TWI504131B - Motor control device - Google Patents
Motor control device Download PDFInfo
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- TWI504131B TWI504131B TW102147145A TW102147145A TWI504131B TW I504131 B TWI504131 B TW I504131B TW 102147145 A TW102147145 A TW 102147145A TW 102147145 A TW102147145 A TW 102147145A TW I504131 B TWI504131 B TW I504131B
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B11/00—Automatic controllers
- G05B11/01—Automatic controllers electric
- G05B11/32—Automatic controllers electric with inputs from more than one sensing element; with outputs to more than one correcting element
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/041—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a variable is automatically adjusted to optimise the performance
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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
- H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
- H02P23/14—Estimation or adaptation of motor parameters, e.g. rotor time constant, flux, speed, current or voltage
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/42—Servomotor, servo controller kind till VSS
- G05B2219/42155—Model
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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
- H02P21/06—Rotor flux based control involving the use of rotor position or rotor speed sensors
- H02P21/08—Indirect field-oriented control; Rotor flux feed-forward control
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- Software Systems (AREA)
- Power Engineering (AREA)
- Control Of Electric Motors In General (AREA)
- Feedback Control In General (AREA)
Description
本發明係關於馬達(motor)控制裝置。The present invention relates to a motor control device.
在對具備馬達與連結該馬達的機械系統之控制對象進行驅動的馬達控制裝置中,當控制對象的慣性矩(moment)和摩擦之類的負載發生變化,便必須根據負載大小重新算出目標位置指令。為此,能夠自動適應目標位置和負載大小而自動產生依據最大轉矩(torque)的定位指令之技術正開發中。In the motor control device that drives the control object of the mechanical system including the motor and the motor, when the load such as the moment of inertia and the friction of the control object changes, the target position command must be recalculated according to the magnitude of the load. . For this reason, a technology capable of automatically adapting a target position and a load size to automatically generate a positioning command according to a maximum torque is under development.
就習知的此類技術而言,例如專利文獻1所揭示的控制裝置,該控制裝置係具備:速度指令產生手段,係依據位置偏差與基準值間之大小關係來切換最大速度指令、零速度指令及與位置偏差成比例的速度指令;及附有反飽和(anti-windup)功能的速度控制器。依據專利文獻1中揭示的技術,前述基準值係設為馬達的實際速度的平方除以根據馬達的大轉矩、控制對象的慣性矩及摩擦求取的加速度的2倍值所得之值,只要給予目標位置,便能夠按照使用最大轉矩的理想的速度模式(pattern)高速地定位。In the conventional control technology, for example, the control device disclosed in Patent Document 1 includes a speed command generation means for switching the maximum speed command and the zero speed in accordance with the magnitude relationship between the positional deviation and the reference value. Commands and speed commands proportional to positional deviation; and speed controllers with anti-windup function. According to the technique disclosed in Patent Document 1, the reference value is obtained by dividing the square of the actual speed of the motor by a value twice the value of the large torque of the motor, the moment of inertia of the control target, and the acceleration obtained by the friction, as long as By giving the target position, it is possible to position at a high speed in accordance with an ideal speed pattern using the maximum torque.
專利文獻1:日本國特開2005-160152號公報Patent Document 1: Japanese Patent Laid-Open Publication No. 2005-160152
然而,在對由馬達與連結該馬達的機械系統所構成之控制對象進行驅動的馬達控制裝置中,當控制對象的負載為未知時,係要求要能夠對應控制對象的慣性矩為馬達的慣性矩的一倍至數十倍程度,然而依據上述的習知技術,響應特性會因為控制對象的負載大小而變化,有當控制對象的負載大小變得跟額定(nominal)值有大幅差異時無法獲得良好的響應的問題。此外,由於速度指令值會從最大速度切換為零速度,因此還有切換所伴隨的過渡變化導致響應有惡化之虞的問題。However, in the motor control device that drives the control object composed of the motor and the mechanical system that connects the motor, when the load of the control target is unknown, it is required to be able to correspond to the moment of inertia of the control object as the moment of inertia of the motor. Depending on the above-mentioned prior art, the response characteristic may vary depending on the load size of the control object, and may not be obtained when the load size of the control object becomes significantly different from the nominal value. A good response to the problem. In addition, since the speed command value is switched from the maximum speed to the zero speed, there is also a problem that the transient change accompanying the switching causes the response to deteriorate.
本發明乃係鑒於上述問題而研創,目的在於獲得實現高速且良好的響應特性之馬達控制裝置,即使是控制對象的慣性矩和摩擦之類的負載為未知時或負載大小大幅變化時,仍能夠自動地產生適應目標位置、限制速度及負載大小的位置指令及速度指令。The present invention has been made in view of the above problems, and an object of the present invention is to provide a motor control device that realizes high-speed and good response characteristics, and can be used even when the load such as the moment of inertia and friction of the control object is unknown or the load magnitude greatly changes. Position commands and speed commands that automatically adapt to the target position, speed limit, and load size are automatically generated.
為了解決上述課題並達成上述目的,本發明的馬達控制裝置係根據速度指令對具備馬達與連結該馬達的機械系統之控制對象進行驅動,該馬達控制裝置係具備:速度模型(model),係根據屬於1個以上變數的第1狀態變數與前述速度指令,算出前述第1狀態變數的變化量並更新前述第1狀態變數,根據更新後的前述第1狀態變數,算出速度前饋(feedforward)及電流前饋並予以輸出;速度控制器,係根據前述馬達的實際速度、前述速度 前饋及前述電流前饋算出屬於1個以上變數的第2狀態變數的變化量並更新前述第2狀態變數,根據前述馬達的前述實際速度、前述速度前饋、前述電流前饋及更新後的前述第2狀態變數,算出電流指令並予以輸出;電流限制器,係以前述電流指令為輸入,輸出限制電流值以下的限制後電流指令;及變化量係數算出部,係根據前述電流指令與前述限制後電流指令,算出屬於前述第1狀態變數與前述第2狀態變數的變化量的補正係數之變化量係數;前述速度模型係在前述第1狀態變數的變化量的算出中,進行乘上前述變化量係數的補正;前述速度控制器係在前述第2狀態變數的變化量的算出中,進行乘上前述變化量係數的補正。In order to solve the above problems and achieve the above object, a motor control device according to the present invention drives a control target including a motor and a mechanical system that connects the motor according to a speed command. The motor control device includes a speed model (model). The first state variable belonging to one or more variables and the speed command calculate a change amount of the first state variable and update the first state variable, and calculate a speed feedforward based on the updated first state variable and The current is fed forward and output; the speed controller is based on the actual speed of the aforementioned motor, the aforementioned speed The feedforward and the current feedforward calculate a change amount of the second state variable belonging to one or more variables and update the second state variable, based on the actual speed of the motor, the speed feedforward, the current feedforward, and the updated The second state variable calculates a current command and outputs the current command, and the current limiter outputs a current command after the current limit is equal to or lower than the current limit command; and the change coefficient calculation unit is based on the current command and the current command The current command is limited to calculate a variation coefficient of the correction coefficient belonging to the first state variable and the change amount of the second state variable, and the velocity model is multiplied by the calculation of the amount of change of the first state variable. The correction of the variation coefficient; the speed controller multiplies the correction of the variation coefficient by the calculation of the amount of change of the second state variable.
依據本發明,可達到能夠獲得實現高速且良好的響應特性之馬達控制裝置的效果,即使是控制對象的慣性矩和摩擦之類的負載為未知時或負載大小大幅變化時,仍能夠自動地產生自動適應於目標位置、速度及負載大小之位置指令及速度指令。According to the present invention, it is possible to achieve an effect of obtaining a motor control device that achieves high speed and good response characteristics, and can automatically generate even when the load such as the moment of inertia and friction of the control object is unknown or the load magnitude greatly changes. Automatically adapt to position and speed commands for target position, speed and load size.
