US 20030015988 A1 Abstract A feedback gain K is determined by using an estimation error e
_{i }of a stator current, and an observed flux and an estimated speed are obtained and output based on the feedback gain K. An induction motor is controlled based on the observed flux and the estimated speed. In this way, a control system, an observer, and a control method, which realize a global stable control of an induction motor drive that does not comprise a speed sensor and/or a rotational position sensor, are implemented. Claims(12) 1. A control system vector-controlling an induction motor that does not comprise at least either a speed sensor or a position sensor, comprising:
an observer unit determining a feedback gain K by using an estimation error of a stator current, and obtaining and outputting at least either of an observed flux and an estimated speed based on the feedback gain K; and a control unit controlling the induction motor based on an output of said observer unit. 2. The control system according to said observer unit determines a value that satisfies as a feedback gain K for a transfer function G _{1 }being a linear portion of a system of the estimation error of the stator current. 3. The control system according to said observer unit determines the feedback gain K based on an equation where L _{r }is a rotor inductance, R_{s }is a stator resistance, R_{r }is a rotor resistance, and ω_{r }is an angular rotor speed, and 4. The control system according to said observer unit determines the feedback gain K a magnitude of which is within a predetermined range if a rotation speed of the induction motor is equal to or higher than a preset value. 5. The control system according to said observer unit determines the feedback gain K by using a value of an angular rotor speed ω _{r}, which is restricted to within a predetermined range. 6. The control system according to said control unit comprises
a vector rotating unit performing vector rotation based on the output of said observer unit, and
a current regulating unit outputting a current command to the induction motor based on the output of said observer unit.
7. A control system vector-controlling an induction motor that does not comprise at least either a speed sensor or a position sensor, comprising:
observer means for determining a feedback gain K by using an estimation error of a stator current, and for obtaining and outputting at least either of an observed flux and an estimated speed based on the feedback gain K; and control means for controlling the induction motor based on an output of said observer means. 8. An observer used to vector-control an induction motor that does not comprise at least either a speed sensor or a position sensor, comprising:
a feedback gain determining unit determining a feedback gain by using an estimation error of a stator current; and an outputting unit obtaining and outputting at least either of an observed flux and an estimated speed based on the feedback gain. 9. The observer according to said feedback gain determining unit determines the feedback gain a magnitude of which is within a predetermined range if a rotation speed of the induction motor is equal to or higher than a preset value. 10. An observer used to vector-control an induction motor that does not comprise at least either a speed sensor or a position sensor, comprising:
feedback gain determining means for determining a feedback gain by using an estimation error of a stator current; and outputting means for obtaining and outputting at least either of an observed flux and an estimated speed based on the feedback gain. 11. A method vector-controlling an induction motor that does not comprise at least either a speed sensor or a position sensor, comprising:
determining a feedback gain by using an estimation error of a stator current; and obtaining at least either of an observed flux and an estimated speed based on the feedback gain. 12. The method according to the feedback gain a magnitude of which is within a predetermined range if a rotation speed of the induction motor is equal to or higher than a preset value. Description [0001] 1. Field of the Invention [0002] The present invention relates to an induction motor drive without a speed sensor and/or a rotational position sensor, and more particularly, to an observer for vector-controlling an induction motor drive. [0003] 2. Description of the Related Art [0004] A typical vector control system for a direct field-oriented induction motor drive without a speed sensor and/or rotational position sensor is shown in FIG. 1. [0005] In the system without a speed sensor, only a stator voltage [0006] Vector control for an induction motor [0007] With the vector control in the system shown in this figure, a speed regulator [0008] The voltage and the current values applied from the inverter [0009] The flux and speed observer [0010] The vector rotator [0011] Additionally, the vector i [0012] An MRAS (Model Reference Adaptive System) based on a flux and speed observer was initially proposed by Ref. 1. [0013] Ref. 1: H. Kubota et al. DSP-based speed adaptive flux observer of induction motor, IEEE Trans. Industry Applicat., vol. 2, no. 2 pp. 343-348, 1993. [0014] According to Ref. 1, a stator current and a rotor flux are used as an independent set of variables in order to explain an induction motor. Accordingly, an equation for an induction motor, which is demonstrated by Ref. 1, can be rewritten to an equation using a stator flux and a rotor flux as state variables. Since the process of this rewrite is a standard linear transformation, it is omitted here. [0015] A classical representation of an induction machine in a stator oriented reference coordinate system (α-β) using a state space notation is as follows.
