限的。
对李雅普诺夫函数求导,结合式(20)、(25)可得
其中,s(0)表示步骤S2中构造的快速积分终端滑模面s在时间为0时的值。
进一步结合步骤S2得到的电机转速跟踪误差在所设计快速积分终端滑模面上收敛至零所用时间t
s,可得到电机转速跟踪误差由初始状态收敛至零,即电机到达目标转速所用时间t
r,满足:
则,通过上述严格的理论分析,证明了本发明所提技术方案可以使电机转速在有限时间内到达其目标值,同时可以有效克服***干扰的影响。
S5:技术方案具体实现
经过步骤S1-S4,可搭建如图2所示的永磁同步电机调速***控制框架,在此对其具体实现进行详细介绍。首先,通过安装在永磁同步电机内的传感器对电机转速ω进行实时测量,在得到电机转速信号ω之后,使其与电机目标转速ω
d作差得到速度跟踪误差e,在得到e之后,可进一步得到快速积分终端滑模面s的值,同时,基于步骤S3,还可以得到自适应模糊***所输出的干扰估计值
将速度跟踪误差e、快速积分终端滑模面s以及干扰估计值
代入步骤S4中所给出的永磁同步电机速度控制器(17),并以此控制器作为永磁同步电机矢量控制框架下的速度环控制器,用来生成q轴定子电流的参考值i
q
*。在电流环中,采用经典的PI控制器,根据输入的定子电流参考值得到d-q坐标系下的电压,并经过反Park变换得到静止坐标系下的电压信号,然后由SVPWM算法生成相应的占空比,得到三相逆变器的开关信号,并通过三相逆变器输出永磁同步电机三相定子电压,进而控制电机转速跟踪到目标转速,实现整个的电机调速过程。
为进一步验证所提技术的有效性及先进性,本发明通过仿真对比其与工业最常用控制框架—“基于PI算法的永磁同步电机调速***矢量控制框架”的控制性能优劣。基于PI算法的永磁同步电机调速***矢量控制框架如图3所示,后续描述中简称其为“PI算法”,因其在速度环以及电流环均采用PI算法,这种控制方案具有调节方便,易于实现的优点,所以在工业领域应用最为广泛。
仿真1:理想条件下的调速性能对比
首先对比在理想条件下,即不存在参数不确定性以及负载转矩干扰时所提技术方案与PI算法的调速性能。***参数设置如下:J=3.78×10
-4kg·m
2,B=1.74×10
-5N·m·s/rad,K
t=1.4N·m/A;同时,设置电机目标转速为ω
d=1200r/min。仿真结果如图4-5所示,图4为使用所提方法与使用PI算法控制下的速度曲线对比图,图5则是采用两种不同方案时i
q
*的响应曲线。结合图4和图5可知,在理想条件下,所提技术方法只需0.0075s就可以使电机到达给定速度,而PI算法所用时间为0.015s左右,大概为本发明所提方法的2倍。同时,还可以看出PI算法的稳态误差明显大于所提方法。仿真1的结果说明,相对于PI算法,本发明技术方案具有更快的响应速度以及更高的控制精度。
仿真2:干扰影响下的调速性能对比
进一步,为验证且对比所提方法与PI算法的抗干扰能力,仿真2综合考虑了***参数不确定性以及外界负载转矩变化等内、外干扰的影响,将电机转动惯量调整为仿真1中的2倍,同时将粘性摩擦系数调整为其原值的5倍,即:J=2×3.78×10
-4kg·m
2,B=5×1.74×10
-5N·m·s/rad;而其它***参数保持不变,同时本发明所提方法以及PI算法的控制器参数也保持与仿真1中的相同取值。此外,为模拟外界未知负载转矩的影响,仿真在0.03s时施加0.5N·m的负载转矩,并在0.035s时将负载转矩撤掉。仿真结果如图6-7所示,图6为使用所提方法与使用PI算法控制下的速度曲线对比图,图7则是采用两种不同方案时i
q
*的响应曲线。结合图6和图7可知,在干扰影响下,所提方法仍然可以保证良好的动态性能以及稳态性能,电机在0.012s左右精准地到达了给定转速,而相应地,PI算法则用了大约0.03s才将电机调整至目标转速,所用时间接近本发明所提方法的3倍。更为重要的是,在外界负载转矩突变时,PI算法控制下的电机转速波动明显,其下降幅度远远大于本发明所提技术方法的转速下降幅度。同时,相比PI算法,本发明所提方法可以更快速地消除干扰影响,使电机转速在很短时间内平稳地回归目标值。仿真2的结果说明,本发明所提方法相较于PI算法,具有非常明显的抗干扰性能优势,能够有效克服***内、外干扰影响,同时保证电机调速***的控制精度及快速性。