1、1a‧‧‧控制對象1, 1a‧‧‧ control objects
2、2b‧‧‧位置模型2, 2b‧‧‧ position model
11‧‧‧馬達11‧‧‧Motor
12‧‧‧機械系統12‧‧‧Mechanical systems
13‧‧‧速度檢測器13‧‧‧Speed detector
14‧‧‧位置檢測器14‧‧‧ position detector
21‧‧‧速度模型21‧‧‧Speed model
22‧‧‧速度指令算出部22‧‧‧Speed Command Calculation Department
23‧‧‧積分器23‧‧‧Integrator
31‧‧‧位置控制器31‧‧‧Location Controller
32‧‧‧微分器32‧‧‧Differentiator
33‧‧‧速度控制器33‧‧‧Speed controller
34‧‧‧電流限制器34‧‧‧ Current limiter
35‧‧‧電流控制器35‧‧‧ Current controller
36‧‧‧變化量係數算出部36‧‧‧Change coefficient calculation unit
37‧‧‧慣性矩推定部37‧‧‧Inertial moment estimation unit
38‧‧‧減速度算出部38‧‧‧Deceleration calculation unit
39‧‧‧最大速度設定部39‧‧‧Max speed setting unit
40‧‧‧模型補正部40‧‧‧Model Correction Department
41‧‧‧切換開關41‧‧‧Toggle switch
211、212‧‧‧積分器211, 212‧‧‧ integrator
213至215‧‧‧乘法器213 to 215‧‧ ‧ multiplier
216、217‧‧‧減法器216, 217‧‧ ‧ subtractor
361‧‧‧轉矩常數乘法器361‧‧‧Torque Constant Multiplier
362‧‧‧非線性轉矩模型362‧‧‧Nonlinear Torque Model
363‧‧‧比率演算器363‧‧‧ ratio calculator
Adec ‧‧‧減速度A dec ‧‧‧deceleration
Aff 、Bff 、Cff 、Dff ‧‧‧矩陣A ff , B ff , C ff , D ff ‧ ‧ matrix
e‧‧‧剩餘距離e‧‧‧Remaining distance
i‧‧‧電流I‧‧‧current
Jhat ‧‧‧慣性矩推定值J hat ‧‧‧Inertial moment estimation
Jn ‧‧‧慣性矩的額定值J n ‧‧‧Moment of inertia
Ki ‧‧‧速度積分增益K i ‧‧‧speed integral gain
Kt ‧‧‧轉矩常數K t ‧‧‧torque constant
Kv ‧‧‧速度比例增益K v ‧‧‧ speed proportional gain
t‧‧‧實際時間T‧‧‧ actual time
T‧‧‧實際轉矩T‧‧‧ actual torque
Tcmd ‧‧‧轉矩指令T cmd ‧‧‧ torque command
U‧‧‧電流指令U‧‧‧current command
Uff ‧‧‧電流前饋U ff ‧‧‧current feedforward
Umax ‧‧‧最大電流指令值U max ‧‧‧Maximum current command value
Usat ‧‧‧限制後電流指令U sat ‧‧‧Restricted current command
V‧‧‧實際速度V‧‧‧ actual speed
Vc ‧‧‧速度補正量V c ‧‧‧speed correction
Vff ‧‧‧速度前饋V ff ‧‧‧speed feedforward
Vmax ‧‧‧最大速度V max ‧‧‧max speed
Vr ‧‧‧速度指令V r ‧‧ ‧ speed command
Wm‧‧‧模型補正增益Wm‧‧‧ model correction gain
Xff ‧‧‧位置前饋X ff ‧‧‧ position feed forward
Xr ‧‧‧目標位置X r ‧‧‧target location
α ‧‧‧變化量係數variation coefficient α ‧‧‧
η ‧‧‧積分變數(第2狀態變數) η ‧‧‧ integral variable (2nd state variable)
ξ ‧‧‧狀態變數(第1狀態變數) ξ ‧‧‧ state variable (the first state variable)
τ ‧‧‧虛擬時間 τ ‧‧‧Virtual time
第1圖係顯示實施形態1的馬達控制裝置的構成之方塊(block)圖。Fig. 1 is a block diagram showing the configuration of a motor control device according to a first embodiment.
第2圖係顯示實施形態1的以非線性函數表示的電流-轉矩特性之圖。Fig. 2 is a view showing current-torque characteristics expressed by a nonlinear function in the first embodiment.
第3圖係顯示實施形態1中令控制對象的負載慣性比變化時的虛擬時間τ 軸上的速度響應之圖。Fig. 3 is a view showing a speed response on the virtual time τ axis when the load inertia ratio of the control target is changed in the first embodiment.
第4圖係顯示實施形態1中實際時間t軸與虛擬時間τ 軸的 速度響應之圖。Fig. 4 is a view showing the speed response of the actual time t-axis and the virtual time τ axis in the first embodiment.
第5圖(A)及(B)係顯示實施形態1中令控制對象的負載慣性比變化時的速度響應與轉矩的響應之圖。Fig. 5 (A) and (B) are diagrams showing the response of the speed response and the torque when the load inertia ratio of the control target is changed in the first embodiment.
第6圖係實施形態2的馬達控制裝置的構成之方塊圖。Fig. 6 is a block diagram showing the configuration of a motor control device of the second embodiment.
第7圖(A)及(B)係顯示實施形態2中令控制對象的負載慣性比變化時的速度響應與轉矩的響應之圖。(A) and (B) are diagrams showing the response of the speed response and the torque when the load inertia ratio of the control target is changed in the second embodiment.
第8圖係顯示實施形態1的速度模型的構成的一例之方塊圖。Fig. 8 is a block diagram showing an example of the configuration of the velocity model of the first embodiment.
第9圖係顯示實施形態3的馬達控制裝置的構成之方塊圖。Fig. 9 is a block diagram showing the configuration of a motor control device according to a third embodiment.
以下,針對本發明的馬達控制裝置的實施形態,根據圖式詳細說明。另外,本發明並不受下述的實施形態所限定。Hereinafter, an embodiment of the motor control device according to the present invention will be described in detail based on the drawings. Further, the present invention is not limited to the embodiments described below.
第1圖係顯示本發明的馬達控制裝置的實施形態1的構成之方塊圖。第1圖中所示的馬達控制裝置係具備:控制對象1、速度模型21、速度控制器33、電流限制器34、電流控制器35及變化量係數算出部36。Fig. 1 is a block diagram showing the configuration of a first embodiment of a motor control device according to the present invention. The motor control device shown in Fig. 1 includes a control target 1, a speed model 21, a speed controller 33, a current limiter 34, a current controller 35, and a change amount coefficient calculating unit 36.
控制對象1係具備:馬達11;機械系統12,係連結馬達11;及速度檢測器13,係檢測馬達11的速度。此外,亦可取代速度檢測器13而改構成為具備位置檢測器(例如編碼器(encoder)或解角器(resolver)),藉由對位置檢測器的輸出進行微分而算出馬達11的速度。此外,亦可取代速度檢測器13而改構成為具備電流檢測器,藉由根據電流檢測器的輸出來推定馬達11的速度。速度檢測器13係輸出所檢測出的實際速度V。The control target 1 includes a motor 11 , a mechanical system 12 that connects the motor 11 , and a speed detector 13 that detects the speed of the motor 11 . Further, instead of the speed detector 13, a position detector (for example, an encoder or a resolver) may be provided, and the speed of the motor 11 may be calculated by differentiating the output of the position detector. Further, instead of the speed detector 13, a current detector may be provided instead, and the speed of the motor 11 may be estimated based on the output of the current detector. The speed detector 13 outputs the detected actual speed V.
