外文翻译--永磁同步电机高性能速度控制的最优模糊PI控制器

1 中文 3150 字 An Optimal Fuzzy-PI Controller for the High-Performance Speed Control of a PMSM Abstract The purpose of this paper is to present an adaptive method for improving the control performance of permanent magnetic synchronous motor (PMSM) in operating condition. The approach allows to reduce speed tracking error and to cope with external disturbance. The methodology of speed control is presented in detail and two controllers are tested, traditional proportional integrative (PI) controller and fuzzy proportional integrative (fuzzy-PI) controller. Both controllers showed good results from experiments presenting similar behaviors. However, the fuzzy-PI stood out positively in some stages. The main motivation of this paper is the extension of fuzzy logic algorithm to improve servo control performance in industrial applications. Keywords-Fuzzy-PI; Speed Control; Disturbance; PMSM Introduction High-performance servo system for permanent magnetic synchronous motor (PMSM) is essential in many applications in the field of mechatronics such as precision engineering, computer numerically controlled machine tools and other applications in a variety of automated industrial plants . Due to the uncertainties, which are composed of unpredictable plant parameter variations, load disturbances, and nonlinear dynamics of the plant , the control performance of PMSM servo system is influenced seriously. In this situation, the servo drive may need to respond relatively swiftly to command changes and to offer enough robustness against the uncertainties. In order to meet the development requirements of high speed and high precision for linear motor, it is thus desired to have an intelligent controller that can own higher anti-disturbance performance according to the disturbances and uncertainties in operating condition. Up to now, a large number of control techniques (fuzzy, PI, PID, etc.) with varying complexity have been proposed . Fuzzy control was first introduced and implemented in the early 1970 in an attempt to design controllers for systems that are structurally difficult to model due to naturally existing nonlinearities and other modeling complexities. Sant et al. present the vector control of PMSM with hybrid fuzzy PI speed controller with switching functions calculated based on the weights. Yen-Shin Lai et al. present a new hybrid PI-type fuzzy controller for direct torque control induction motor drives with fast tracking capability, less steady state error, and robust to load disturbance. In summary, fuzzy logic control appears very useful when the processes are too complex to analyze by conventional quantitative techniques. It seems clear to everyone that speed control techniques have allowed to execute increasingly more complex tasks in servo system field. The performance of the fuzzy-PI controllers also depends on the choice of a suitable optimization algorithm. In this paper, an adaptive speed controller is proposed to minimize or 2 eliminate the speed tracking error. The designed hybrid fuzzy-PI controller improves system performance in the transient and steady state. This paper is organized as follows. In section 2, the vector control and disturbance effects for PMSM are described in detail. The adaptive fuzzy-PI controller is explained in section 3, whilst experimental results are presented in section 4 and conclusions are drawn in the final section. Pmsm vector control In the PMSM, excitation flux is set-up by magnets; subsequently magnetizing current is not needed from the supply . This easily enables the application of the flux orientation mechanism by forcing the magnetizing current component of the stator current vector to be zero. As a result, the electromagnetic torque will be directly proportional to the torque current component of the stator current vector, hence better dynamic performance is obtained by controlling the electromagnetic torque separately. A system configuration of a vector control PMSM servo system is shown in Fig. 1. In the vector control scheme, torque control can be carried out by suitable regulation of the