[0016] where: [0017] [0018] are space vectors associated with a stator flux, a rotor flux, a stator current, and a stator voltage respectively. [0019] Other symbols are as follows.
[0020] R [0021] L [0022] σ=1−L [0023] ω [0024] Furthermore, according to Ref. 1, observed flux values are represented as follows. Note that observation and an observed value referred to in this specification represent observation and an observed value in modern control theory, and indicate the estimation of a state variable value from an output and its estimated value. In the following equation, observed values are marked with ^ .
[0025] An output feedback gain K in the equation (2) is used to modify the dynamic characteristics of an estimation error and its determination. [0026] The speed is evaluated with the following equation.
[0027] where k [0028] According to Ref. 1, the feedback gain K in the observer equation (2) is used along with a constant of proportionality k in order to obtain four eigenvalues λ λ [0029] The equation (4) is proved in the following document. [0030] Ref. 2: Y. Kinpara and M. Koyama, Speed Sensorless Vector Control Method of Induction Motor Including A Low Speed Region, The Journal D of the Institute of Electrical Engineers of Japan, vol. 120-D, no.2, pp. 223-229, 2000. [0031] With a selection method for a feedback gain K, which is proposed by Ref. 2, several unstable operation conditions are imposed on the induction motor. Especially, when a stator frequency approaches 0, an observer does not converge, leading to inability of the operations of the motor drive. [0032] An unstable region on a torque-speed plane of the induction motor drive depends on the value of the constant of proportionality k in the equation (4). This unstable area converges to a single line corresponding to the primary frequency that is exactly 0 when the constant k converges to 0. Accordingly, the dynamic characteristics resultant from the flux observer become unacceptably slow for a very small value of k. Therefore, this selection method for the feedback gain K is not a good solution. [0033] Ref. 2 proposes a method based on a Riccati equation as a selection method for the output feedback gain K in the equation (2), which stabilizes the drive. [0034] With this method, if G, Q, and R are defined as follows
R=ε _{I} I
[0035] the output feedback gain K is obtained with the following equation.
[0036] where P is a sole positive definite solution that satisfies the following equation. [0037] With the method using the Riccati equation, the stability of the flux and speed observer is improved, but one arbitrary parameter (ε [0038] The present invention was developed to overcome the above described problems, and aims at providing a control system, an observer, and a control method for an induction motor drive without a speed sensor or a position sensor, the operations of which are stable for global operation frequencies. [0039] The present invention assumes a device or a method performing vector control for an induction motor that does not comprise at least either a speed sensor or a position sensor. [0040] The control system according to the present invention comprises an observer unit and a control unit. [0041] The observer unit determines a feedback gain K by using an estimation error of a stator current, and obtains and outputs at least either of an observed magnetic flux and an estimated speed based on the feedback gain K. [0042] The control unit controls the induction motor based on the output of the observer unit. [0043] With this system, only the restriction on the determination of the feedback gain K is, for example, an equation
[0044] That is, the feedback gain K which satisfies a condition based on a different factor can be determined with almost no restrictions. [0045] Furthermore, the observer unit can be configured to determine the feedback gain K the magnitude of which is within a predetermined range, if the rotation speed of the induction motor is equal to or higher than a preset speed. [0046] With this configuration, a stable operation can be realized even at an operating frequency in the vicinity of 0. [0047]FIG. 1 shows a typical system of a direct field-oriented induction motor drive without a speed sensor and/or rotational position sensor; [0048]FIG. 2 exemplifies an output error block according to a preferred embodiment of the present invention; [0049]FIG. 3 shows a system of a direct field-oriented induction motor drive without a speed sensor or a rotational position sensor according to the preferred embodiment; [0050]FIG. 4 exemplifies the configuration of a flux and speed observer; and [0051]FIG. 5 exemplifies the simplest configuration of a stabilizing gain calculator. [0052] Preferred embodiments according to the present invention will be explained below with reference to the drawings. [0053] The present invention adopts several results established so far in non-linear control theory. In consequence, a feedback gain K that ensures the stability of a flux and speed observer under every possible operating condition can be obtained without much degrading the dynamic characteristics of the observer. [0054] Since the feedback gain K is obtained as a very simple function of almost no motor parameters and operating speed, its realization and implementation can be made with significant ease. Furthermore, unlike the methods proposed so far, a feedback gain the value of which does not become infinite can be derived even if the primary frequency approaches 0, according to the present invention (singular condition). [0055] If an error of an angular rotor speed is set as Δω [0056] where s is a Laplace operator. [0057]FIG. 2 exemplifies an output error block satisfying the equation (5). [0058] As exemplified in FIG. 2, a stator current estimation error system can be recognized as an interconnection of a non-linear feedback transfer function and a linear transfer function. [0059] If the following two conditions are satisfied in this figure, the flux and speed observer is stabilized. [0060] Condition 1: A non-linear feedback ∫ [0061] Condition 2: A linear transfer function GI(s) of a linear steady-state block [0062] Since mechanical constituent elements have relatively slow dynamic characteristics as for Condition 1, it becomes easy to implement u [0063] The following equation can be derived from the above provided equations (3) and (6).