速度模型(model)21乃係根據從外部輸入的速度指 令Vr ,使用下述式(1)所示的狀態方程式將速度前饋Vff 及電流前饋Uff 算出並輸出之模型。The speed model 21 is a model that calculates and outputs the speed feedforward V ff and the current feedforward U ff based on the state command equation (V) input from the outside using the speed command V r input from the outside.
另外,式(1)中的矩陣Aff 、Bff 、Cff 、Dff 係予先設定好的矩陣,變化量係數α 係如後述藉由變化量係數算出部36算出,而屬於1個以上變數的狀態變數ξ 乃係表示速度模型21的狀態變數之向量(vector)。式(1)中的第1式乃係狀態變數ξ 的更新演算,藉由式(1)的第1式算出狀態變數ξ 的變化量,並對該變化量進行逐次積分,藉此算出各個狀態變數ξ 。Further, the matrices A ff , B ff , C ff , and D ff in the equation (1) are pre-set matrices, and the variation coefficient α is calculated by the variation coefficient calculation unit 36 as will be described later, and belongs to one or more. The state variable 变 of the variable is a vector representing the state variable of the velocity model 21. Formula (1) Formula 1 is the system phase calculation updates variables ξ, by the formula (1) a first change amount calculated by the formula of the state variables ξ, and sequentially integrating the amount of change, whereby the respective states calculated Variable ξ .
此處,若設α =1,則式(1)乃係稱為一般性模型追隨(model following)控制的控制方式中的速度模型的狀態方程式。在稱為一般性模型追隨控制的控制方式中,係藉由速度模型,根據從外部輸入的速度指令Vr 算出速度前饋Vff 及電流前饋Uff 。就該速度前饋Vff 而言,輸出的是對於速度指令Vr 形成理想的響應波形之信號。此外,就電流前饋Uff 而言,輸出的是對速度前饋Vff 進行微分,乘上控制對象1的慣性矩的額定值Jn 後之信號。此時,電流前饋Uff 與速度前饋Vff 的特性係與控制對象1的理論模型(nominal model)的輸入/輸出特性一致。矩陣Aff 、Bff 、Cff 、Dff 係以令速度模型21形成上述特性的方式設定。Here, if α =1, the equation (1) is a state equation of the velocity model in the control mode of the general model following control. In the control method called general model follow-up control, the speed feedforward V ff and the current feedforward U ff are calculated from the speed command V r input from the outside by the velocity model. For this speed feedforward V ff , the output is a signal that forms an ideal response waveform for the speed command V r . Further, in the case of the current feedforward U ff , the output is a signal obtained by differentiating the speed feedforward V ff and multiplying the nominal value J n of the moment of inertia of the control object 1 . At this time, the characteristics of the current feedforward U ff and the speed feedforward V ff coincide with the input/output characteristics of the nometic model of the control object 1. The matrices A ff , B ff , C ff , and D ff are set such that the velocity model 21 forms the above characteristics.
於第8圖顯示能夠獲得如上述特性的速度模型21的構成的一例之方塊圖。第8圖中所示的速度模型21係具備:積分 器211、212、乘法器213、214、215、以及減法器216、217。在第8圖中,若設α =1,則從速度指令Vr 到速度前饋Vff 為止的輸入/輸出特性係成為線性的低通(low pass)特性,電流前饋Uff 係輸出將相當於速度前饋Vff 的微分之信號乘上控制對象1的慣性矩的額定值Jn 而得之信號。此外,積分器211、212係以輸入至積分器的輸入信號與變化量係數α 之積做為積分變數的變化量,於各時刻對前述變化量進行積分,藉此計算積分變數的值。設積分器211、212的值分別為ξ 1 、ξ 2 ,則第8圖所示的方塊圖的狀態方程式係能夠以下述式(2)表示。藉此,藉由將矩陣Aff 、Bff 、Cff 、Dff 及狀態變數向量ξ 設定如下式(3),便能夠以式(1)來表示第8圖的方塊圖的計算式。Fig. 8 is a block diagram showing an example of a configuration of the velocity model 21 capable of obtaining the above characteristics. The velocity model 21 shown in Fig. 8 includes integrators 211 and 212, multipliers 213, 214, and 215, and subtractors 216 and 217. In Fig. 8, if α = 1, the input/output characteristics from the speed command V r to the speed feedforward V ff become a linear low pass characteristic, and the current feedforward U ff output will The signal corresponding to the differential value of the speed feedforward V ff is multiplied by the nominal value J n of the moment of inertia of the control object 1. Further, the integrators 211 and 212 calculate the value of the integral variable by integrating the product of the input signal input to the integrator and the variation coefficient α as the amount of change of the integral variable, and integrating the amount of change at each time. The values of the integrators 211 and 212 are ξ 1 and ξ 2 , respectively, and the equation of state of the block diagram shown in Fig. 8 can be expressed by the following formula (2). Thereby, by setting the matrices A ff , B ff , C ff , D ff and the state variable vector 如下 to the following equation (3), the calculation formula of the block diagram of FIG. 8 can be expressed by the equation (1).
另外,在本實施形態中雖然係針對速度模型21具備 兩個積分器時的情形亦即速度模型21的次數為2次時的情形進行說明,但並不限定於此。速度模型的次數只要是自然數即可。Further, in the present embodiment, the speed model 21 is provided. The case of the two integrators, that is, the case where the number of times of the velocity model 21 is two is described, but the present invention is not limited thereto. The number of speed models can be as long as it is a natural number.
速度控制器33係根據速度前饋Vff 與實際速度V之差及電流前饋Uff 、預先設定好的常數Kv (速度比例增益(gain))、Ki (速度積分增益)、變化量係數α ,使用下式(4)所示的狀態方程式將電流指令U算出並輸出。The speed controller 33 is based on the difference between the speed feedforward V ff and the actual speed V and the current feed forward U ff , a preset constant K v (speed proportional gain (gain)), K i (speed integral gain), and the amount of change. The coefficient α is calculated and output by the current command U using the equation of state shown in the following equation (4).
此處,設α =1,式(4)係表示一般性的速度比例積分(PI)控制。另外,積分變數η (第2狀態變數)係表示速度控制器33的積分變數之純量(scalar)值。其中,在本實施形態的馬達控制裝置中,實際的積分變數η 的變化量係與式(1)同樣設為對藉由一般的比例積分演算而得的積分變數的變化量乘上變化量係數α 而得之值。另外,若在速度控制器33增設例如低通濾波器(low pass filter),則積分變數η 係成為由比例積分演算的積分變數與所增設的低通濾波器的演算的狀態變數所組成的向量。Here, let α = 1, and Equation (4) represents general speed proportional integral (PI) control. Further, the integral variable η (second state variable) is a scalar value indicating the integral variable of the speed controller 33. In the motor control device according to the present embodiment, the amount of change in the actual integral variable η is multiplied by the amount of change in the integral variable obtained by the general proportional-integral calculation as in the equation (1). The value obtained by α . Further, when a low pass filter is added to the speed controller 33, the integral variable η is a vector composed of the integral variable of the proportional integral calculation and the state variable of the added low-pass filter. .
電流限制器34係以電流指令U為輸入,且以所輸入的電流指令U的絕對值會成為預先設定好的最大電流指令值Umax 以下之方式輸出限制後電流指令Usat 。亦即,當所輸入的電流指令U的絕對值為最大電流指令值Umax 以下時,限制後電流指令Usat 等於所輸入的電流指令U,當所輸入的電流指令U的絕對值超過最大電流指令值Umax 時,限制後電流指令Usat 為最大電流指令值Umax 。The current limiter 34 receives the current command U as an input, and outputs the limited current command U sat such that the absolute value of the input current command U becomes equal to or smaller than the preset maximum current command value U max . That is, when the absolute value of the input current command U is less than the maximum current command value U max , the limited current command U sat is equal to the input current command U, when the absolute value of the input current command U exceeds the maximum current When the command value U max is reached, the current command U sat is limited to the maximum current command value U max .