stator current vector; this implies that accurate speed control depends on the regulated current vector. r f iqr idr = 0 iqf idf ia ib Figure 1. The system configuration of a vector control PMSM Speed control system of PMSM is also multi-variable, nonlinear, strong-coupled system, and the disturbances mainly include the load inertia and load torque. In the running of servo system, system inertia may change. When the system inertia increases, the response of servo system will slow down, which is likely to cause system instability and result in climb. On the contrary, when the system inertia decreases, dynamic response will speed up with speed overshoot as well as turbulence. Meanwhile, the main role of servo system is to drive the load operation, but in many industries, the load carried by servo system is not constant. Changes in the load torque will have significant impact on servo control performance: in the running of servo system, the sudden increase or reduce of load torque would result in fluctuations in servo speed control, affecting the accuracy of positioning and control performance. Design of speed controller In this paper, we are proposing a speed control scheme based on fuzzy logic to improve the control performance for PMSM. Speed controller can be implemented using several approaches, such as PI, fuzzy, etc. However, when implementing a speed controller the following conditions should be considered: Simplicity: The speed control law must be simple and easy to compute in order to enable fast servo adaptation. PI-type control: In order to achieve a null steady state error, a PI type speed control law 3 i (i) should be selected and implemented. Implementation requirements should not include significant changes to the original control system. Given our objective and system requirements, two control algorithms, PI and fuzzy logic, are chosen. The choice for PI controller is due to its good performance when applied in practical situations, and the preference for fuzzy controller is due to no requirement of the rigorous mathematical system model. Fuzzy Control Architecture Fuzzy logic was conceived to apply a more human-like way of thinking in computer programming. It is ideal for controlling nonlinear systems and model complex systems where ambiguity is common. It is also potentially very robust, maintaining good closed-loop system performance over a wide range of operating conditions. In our system, speed controller input variables are the speed error e and change of the speed error de : e(k) = r (k) f (k ) (1) de(k) = e(k ) e(k 1) (2) Where r is the speed command and f is the actual speed. Fuzzy-PI From the conventional PI control algorithm, we can obtain the following discrete equations: iq (k) = iq1 (k) + iq (k) (3) iq (k) = k p de(k) + ki e(k) (4) If e and de are fuzzy variables, (3) and (4) become a fuzzy control algorithm. Then, the centre of area method is selected for defuzzify the output fuzzy set inferred by the controller: iq n = i=1 i q n i=1 i (5) Where i is the membership function, which takes values in the interval 0, 1. Knowledge Base The knowledge base of fuzzy logic controller is composed of two components, namely, a database and a fuzzy control rule base. The well-known PI-like fuzzy rule base is used in this paper (Table 1). The surface of rule base is shown in Fig. 2. It allows fast working convergence without significant oscillations and prevents overshoots and undershoots. TABLE 1 FUZZY RULE BASE 4 e de NL NM NS ZR PS PM PL NL nl nl nl nl nm ns ze NM nl nl nm nm ns ze ps NS nm nm nm ns ze ps ps NZ nm nm ns ze ps ps pm PZ nm ns ns ze ps pm pm PS ns ns ze ps pm pm pm PM ns ze ps pm pm pl pl PL ze ps pm pl pl pl pl Figure 2. The surface of rule base Tuning Strategy Fuzzy logic design is involved with two important stages: knowledge base design and tuning. However, at present there is no systematic procedure to do that. The control rules are normally extracted from practical experience, which may make the result focused in a specific application. The objective of tuning is to select the proper combination of all control parameters so that the