[0064] It is evident that the equation (7) satisfies Popov's inequality (6), since the equation (7) includes the feedback gain K. Hence, FIG. 2 satisfies Condition 1. [0065] Next, the linear transfer function G [0066] Suppose that there is no feedback gain K (K=0). In this case, although the transfer function G [0067] Accordingly, for the stability of the system shown in FIG. 2, it is necessary to determine a gain matrix K such that the Popov's stability condition is satisfied, and the whole of a dynamic matrix (A+KC) of the flux observer itself remains stable. [0068] The transfer function G [0069] This equation means that the only way to achieve the stability when the primary frequency is a small positive or negative value is to ensure the following equation.
[0070] This equation (9) is satisfied whenever the feedback gain K that satisfies the following equation (10) is suitably selected.
[0071] As far as the equation (10) is satisfied, any feedback gain K in the form represented by the equation (2) is acceptable, and the flux and speed observer is globally stabilized. [0072] The feedback gain K can be defined as follows from the equation (2).
[0073] There are four parameters (k [0074] This selection method for the feedback gain K can be simplified, for example, by selecting the parameters as follows. [0075] When it is verified that the parameter k [0076] Considering this fact, the parameter k [0077] From the above discussion, the following simple equation for deriving the feedback gain K can be obtained.
[0078] The feedback gain K that satisfies the equation (14) stabilizes the observer at any speed or at any primary frequency in which the flux and speed observer has one of its poles at the origin (stability limit) except for the singular condition that the primary frequency, is exactly 0. [0079] It is proved from the equation (13) that the parameter k [0080] To address this problem, an upper limit is set for the value of the feedback gain K, which is obtained from the equation (14), and the value is clipped to fall within a particular range if it exceeds the range. For example, an operating speed approximately twice (or three times) the rated slip ω [0081] Whichever value the parameter k [0082] Any standard technique may be available as the selection of the parameter k [0083] Whichever value is selected for the parameter k [0084]FIG. 3 shows the control system for a direct field-oriented induction motor drive without a speed sensor and/or a rotational position sensor, according to this preferred embodiment. [0085] Comparing with the system configuration shown in FIG. 1, a flux and speed observer [0086] The globally stable flux and speed observer [0087] Additionally, the flux and speed observer [0088]FIG. 4 exemplifies the configuration of the flux and speed observer [0089] In the configuration shown in FIG. 4, the observed rotor flux [0090] In the flux and speed observer [0091] The multiplier [0092] Additionally, in the flux and speed observer [0093] The output of the integrator [0094] The multiplier [0095] The stabilizing gain calculator [0096]FIG. 5 exemplifies the simplest configuration of the stabilizing gain calculator [0097] The stabilizing gain calculator [0098] Calculation of the parameter k [0099] Then, a multiplier [0100] As described above in detail, stable operations can be realized for global operating frequencies according to the present invention. [0101] Additionally, since the procedures proposed to evaluate the feedback gain of an MRAS-based flux and speed observer are used, it become possible to overcome problems that are associated with a regenerative operation at a low speed even if a primary frequency approaches 0, which makes a flux and speed observer causes an error with a conventional method. As a result, global stable operations of the drive can be achieved. [0102] Furthermore, a feedback gain the value of which does not become-infinite can be derived even if the primary frequency approaches 0. [0103] Still further, a stabilization gain can be obtained by solving a simple algebraic equation. [0104] Still further, a feedback gain K is obtained as a very simple function of almost no motor parameters and operating speed. Therefore, the feedback gain K that ensures the stability of a flux and speed observer under every possible operating condition can be obtained without much degrading the dynamic characteristics of the observer. Accordingly, it is very easy to industrially realize and implement the present invention. Referenced by
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