電流控制器35係以限制後電流指令Usat 為輸入,輸出馬達11的電流i。The current controller 35 receives the current i of the motor 11 with the current limit command U sat as an input.
變化量係數算出部36係具備轉矩常數乘法器361、非線性轉矩模型362及比率演算器363,藉由電流指令U與限制後電流指令Usat 之比率算出變化量係數α 。轉矩常數乘法器361係以電流指令U為輸入,乘上預先設定好的轉矩常數Kt 而算出轉矩指令Tcmd 並輸出。非線性轉矩模型362係使用預先設定好的馬達11的電流-轉矩特性,從所輸入的限制後電流指令Usat 算出馬達11的實際轉矩T並輸出之模型。另外,此處,非線性轉矩模型362所使用的電流-轉矩特性係以考量馬達11的磁飽和及電壓飽和後的非線性函數表示。第2圖係顯示以如上述非線性函數(實線)表示的電流-轉矩特性之圖。比率演算器363係對實際轉矩T乘上轉矩指令Tcmd 的倒數而算出變化量係數α 並輸出。另外,當轉矩指令Tcmd 為0時,比率演算器363輸出的變化量係數α 係定為1。The change amount coefficient calculation unit 36 includes a torque constant multiplier 361, a nonlinear torque model 362, and a ratio calculator 363, and calculates a change amount coefficient α by a ratio of the current command U to the limited current command U sat . The torque constant multiplier 361 receives the current command U as an input, multiplies the preset torque constant K t , and calculates and outputs the torque command T cmd . The nonlinear torque model 362 calculates a model of the actual torque T of the motor 11 from the input limited current command U sat using the current-torque characteristic of the motor 11 set in advance. In addition, here, the current-torque characteristic used by the nonlinear torque model 362 is expressed by a nonlinear function after considering the magnetic saturation and voltage saturation of the motor 11. Fig. 2 is a graph showing current-torque characteristics expressed by a nonlinear function (solid line) as described above. The ratio calculator 363 calculates the change amount coefficient α by multiplying the actual torque T by the reciprocal of the torque command T cmd and outputs it. Further, when the torque command T cmd is 0, the variation coefficient α output from the ratio calculator 363 is set to 1.
接著,說明實施形態1的馬達控制裝置的動作原理。Next, the principle of operation of the motor control device according to the first embodiment will be described.
假設控制對象1所具備的機械系統12的剛性高到能夠將控制對象1視為是慣性矩J的剛體之程度且電流控制器35所導致的延遲能夠忽略,則從控制對象1的電流指令U到實際速度V為止的動態特性係以下式(5)的狀態方程式表示。Assuming that the rigidity of the mechanical system 12 included in the control object 1 is so high that the control object 1 can be regarded as the rigid body of the moment of inertia J and the delay caused by the current controller 35 can be ignored, the current command U from the control object 1 is assumed. The dynamic characteristic up to the actual speed V is expressed by the equation of state of the following equation (5).
另外,此處,g(U)係電流指令U的函數,係表示由電流限制器34致生的非線性特性及馬達11的電流-轉矩特性。亦 即,g(U)代表實際轉矩T。Here, the function of the g(U) current command U is a nonlinear characteristic generated by the current limiter 34 and a current-torque characteristic of the motor 11. also That is, g(U) represents the actual torque T.
此外,轉矩常數乘法器361中使用的轉矩常數Kt 係以下式(6)表示。Further, the torque constant K t used in the torque constant multiplier 361 is expressed by the following formula (6).
此外,變化量係數α 乃係對實際轉矩T=g(U)乘上轉矩指令Tcmd =Kt *U的倒數而算出之值,因此變化量係數α 係以下式(7)表示。Further, the variation coefficient α is a value calculated by multiplying the actual torque T=g(U) by the reciprocal of the torque command T cmd =K t *U, and therefore the variation coefficient α is expressed by the following formula (7).
此處,以下式(8)定義虛擬時間τ 。Here, the virtual time τ is defined by the following formula (8).
虛擬時間τ 乃係由實際時間t伸縮形成,其變化率乃係由實際時間t的變化率乘上述式(8)的倒數。虛擬時間τ 軸上的控制對象1的狀態方程式(於實際時間t軸上為式(5))於虛擬時間τ 軸上係以下式(9)表示。The virtual time τ is formed by the actual time t expansion and contraction, and the rate of change is multiplied by the reciprocal of the above formula (8) by the rate of change of the actual time t. The state equation of the control object 1 on the virtual time τ axis (formula (5) on the actual time t-axis) is represented by the following equation (9) on the virtual time τ axis.
由於慣性矩J及轉矩常數Kt 為常數,因此式(9)為線 性。Since the moment of inertia J and the torque constant K t are constant, the equation (9) is linear.
同樣地,由於式(8)右邊為式(5)右邊的倒數,因此虛擬時間τ 軸上的速度模型21的狀態方程式於虛擬時間τ 軸上係以下式(10)表示。Similarly, since formula (8) is the reciprocal of the right side of the right side of formula (5), and therefore the velocity model virtual time τ axis 21 state equation based on the virtual time axis τ represented by the following formula (10).
此外,同樣地,虛擬時間τ 軸上的速度控制器33的狀態方程式於虛擬時間τ 軸上係以下式(11)表示。Further, in the same manner, the virtual time axis τ speed controller 33 is a state equation based on the virtual time axis τ represented by the following formula (11).
上述式(9)、(10)、(11)皆為線性,且電流指令U方面無限制。因此,虛擬時間τ 軸上的控制對象1的響應係不受電流限制器34中的電流限制的影響。此外,虛擬時間τ 軸上的控制對象1的響應也不受馬達11的電流-轉矩特性為非線性的影響。The above formulas (9), (10), and (11) are all linear, and the current command U is not limited. Therefore, the response of the control object 1 on the virtual time τ axis is not affected by the current limitation in the current limiter 34. Further, the response of the control object 1 on the virtual time τ axis is also not affected by the nonlinearity of the current-torque characteristic of the motor 11.
此外,如上述說明,第1圖中所示的馬達控制裝置的控制系統係以模型追隨控制為基礎,即以速度模型21產生所期望的響應,並以令控制對象1追隨該響應的方式進行回饋(feedback)控制,因此,速度控制系統的響應特性係能夠藉由速度模型21的矩陣Aff 、Bff 、Cff 、Dff 而以與速度控制器33的特性分別獨立的方式設定。Further, as described above, the control system of the motor control device shown in Fig. 1 is based on the model following control, that is, the speed model 21 generates a desired response, and the control object 1 follows the response. Since the feedback control is performed, the response characteristics of the speed control system can be set independently of the characteristics of the speed controller 33 by the matrices A ff , B ff , C ff , D ff of the speed model 21 .
第3圖係顯示以速度控制器33的誤差抑制性能相較 於速度模型21的響應特性變得足夠高(亦即,達到相對於速度模型21的響應特性誤差獲得抑制之程度)的方式設定的情形中,令控制對象1的負載慣性比(慣性矩)變化時的虛擬時間τ 軸上的速度響應之圖。當以速度控制器33的誤差抑制性能相較於速度模型21的響應特性變得足夠高的方式設定矩陣Aff 、Bff 、Cff 、Dff 及常數Kv 、Ki ,便能夠實現即使控制對象1的慣性矩發生變化,響應特性的變化也會很小的控制系統。3 is a diagram showing a manner in which the error suppression performance of the speed controller 33 is set to be sufficiently higher than the response characteristic of the velocity model 21 (that is, the degree of suppression of the response characteristic error with respect to the velocity model 21 is achieved). In the case, a map of the speed response on the virtual time τ axis when the load inertia ratio (inertia moment) of the control object 1 is changed. When the matrix A ff , B ff , C ff , D ff and the constants K v , K i are set in such a manner that the error suppression performance of the speed controller 33 is sufficiently high compared to the response characteristic of the velocity model 21, even The control system 1 changes the moment of inertia of the object 1 and changes the response characteristics to a small control system.