resulting closed-loop response best meets the desired design criteria. In order to adapt servo system to different disturbances, the scaling factors should be tuned. The controller should also be adjusted with characteristics representing the scenario to be controlled. These adjustments can be made through the scaling factors, usually applied in any PI controller. S.T. Lin et al. 10 proposed an adjustment where the scaling factors are dynamic and thus they have been adjusted along the task. In this paper, the scaling factors are set to appropriate constant values, achieved by the method of trial and error. Experiment The apparatus for the experiment contains three major parts and some data transferring buses, as shown in Fig. 3. These three major parts are: 1) a PC and a PCI with sampling time equal to 1ms; 2) AC servo drive using a DSP plus a FPGA, where DSP TMS320F2812 mainly accomplishes position, velocity and torque control, and FPGA EP2C8Q208C8N is responsible for the analysis and realization of absolute ruler and NCUC-Bus protocols; 3) PMSM with the parameters described in Table 2. Through the PCI controller, PC sends the speed command 5 and control parameters to servo drive, and receives expected torque current and feedback velocity from servo drive for the model identification. Figure 3. The apparatus for the experiment TABLE 2 MOTOR PARAMETERS Motor Rating Torque coefficient 0.75Nm/A Rated speed 1000r/min Rated Torque 4.5Nm Friction coefficient 0.0008Nms/rad Inertia 0.0028Nms2/rad Poles 3 In the experimental tests without applied load torque, a trapezium-type speed command, the maximum speed of which is 1000r/min, is applied. To evaluate the control performance, a fixed PI controller is considered. Fig. 4 shows the speed response with PI controller, it indicates that the maximum speed error is about 34r/min at the acceleration stage and the maximum speed error fluctuation is about 7r/min at the constant speed stage. Speed response with fuzzy-PI controller is shown in Fig. 5, it has better speed tracking performance with the maximum speed error is about 15r/min at the acceleration stage and the maximum speed error fluctuations is about 3r/min at the constant speed stage. In the experimental tests without applied load torque, a trapezium-type speed command, the maximum speed of which is 1000r/min, is applied. To evaluate the control performance, a fixed PI controller is considered. Fig. 4 shows the speed response with PI controller, it indicates that the maximum speed error is about 34r/min at the acceleration stage and the maximum speed error fluctuation is about 7r/min at the constant speed stage. Speed response with fuzzy-PI controller is shown in Fig. 5, it has better speed tracking performance with the 6 Speed Response (r/min)Speed Response (r/min)Speed error (r/min)Speed error(r/min)maximum speed error is about 15r/min at the acceleration stage and the maximum speed error fluctuations is about 3r/min at the constant speed stage. 1200 1000 800 600 400 200 0 0 1 2 3 4 5 6 Time (s) 20 10 0 -10 -20 -30 -40 0 1 2 3 4 5 6 Time (s) Figure 4. The speed response with PI controller (no load torque) 1200 1000 800 600 400 200 0 0 1 2 3 4 5 6 Time (s) 10 5 0 -5 -10 -15 0 1 2 3 4 5 6 Time (s) Figure 5. The speed response with fuzzy-PI controller (no load torque) In the experimental tests with changed applied load torque, a slope-type speed command, the maximum speed of which is 1000r/min, is applied. When t = 2s , the applied load torque is 2Nm. When t = 5s , the applied load torque is suddenly became to 8Nm. To evaluate the control performance, a fixed PI controller is also considered. Fig. 6 shows the speed response with PI controller. When 2s t 5s , the maximum speed error is about 95r/min at the acceleration stage and marked speed overshoot at the constant speed stage. When 5s t 10s , it is clear that the maximum speed error fluctuation is about 50r/min and the tracking response does not meet the design specifications. Speed response with fuzzy-PI controller is shown in Fig. 7. When 2s t 5s , the maximum speed error is only about 48r/min at the acceleration stage