总结而言,仿真1和仿真2的结果说明相对于工业常用的PI算法控制方案,本发明所提 出的技术方案具有更快的响应速度和更高的控制精度,可以在更短时间内使将电机速度精准地调节至给定值。同时,所提技术方案在抗干扰能力方面更具优势,能够有效克服包含***参数不确定性以及未知负载转矩干扰的影响,这意味着本发明更具实用性,适合被应用于实际***之中。
以上所述实施例仅表达本发明的实施方式,但并不能因此而理解为对本发明专利的范围的限制,应当指出,对于本领域的技术人员来说,在不脱离本发明构思的前提下,还可以做出若干变形和改进,这些均属于本发明的保护范围。
Claims (2)
- 一种基于快速积分终端滑模及干扰估计的永磁同步电机有限时间调速控制方法,其特征在于,包括以下步骤:S1.确定受***参数不确定性以及未知负载转矩影响下的永磁同步电机速度环数学模型:在d-q坐标系下,隐极式永磁同步电机的速度环数学模型为:式中,ω为电机转速;i q表示q轴定子电流;K t为转矩常数;J表示转动惯量;且B为粘性摩擦系数;T L表示负载转矩;考虑***参数不确定性、未知负载转矩以及电流环追踪误差影响,永磁同步电机速度环数学模型为:式中,B o和J n分别表示粘性摩擦系数以及转动惯量的标称值;ΔB=B-B o和ΔJ=J-J n则分别指的是粘性摩擦系数和转动惯量的真实值与其标称值之间的偏差;i q *表示q轴定子电流的参考值,即需设计的永磁同步电机速度控制器;将上述考虑***干扰的永磁同步电机速度环数学模型处理后得到:式中,d(t)表示集总干扰项;a为一个已知常值系数;S2.构造快速积分终端滑模面:首先,定义速度跟踪误差:e=ω-ω d,其中,ω d表示电机目标转速;求解上述方程得出电机速度跟踪误差从到达滑模面开始收敛至零的时间为:S3.基于自适应模糊***对集总干扰项进行干扰估计:式中, 为最佳逼近时的权值向量,r为模糊规则个数;ε表示估计误差,其满足|ε|<ρ,而ρ>0为正常数,且ε的值可以通过增加模糊规则个数来无限缩小;x=[x 1,x 2,...,x n] T为模糊***的输入向量,n为模糊输入的个数;选用快速积分终端滑模面以及速度跟踪误差作为模糊***输入,即x=[s,e] T,而H(x)=[h 1(x),h 2(x),...,h r((x))] T表示模糊基函数向量,且:其中,Γ∈R r×r为正定对称矩阵;s表示步骤S2构造的快速积分终端滑模面;S4.设计永磁同步电机速度控制器:基于步骤S2和S3,设计如下形式的永磁同步电机速度控制器:基于上述永磁同步电机速度控制器可以使转速跟踪误差在时间t o内收敛至滑模面,t o满足如下关系式:式中,λ=k 2-ρ-l,表示常值系数;s(0)表示步骤S2中构造的快速积分终端滑模面s在时间为0时的值;S5.技术方案具体实现:5.1)首先,通过安装在永磁同步电机内的传感器对电机转速ω进行实时测量,在得到电机转速信号ω之后,使其与电机目标转速ω d作差得到速度跟踪误差e;得到e之后,进一步得到快速积分终端滑模面s的值,同时,基于步骤S3得到自适应模糊***所输出的干扰估计值5.2)其次,将速度跟踪误差e、快速积分终端滑模面s以及干扰估计值 代入步骤S4中所给出的永磁同步电机速度控制器,并以此控制器作为永磁同步电机矢量控制框架下的速度环控制器,用来生成q轴定子电流的参考值i q *;5.3)在电流环中,采用经典的PI控制器,根据输入的定子电流参考值得到d-q坐标系下的电压,并经过反Park变换得到静止坐标系下的电压信号,生成相应的占空比,得到三相逆变器的开关信号,并通过三相逆变器输出永磁同步电机三相定子电压,进而控制电机转速跟踪到目标转速,实现整个的电机调速过程。
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