亦即,即使控制對象1的慣性矩的額定值Jn 與控制對象1的慣性矩J之間存在有誤差,仍能夠有良好的響應。That is, even if there is an error between the rated value J n of the moment of inertia of the control object 1 and the moment of inertia J of the control object 1, a good response can be obtained.
第4圖係顯示實際時間t軸與虛擬時間τ 軸的控制對象1的速度響應之圖。實際時間t軸上的控制對象1的速度響應乃相應於以式(8)求取的實際時間t與虛擬時間τ 之關係,將根據屬於線性的狀態方程式之式(9)、式(10)、式(11)求取的虛擬時間τ 軸上的速度響應沿時間軸方向伸展後的響應。因此,為了防止實際時間t軸上的速度響應發生過衝(overshoot),只要以使速度響應在虛擬時間τ 軸上不會發生過衝的方式設定速度模型21及速度控制器33的動態特性即可。此即代表前面說明過的本實施形態的控制系統含有反飽和效果,即使採用步階(step)信號的形式在速度指令Vr 輸入大的值而形成U≧Umax 時,仍能夠以不使過衝發生的方式控制實際速度V。因此,藉由構成為如上述,即使控制對象1的慣性矩J為未知(Umax 的最大加速度為未知),只要採用步階信號的形式在速度指令Vr 輸入目標速度,便能夠實現以最大加速度進行的高速速度響應。Fig. 4 is a view showing the speed response of the control object 1 of the actual time t-axis and the virtual time τ axis. The velocity response of the control object 1 on the t-axis of the actual time corresponds to the relationship between the actual time t obtained by the equation (8) and the virtual time τ , and will be based on the equations (9) and (10) of the equation of state belonging to linearity. The response of the velocity response on the virtual time τ axis obtained by equation (11) is extended in the time axis direction. Therefore, in order to prevent overshoot of the speed response on the actual time t-axis, the dynamic characteristics of the speed model 21 and the speed controller 33 are set so that the speed response does not overshoot on the virtual time τ axis. can. This means that the control system of the present embodiment described above has a reverse saturation effect, and even if a large value is input in the form of a step signal in the form of a step signal V r to form U ≧ U max , it is possible to prevent The way the overshoot occurs controls the actual speed V. Therefore, by configuring as described above, even if the moment of inertia J of the control object 1 is unknown (the maximum acceleration of U max is unknown), the maximum speed can be achieved by inputting the target speed at the speed command V r in the form of a step signal. High speed response of acceleration.
第5圖係顯示令控制對象1的負載慣性比(慣性矩J) 變化時的速度響應(第5圖(A))與轉矩的響應(第5圖(B))之圖。依據第5圖(A)及(B),不論在哪個負載慣性比,即使以最大轉矩(最大加速度)進行加速,實際速度V也不會發生過衝。Figure 5 shows the load inertia ratio (inertia moment J) of the control object 1. Diagram of the speed response (Fig. 5(A)) and the torque response (Fig. 5(B)) when changing. According to Fig. 5 (A) and (B), the actual speed V does not overshoot even if it is accelerated by the maximum torque (maximum acceleration) regardless of the load inertia ratio.
如上述說明,在本實施形態的馬達控制裝置中,係即使控制對象的慣性矩為未知時或負載大小大幅變化時,只要給予目標速度,便能夠實現自動適應目標速度及慣性矩之高速且良好的速度響應。此外,在本實施形態的馬達控制裝置中,係對馬達的電流-轉矩特性(非線性轉矩模型的特性)的非線性特性進行補償,從而能夠防止因馬達的電流-轉矩特性為非線性所造成的響應之劣化。As described above, in the motor control device of the present embodiment, even when the moment of inertia of the control target is unknown or the load magnitude largely changes, the target speed can be automatically adapted to the target speed and the moment of inertia. The speed response. Further, in the motor control device of the present embodiment, the nonlinear characteristic of the current-torque characteristic (characteristic of the nonlinear torque model) of the motor is compensated, and the current-torque characteristic of the motor can be prevented from being non-linear. Degradation of the response caused by linearity.
另外,在上述的說明中係針對控制對象1無摩擦時的情形進行說明。設控制對象1有摩擦產生,黏性摩擦係數為c,此時控制對象1的動態特性係以下式(12)的狀態方程式表示。In addition, in the above description, the case where the control object 1 is not rubbed is demonstrated. It is assumed that the control object 1 has friction and the viscous friction coefficient is c. At this time, the dynamic characteristic of the control object 1 is expressed by the state equation of the following formula (12).
若對於有摩擦產生的控制對象1同樣也進行與無摩擦時相同的控制,則虛擬時間τ 軸的控制對象1係以下式(13)的狀態方程式表示。When the same control as in the case of no friction is performed for the control target 1 having friction, the control target 1 of the virtual time τ axis is expressed by the equation of the following equation (13).
上述式(13)係能夠視為是黏性摩擦係數c依變化量係數α 而變化的線性時變性的狀態方程式。如上述說明,模型追 隨控制的控制系統不易受控制對象1的誤差與變動的影響,因此,即使慣性矩J變動,響應特性也幾乎不會變化,同樣地,即使摩擦係數有變化,響應特性也幾乎不會變化。因此,本實施形態的馬達控制裝置幾乎不受摩擦的影響,僅給予目標速度便能夠實現高速且良好的速度響應。The above formula (13) can be regarded as a state equation of linear time-varying in which the viscous friction coefficient c changes according to the variation coefficient α . As described above, the control system of the model following control is less susceptible to the error and variation of the control target 1. Therefore, even if the moment of inertia J changes, the response characteristic hardly changes. Similarly, even if the friction coefficient changes, the response characteristic also changes. It hardly changes. Therefore, the motor control device of the present embodiment is hardly affected by friction, and a high speed and good speed response can be realized only by giving the target speed.
另外,當慣性矩J及黏性摩擦係數c已預先設定時,亦能夠在變化量係數算出部36藉由下式(14)算出變化量係數α 。In addition, when the moment of inertia J and the viscous friction coefficient c are set in advance, the variation coefficient calculation unit 36 can calculate the variation coefficient α by the following equation (14).
此時,取代上述式(8)改以下式(15)定義虛擬時間τ 。At this time, instead of the above formula (8), the virtual time τ is defined by the following formula (15).
如此一來,虛擬時間τ 軸上的控制對象1的狀態方程式係以下式(16)表示。As a result, the equation of state of the control object 1 on the virtual time τ axis is expressed by the following equation (16).
上式(16)的狀態方程式係不同於上述式(13),能夠視為是不含變化量係數α 的線性非時變性的狀態方程式。如上述,在變化量係數算出部36算出的變化量係數α 之算出方法並不限定於上述,係能夠運用各種方法。The equation of state of the above equation (16) is different from the above equation (13) and can be regarded as a linear time-invariant state equation without the variation coefficient α . As described above, the method of calculating the variation coefficient α calculated by the variation coefficient calculation unit 36 is not limited to the above, and various methods can be employed.
另外,在上述中乃係使用連續時間的狀態方程式進 行說明,而在為離散時間的情形中,藉由設各取樣(sampling)時刻的狀態變數其與前取樣時刻間的變化量為以習知的狀態變數的更新演算所求得之值的α 倍,便能夠同樣實現上述的特性。In addition, in the above description, the state equation of continuous time is used for description, and in the case of discrete time, it is known by changing the amount of change between the state variable of each sampling time and the time of the previous sampling. The above characteristics can be achieved in the same manner by α times the value obtained by the update calculation of the state variable.