and unobvious speed overshoot at the constant speed stage. When 5s t 10s , it is clear that the maximum speed 7 Speed Response(r/min)Speed Response (r/min) Speed Error (r/min)Speed Error(r/min) error fluctuations is only about 8r/min. servo system with fuzzy-PI controller has better speed tracking performance and can suppress the load torque well. 1200 1000 800 600 400 200 0 0 1 2 3 4 5 6 7 8 9 10 Time (s) 50 0 -50 -100 0 1 2 3 4 5 6 7 8 9 10 Time (s) Figure 6. The speed response with PI controller 1000 500 0 0 1 2 3 4 5 6 7 8 9 10 Time (s) 50 0 -50 0 1 2 3 4 5 6 7 8 9 10 Time (s) Figure 7. The speed response with fuzzy-PI controller Conclusions This paper has presented an adaptive fuzzy-PI speed control scheme for PMSM drive. The effectiveness of the proposed approach was proved through experiments, showing that the hybrid control improves significantly servo performance, making servo system more human-like, flexible and with capacity to make decisions. Substantially, the fuzzy-PI controller can occur a small overshoot against a large overshoot when using the PI controller. Furthermore, in some situations the fuzzy-PI controller showed to be a better solution to reach the set-point faster. 8 永磁同步电机高性能速度控制的最优模糊 PI 控制器 摘要：本文的目的是介绍改进的永磁同步电机（ PMSM）工作的控制性能的自适应方法。该方法允许降低速度追踪误差及应对外部干扰。本文提出了详细速度控制的方法，并针对两个控制器进行测试，传统的综合比例（ PI）控制器和模糊综合成正比（模糊 -PI）控制器。从有着 类似动作的实验中，两个控制器都表现出了良好的效果。然而，模糊 -PI在某些方面脱颖而出。本文的主要目的是模糊逻辑算法的扩展，以提高工业应用中的伺服控制性能。 关键词：模糊 PI； 速度控制 ； 干扰 ； 永磁同步电机 1 引言 用于永磁同步电机（ PMSM）的高性能伺服系统在机电一体化，如精密工程，电脑数控机床及各种自动化工业厂房的其他应用领域的许多应用中是必不可少的。由于不确定性因素，例如不可预测的工厂参数变化，负载扰动，以及固有的非线性动态过程，永磁同步电机伺服系统的控制性能受到严重影响。在这种情况下，伺服驱动器可能需要比较快地响应命令的变化，并对于不确定性有足够的鲁棒性。为了满足高速、高精度的直线电机的发展要求，我们希望有一个可以针对操作环境的干扰和不确定性有更高的抗扰动性能的智能 控制器。 目前为止，已经有大量的具有不同的复杂性的控制技术（模糊， PI， PID 等）被提出。模糊控制在 1970 年初首次被提出并实施是在一次设计控制器的实验中，那是在结构上很难建模由于自然存在的非线性和其他建模复杂系统。桑特等在永磁同步电机的矢量控制与交换计算功能的基础上，提出了权重混合模糊 PI 速度控制器。颜善等人提出的直接转矩控制异步电机驱动具有快速跟踪能力，更低的稳态误差，和强大的负载扰动，是一种新的混 PI 型模糊控制器。总之，当流程过于复杂时，通过常规的定量技术来分析模糊逻辑控制显得非常有用。众所周知，调速技术已能够在伺服系统领域执行越来越复杂的任务。 模糊 -PI 控制器的性能还取决于选择合适的优化算法。在本文中，提出了一种自适应速度控制器，它以最小化或消除的速度跟踪误差，所设计的混合模糊 PI 控制器改善了瞬态和稳态系统性能。本文的结构如下：第 2 节详细描述了永磁同步电机矢量控制和干扰的影响，第 3 节解释了自适应模糊 PI 控制器的，第 4 节列出了实验结果，最后一节得出了结论。 2 永磁同步电机矢量控制 对于永磁同步电机，磁铁建立励磁磁通，随后的磁化电流不从供给获得。这很容易通过迫使定子电流向量的励磁电流分量为零使磁场定向的机制作用。其结果是，电磁转矩通过分别控制电磁转矩，将定 子电流向量和扭矩电流分量作用成正比，因此获得更好的动态性能。矢量控制的永磁同步电动机伺服系统的系统结构如图 1 所示，在矢量控制9 方案中，扭矩控制可以进行对定子电流向量的适当调节，这意味着精确的速度控制取决于电流矢量的调节。 S p e e d c o n t r o l l e rP IC o n t r o l l e rVSISVPWMV e c t o rT r a n s f o r m1 / sP M S M-+rf aibiP IC o n t r o l l e rP o s i t i o n s e n s o r0dri qriqfi dfi图 1.矢量控制的永磁同步电机的系统配置 永磁同步电机调速系统是多变量、非线性、强耦合的系统，其干扰主要包括负载惯量和负载转矩。在伺服系统的运行，系统的惯性可能会改变。当系统惯量增大，伺服系统的响应会变慢，这很可能会导致系统不稳定。反 之，当系统的惯性减小，动态响应将加快、速度超调。同时，伺服系统的主要作用是驱动负载的运行，但在许多行业中，通过伺服系统承载的负荷不是恒定的，变动负载转矩将不会对伺服控制性能显著的影响：在伺服系统中，突然增加或减少负载转矩的运行会导致伺服调速的波动，影响了定位和控制性能的准确性。 3 速度控制器的设计 在本文中，我们提出一种基于模糊逻辑、以改善永磁同步电机控制性能速度控制方案。速度控制器可以使用几种方法，如 PI，模糊等。然而，实施速度控制时，应考虑下列情况： 简单：速度控制算法必须是简单且容易计算，以实现快速的伺服适应。 PI 型控制：为了实现零稳态误差，应该选择和实施 PI 型转速控制规律。 实施要求不应该包括明显改变原有的控制系统。 由于目标和系统需求，我们选择两种控制算法 PI 和模糊逻辑。当在实际情况中对于 PI 控制器的选择是由于其良好的性能，而倾向于选择模糊控制器是由于其对于严格的数学系统模型的不作要求。 A.模糊控制架构 模糊逻辑的构想采用更类似人类在计算机编程的思维方式。它在理想的非线性控制系统和模型的复杂系统中歧义很常见。它也可能保持 在一个宽范围的操作条件良好的闭环系统的性能。在我们的系统中，速度控制器的输入变量是速度误差和速度误差的变化： )()()( kkke fr (1) )1()()( kekekde (2) 其中， r 是速度指令，f是实际速度。 B.模糊 PI 由传统的 PI 控制算法，我们可以得到如下离散方程： )()()( 1 kikiki qqq (3) 10 )()()( kekkdekki ipq (4) 如果 e 和 de 是模糊变量，由（ 3）和（ 4）得到一个模糊控制算法。然后，选择区域方式的中心为 defuzzify 的输出模糊集合，控制器可得： ni ini qiqiii11 )( (5) 其中i是隶属函数，在 0,1中取值。 C.知识库 模糊逻辑控制器的知识库由两部分组成，即一个数据库和模糊控制规则库。众所周知， PI 模糊规则库是如本文中（表 1），规则库中的表面如图 2 所示，它使快速的工作交替不产生显著波动，防止超调和下冲。 表 1.模糊规则库 e de NL NM NS ZR PS PM PL NL nl nl nl nl nm ns ze NM nl nl nm nm ns ze ps NS nm nm nm ns ze ps ps NZ nm nm ns ze ps ps pm PZ nm ns ns ze ps pm pm PS ns ns ze ps pm pm pm PM ns ze ps pm pm pl pl PL ze ps pm pl pl pl pl 图 2 .规则库的表面 D.调整策略 模糊逻辑的设计涉及两个重要阶段：知识库的设计和调整。然而，目前还没有系统的程序来做到这一点。控制规则通常由实际经验提取的，这可能使结果集中在一个特定的应用程序。调谐的目的是选择所有控制参数的适当组合，使所得到的闭环响应最佳地满足所需的设计准则。 11 为了使伺服系统适应不同的干扰，比例因子应该进行调整。该控制器还应根据不用情况下被控制量的特点进行调整。这些调整可以通过 PI 控制器的应用进行缩放因子。 S.T. Lin 等人提出了一种调整，其中的缩放因子是动态的，因此它们是随着任务而调整。在本文中，缩放因子被设置为适当的 恒定值，通过反复试验来实现。 4 实验 用于实验的装置包含三个主要部件和一些数据传