另外,當馬達11的電流-轉矩特性的非線性特性小到能夠忽略或是僅動作在該能夠忽略非線性特性的範圍內時,於變化量係數算出部36便不需設置轉矩常數乘法器361及非線性轉矩模型362,只要將電流指令U與限制後電流指令Usat 輸入比率演算器363即可。藉由構成如上述,便只要考慮由電流限制器34的屬於電流指令的限制值之最大電流指令值Umax 所致生的非線性特性。Further, when the nonlinear characteristic of the current-torque characteristic of the motor 11 is small enough to be negligible or only the range in which the nonlinear characteristic can be ignored, the variation coefficient calculation unit 36 does not need to set the torque constant multiplication. The 361 and the nonlinear torque model 362 may be input to the ratio calculator 363 by inputting the current command U and the limited current command U sat . By configuring as described above, it is only necessary to consider the nonlinear characteristic caused by the maximum current command value U max of the current limiter 34 which is the limit value of the current command.
另外,當在速度控制器33設置有低通濾波器和抑制機械之共振的陷波濾波器(notch-filter)時,即使電流飽和發生,該些濾波器(filter)也不會蓄積誤差,因此該些濾波器的狀態變數的變化量並不需乘上變化量係數α 。尤其在陷波濾波器中,若對狀態變數的變化量乘上變化量係數α ,則相應於機械的共振頻率而設定的陷波頻率(notch)便會變化,因此並不需乘上變化量係數α 。Further, when the speed controller 33 is provided with a low-pass filter and a notch filter that suppresses the resonance of the machine, even if current saturation occurs, the filters do not accumulate errors, so The amount of change in the state variables of the filters does not need to be multiplied by the variation coefficient α . In particular, in the notch filter, if the amount of change in the state variable is multiplied by the variation coefficient α , the notch frequency (notch) set corresponding to the resonance frequency of the machine changes, so it is not necessary to multiply the amount of change. Coefficient α .
如上述,本實施形態的馬達控制裝置係根據速度指令對具備馬達與連結該馬達的機械系統之控制對象進行驅動,該馬達控制裝置係具備:速度模型,係根據屬於1個以上變數的第1狀態變數與前述速度指令,算出前述第1狀態變數的變化量並更新前述第1狀態變數,根據更新後的前述第1狀態變數,算出速度前饋及電流前饋並予以輸出;速度控制器,係根據前述馬達的實際速度、前述速度前饋及前述電流前饋而算出屬於1個以上變數的第2狀態變數的變化量並更新前述第2狀態變數,根據前 述馬達的前述實際速度、前述速度前饋、前述電流前饋及更新後的前述第2狀態變數,算出電流指令並予以輸出;電流限制器,係以前述電流指令為輸入,輸出限制電流值以下的限制後電流指令;及變化量係數算出部,係根據前述電流指令與前述限制後電流指令,算出屬於前述第1狀態變數與前述第2狀態變數的變化量的補正係數之變化量係數;前述速度模型係在前述第1狀態變數的變化量的算出中,進行乘上前述變化量係數的補正;前述速度控制器係在前述第2狀態變數的變化量的算出中,進行乘上前述變化量係數的補正。As described above, the motor control device according to the present embodiment drives the control target including the motor and the mechanical system that connects the motor according to the speed command, and the motor control device includes the speed model based on the first one or more variables. The state variable and the speed command calculate a change amount of the first state variable, update the first state variable, calculate a speed feedforward and current feedforward based on the updated first state variable, and output the speed controller; Calculating a change amount of the second state variable belonging to one or more variables based on the actual speed of the motor, the speed feedforward, and the current feedforward, and updating the second state variable, according to the former The actual speed of the motor, the speed feedforward, the current feedforward, and the updated second state variable are calculated and outputted; and the current limiter is input with the current command as an output current limit value And a change amount coefficient calculation unit that calculates a change coefficient of the correction coefficient belonging to the first state variable and the change amount of the second state variable based on the current command and the current command after the restriction; In the calculation of the amount of change in the first state variable, the speed model is multiplied by the correction of the change amount coefficient, and the speed controller multiplies the change amount by the amount of change in the second state variable. Correction of the coefficient.
第6圖係顯示本發明的馬達控制裝置的實施形態2的構成之方塊圖。在實施形態2中,功能與實施形態1中相同的構成要素係標註相同的元件符號並省略說明。第6圖中所示的馬達控制裝置係具備:控制對象1a、含有速度模型21的位置模型2、位置控制器31、微分器32、速度控制器33、電流限制器34、電流控制器35、變化量係數算出部36、慣性矩推定部37、減速度算出部38及最大速度設定部39。Fig. 6 is a block diagram showing the configuration of a second embodiment of the motor control device of the present invention. In the second embodiment, the same components as those in the first embodiment are denoted by the same reference numerals, and their description is omitted. The motor control device shown in Fig. 6 includes a control target 1a, a position model including the velocity model 21, a position controller 31, a differentiator 32, a speed controller 33, a current limiter 34, and a current controller 35. The variation coefficient calculation unit 36, the inertia moment estimation unit 37, the deceleration calculation unit 38, and the maximum speed setting unit 39.
控制對象1a係具備:馬達11;機械系統12,係連結馬達11;及位置檢測器14,係檢測馬達11的位置。就位置檢測器14而言,係例如使用編碼器或解角器即可。The control object 1a includes a motor 11 , a mechanical system 12 that connects the motor 11 , and a position detector 14 that detects the position of the motor 11 . As the position detector 14, for example, an encoder or a retractor can be used.
位置模型2係具備:速度模型21、速度指令算出部22及積分器23。The position model 2 includes a speed model 21, a speed command calculation unit 22, and an integrator 23.
速度指令算出部22係接受剩餘距離e(目標位置Xr 與位置前饋Xff 間之偏差)、預先設定好的最大速度Vmax 及如後述 藉由減速度算出部38算出的減速度Adec 之輸入,輸出速度指令Vr 。另外,最大速度Vmax 係由最大速度設定部39設定。The speed command calculation unit 22 receives the remaining distance e (deviation between the target position X r and the position feedforward X ff ), the preset maximum speed V max , and the deceleration A dec calculated by the deceleration calculation unit 38 as will be described later. Input, output speed command V r . Further, the maximum speed V max is set by the maximum speed setting unit 39.
速度模型21乃係以速度指令Vr 為輸入,同實施形態1將速度前饋Vff 及電流前饋Uff 算出並輸出之模型。21 is the line velocity model speed command V r as input, the model with the feedforward U ff embodiment calculates the feedforward current before and V ff Form 1 and outputs the speed.
積分器23係對從速度模型21輸出而輸入的速度前饋Vff 進行積分,輸出位置前饋Xff 。The integrator 23 integrates the speed feedforward V ff input from the speed model 21 and outputs a position feedforward X ff .
位置控制器31係以從積分器23輸出的位置前饋Xff 與以位置檢測器14檢測出的實際位置X間之偏差為輸入,使用預先設定的位置增益,輸出速度補正量Vc 。The position controller 31 receives the deviation between the position feedforward X ff output from the integrator 23 and the actual position X detected by the position detector 14 as an input, and outputs a speed correction amount V c using a preset position gain.
微分器32係對實際位置X進行微分,輸出實際速度V。The differentiator 32 differentiates the actual position X and outputs the actual speed V.
速度控制器33係以速度前饋Vff 與速度補正量Vc 的和與實際速度V間之差以及電流前饋Uff 為輸入,同實施形態1輸出電流指令U。The speed controller 33 receives the difference between the sum of the speed feedforward V ff and the speed correction amount V c and the actual speed V and the current feed forward U ff as an input, and outputs the current command U in the same manner as in the first embodiment.
電流限制器34、電流控制器35及變化量係數算出部36係與實施形態1相同。The current limiter 34, the current controller 35, and the variation coefficient calculation unit 36 are the same as those in the first embodiment.
慣性矩推定部37係以電流控制器35輸出的電流i與實際位置X或實際速度V為輸入,輸出控制對象1a的慣性矩推定值Jhat 。例如只要使用對實際位置X進行二階微分或對實際速度V進行一階微分而算出的加速度與電流i,逐次推定來算出慣性矩推定值Jhat 即可。The moment of inertia estimation unit 37 receives the current i output from the current controller 35 and the actual position X or the actual speed V as an input, and outputs the inertia moment estimated value J hat of the control target 1a. For example, the inertia moment estimated value J hat may be calculated by successively estimating the acceleration and the current i calculated by second-order differentiation of the actual position X or first-order differentiation of the actual velocity V.
減速度算出部38係以慣性矩推定值Jhat 為輸入,使用從預先設定好的最大電流指令值Umax 算出的最大轉矩Tmax ,將減速度Adec 算出並輸出。減速度Adec 係藉由下式(17)算出。The deceleration calculation unit 38 receives the inertia moment estimated value J hat as an input, and calculates and outputs the deceleration A dec using the maximum torque T max calculated from the preset maximum current command value U max . The deceleration A dec is calculated by the following formula (17).
[數式17]Adee =Tmax /Jhat ×γ…(17)[Expression 17] A dee = T max / J hat × γ (17)
此處,上式(17)中的常數γ 乃係預先設定好的1以下的正常數,為了使減速時的轉矩比最大轉矩小,約設為0.8至0.9。此外,當控制對象1a的摩擦的大小已預先設定時,亦能夠考量摩擦而將減速度Adec 設為比藉由上述式(17)算出的值大。Here, the constant γ in the above formula (17) is a normal number of 1 or less set in advance, and is approximately 0.8 to 0.9 in order to make the torque at the time of deceleration smaller than the maximum torque. Further, when the control target friction 1a size has been set in advance, also possible to consider the friction deceleration is set larger than A dec calculated by the above formula (17) value.
此處,針對速度指令算出部22的動作進行說明。速度指令算出部22係使用稱為PTOS(Proximate Time-Optimal Servomechanism)法的控制方式的目標速度函數。該目標速度函數係以下式(18)至式(20)表示。另外,e係目標位置Xr 與位置前饋Xff 間之剩餘距離。Here, the operation of the speed command calculation unit 22 will be described. The speed command calculation unit 22 uses a target speed function of a control method called PTOS (Proximate Time-Optimal Servomechanism). The target speed function is expressed by the following equations (18) to (20). In addition, the remaining distance between the e-target position X r and the position feedforward X ff .
當使用如上述的目標速度函數,由於目標速度函數係相應於剩餘距離e連續地切換,因此能夠以不使過渡響應惡化的方式進行速度指令Vr 的切換。When the target speed function as described above is used, since the target speed function is continuously switched corresponding to the remaining distance e, the switching of the speed command V r can be performed in a manner that does not deteriorate the transient response.
接著,說明實施形態2的馬達控制裝置的動作。Next, the operation of the motor control device of the second embodiment will be described.
當設定了離現在的實際位置X夠遠的目標位置Xr 時,依據式(19),速度指令算出部22輸出最大速度Vmax ,速度指令Vr 係從0切換為Vmax 。如此一來,該控制系統係在速度迴路(loop)中含有與實施形態1的速度控制系統同等的控制系統,因此會自動對應電流限制和馬達11的電流-轉矩特性的非線性特性,馬達11的實際速度V係在高速且良好的響應下加速至最大速度Vmax 。When the target position X r far enough from the current actual position X is set, the speed command calculation unit 22 outputs the maximum speed V max according to the equation (19), and the speed command V r is switched from 0 to V max . In this way, the control system includes a control system equivalent to the speed control system of the first embodiment in the speed loop, and therefore automatically corresponds to the current limit and the nonlinear characteristic of the current-torque characteristic of the motor 11, the motor The actual speed V of 11 is accelerated to a maximum speed V max at a high speed and good response.
此時,若於加速中發生電流飽和,速度前饋Vff 的響應便會藉由變化量係數α 自動調整。因此,對速度前饋Vff 進行積分而得的位置前饋Xff 的響應亦同樣形成為相對於電流飽和自動進行過調整。此外,於加速中,慣性矩推定部37係推定控制對象1a的慣性矩,輸入至速度指令算出部22的減速度Adec 係藉由上述式(17)設定。At this time, if current saturation occurs during acceleration, the response of the speed feedforward V ff is automatically adjusted by the variation coefficient α . Therefore, the response of the position feedforward X ff obtained by integrating the speed feedforward V ff is also formed to be automatically adjusted with respect to current saturation. In the acceleration, the moment of inertia estimation unit 37 estimates the moment of inertia of the control target 1a, and the deceleration A dec input to the speed command calculation unit 22 is set by the above equation (17).
若剩餘距離e減少,速度指令算出部22的目標速度函數Vr ’便會切換為式(18)中的第1式。因此,速度指令Vr 係以減速度Adec 進行定減速。在此期間,馬達11的實際速度V也會以減速度Adec 進行減速。由於減速度Adec 的值係藉由控制對象1a的慣性矩推定值Jhat 而設定,因此能夠實現最大限度使用馬達11所能產生的轉矩之理想的減速響應。When the remaining distance e decreases, the target speed function V r ' of the speed command calculation unit 22 is switched to the first expression in the equation (18). Therefore, the speed command V r is decelerated at the deceleration A dec . During this time, the actual speed V of the motor 11 is also decelerated at the deceleration A dec . Since the value of the deceleration A dec is set by the moment of inertia estimated value J hat of the control object 1a, it is possible to achieve an ideal deceleration response that maximizes the torque that can be generated by the motor 11.
最後,若剩餘距離e降到藉由上述式(20)算出的e1 以下,速度指令算出部22的目標速度函數Vr ’便會切換為上述式(18)中的第2式,目標速度函數Vr ’(速度指令Vr )係與剩餘距離e成比例。此時,位置模型2整體成為線性,因此位置前饋Xff 係滑順地收斂至目標位置Xr 。藉由位置控制器31,位置前饋Xff 與實 際位置X之誤差獲得抑制,因此實際位置X亦滑順地到達目標位置Xr 。Finally, when the remaining distance e falls below e 1 calculated by the above formula (20), the target speed function V r ' of the speed command calculation unit 22 is switched to the second expression in the above formula (18), and the target speed. The function V r ' (speed command V r ) is proportional to the remaining distance e. At this time, the position model 2 as a whole becomes linear, and therefore the position feedforward X ff smoothly converges to the target position X r . By the position controller 31, the error of the position feedforward X ff and the actual position X is suppressed, so that the actual position X also smoothly reaches the target position X r .
如上述說明,在本實施形態的馬達控制裝置中,僅藉目標位置Xr 之輸入,以使速度響應成為理想的梯形波形之方式自動產生位置前饋Xff 、速度前饋Vff 及電流前饋Uff ,從而能夠實現高速且良好的定位響應。As described above, in the motor control device of the present embodiment, the position feedforward X ff , the speed feedforward V ff , and the current are automatically generated only by the input of the target position X r so that the speed response becomes an ideal trapezoidal waveform. Feeding U ff enables high speed and good positioning response.
在本實施形態中係具有以實施形態1中說明過的構成所進行的速度控制系統,因此,相較於習知的PTOS控制法,對於例如控制對象1a的負載的變動和電流限制之類的非線性特性能夠有更為強建(robust)的控制。此外,在習知的PTOS控制法中,減速度Adec 為固定值,而在本實施形態中,減速度Adec 係藉由控制對象1a的慣性矩推定值Jhat 而動態地設定,因此即使控制對象1a的負載大小為未知,加速、減速仍皆能夠獲得理想的響應。In the present embodiment, since the speed control system is configured by the configuration described in the first embodiment, for example, the fluctuation of the load of the control target 1a and the current limitation are compared with the conventional PTOS control method. Nonlinear features can have more robust control. Further, in the conventional PTOS control method, the deceleration A dec is a fixed value, and in the present embodiment, the deceleration A dec is dynamically set by the moment of inertia estimated value J hat of the control object 1a, so even The load size of the control object 1a is unknown, and the acceleration and deceleration are still able to obtain an ideal response.
此外,即使在移動距離小時,仍係將與剩餘距離e相應的速度指令Vr 算出,藉由速度指令Vr 與速度前饋Vff 的大小自動地進行加速與減速的切換,因此會以使速度響應成為理想的三角波形之方式產生位置前饋Xff 、速度前饋Vff 、電流前饋Uff 。Further, even when the moving distance is small, the speed command V r corresponding to the remaining distance e is calculated, and the speed command V r and the speed feed forward V ff are automatically switched between acceleration and deceleration, so that The positional feedforward X ff , the speed feedforward V ff , and the current feed forward U ff are generated in such a manner that the speed response becomes an ideal triangular waveform.
第7圖係顯示令控制對象1a的負載慣性比(慣性矩J)變化時的速度響應(第7圖(A))與轉矩的響應(第7圖(B))之圖。依據第7圖,不論在哪個負載慣性比,皆能夠進行以理想的速度模式進行的高速的定位。Fig. 7 is a view showing a speed response (Fig. 7(A)) and a torque response (Fig. 7(B)) when the load inertia ratio (inertia moment J) of the control object 1a is changed. According to Fig. 7, high-speed positioning in an ideal speed mode can be performed regardless of the load inertia ratio.
如上述說明,在本實施形態的馬達控制裝置中,即使控制對象的負載大小為未知時或負載大小大幅變化時,只要給予目標位置,便能夠實現自動適應目標位置及控制對象的負載大 小之高速且良好的定位。As described above, in the motor control device according to the present embodiment, even when the load size of the control target is unknown or the load size largely changes, the load that automatically adapts to the target position and the control target can be realized by giving the target position. Small high speed and good positioning.
另外,在本實施形態中雖然係針對當給予目標位置便能夠自動進行定位控制的控制系統進行說明,但不限定於此,本實施形態係亦能夠適用於對以時間序列(例如脈波(pulse)序列)給予的位置指令進行追隨控制的控制系統。此時,速度指令算出部22以不論剩餘距離e為何均輸出與剩餘距離e成比例的速度指令Vr 之方式設定。此外,在如此的控制系統中,於電流未飽和的狀況下,係與以稱為一般性模型追隨控制的控制方式所進行的位置控制一致,因此馬達11的實際位置X係以追隨所給予的位置指令之方式受到控制。另一方面,當發生電流飽和時,係藉由變化量係數α使速度模型21與速度控制器33雙方獲得補償,因此能夠得到反飽和效果,從而能夠以不會造成例如過衝之類的不穩定響應之方式進行控制。Further, in the present embodiment, the control system capable of automatically performing the positioning control when the target position is given is described. However, the present embodiment is also applicable to the pair of time series (for example, pulse wave (pulse). The sequence command given by the sequence is followed by a control system for follow-up control. At this time, the speed command calculation unit 22 sets the speed command V r that is proportional to the remaining distance e regardless of the remaining distance e. Further, in such a control system, in the case where the current is not saturated, the position control is performed in a control mode called a general model follow control, and therefore the actual position X of the motor 11 is followed by the given The way the position command is controlled. On the other hand, when current saturation occurs, both the velocity model 21 and the speed controller 33 are compensated by the variation coefficient α, so that the reverse saturation effect can be obtained, so that it is possible not to cause, for example, overshoot. Control in a stable manner.
如上述說明,本實施形態的馬達控制裝置係根據位置指令對具備馬達的控制對象進行驅動,該馬達控制裝置係具備:速度指令算出部,係根據前述位置指令與位置前饋間之偏差,輸出速度指令;速度模型,係根據屬於1個以上變數的第1狀態變數與前述速度指令,算出前述第1狀態變數的變化量並更新前述第1狀態變數,根據更新後的前述第1狀態變數,算出速度前饋及電流前饋並予以輸出;積分器,係對前述速度前饋進行積分,輸出前述位置前饋;位置控制器,係根據前述馬達的實際位置與前述位置前饋間之差分,輸出速度補正量;速度控制器,係根據前述馬達的實際速度、前述速度補正量、前述速度前饋及前述電流前饋,算出屬於1個以上變數的第2狀態變數的變化量並更新 前述第2狀態變數,根據前述馬達的前述實際速度、前述速度補正量、前述速度前饋、前述電流前饋及更新後的前述第2狀態變數,算出電流指令並予以輸出;電流限制器,係以前述電流指令為輸入,輸出限制電流值以下的限制後電流指令;及變化量係數算出部,係根據前述電流指令與前述限制後電流指令,算出屬於前述第1狀態變數與前述第2狀態變數的變化量的補正係數之變化量係數;前述速度模型係在前述第1狀態變數的變化量的算出中,進行乘上前述變化量係數的補正;前述速度控制器係在前述第2狀態變數的變化量的算出中,進行乘上前述變化量係數的補正。As described above, the motor control device according to the present embodiment drives the control target including the motor based on the position command, and the motor control device includes a speed command calculation unit that outputs based on the deviation between the position command and the position feedforward. The speed command and the speed model calculate the amount of change in the first state variable based on the first state variable belonging to one or more variables and the speed command, and update the first state variable, and based on the updated first state variable, Calculating speed feedforward and current feedforward and outputting; the integrator integrates the aforementioned speed feedforward to output the position feedforward; and the position controller is based on the difference between the actual position of the motor and the position feedforward. The output speed correction amount is obtained by calculating the amount of change of the second state variable belonging to one or more variables based on the actual speed of the motor, the speed correction amount, the speed feedforward, and the current feedforward. The second state variable calculates a current command based on the actual speed of the motor, the speed correction amount, the speed feedforward, the current feedforward, and the updated second state variable; and the current limiter is The current command is outputted as a current command after the current limit value is output, and the change amount coefficient calculation unit calculates the first state variable and the second state variable based on the current command and the current command after the limit. a coefficient of change of the correction coefficient of the amount of change; wherein the velocity model is corrected by multiplying the amount of change in the first state variable; and the speed controller is in the second state variable In the calculation of the amount of change, the correction of the variation coefficient is multiplied.
第9圖係顯示本發明的馬達控制裝置的實施形態3的構成之方塊圖。在第9圖中,功能與第1圖、第6圖中相同的構成要素係標註相同的元件符號並省略說明。Fig. 9 is a block diagram showing the configuration of a third embodiment of the motor control device of the present invention. In the ninth embodiment, the same components as those in the first and sixth figures are denoted by the same reference numerals, and their description will be omitted.
第9圖中所示的馬達控制裝置係具備:控制對象1a、位置模型2b、位置控制器31、微分器32、速度控制器33、電流限制器34、電流控制器35、變化量係數算出部36、慣性矩推定部37、減速度算出部38、最大速度設定部39、模型補正部40及切換開關(switch)41。亦即,第9圖中所示的馬達控制裝置乃係在第6圖所示的馬達控制裝置中增設模型補正部40及切換開關41而成者。The motor control device shown in Fig. 9 includes a control target 1a, a position model 2b, a position controller 31, a differentiator 32, a speed controller 33, a current limiter 34, a current controller 35, and a variation coefficient calculation unit. 36. The inertia moment estimating unit 37, the deceleration calculating unit 38, the maximum speed setting unit 39, the model correcting unit 40, and a switch 41. In other words, the motor control device shown in Fig. 9 is a model in which the model correcting unit 40 and the changeover switch 41 are added to the motor control device shown in Fig. 6.
另外,在本實施形態中,電流限制器34係構成為能輸出電流限制之有無。此外,積分器23係輸入有從速度模型21輸出的速度前饋Vff 與切換開關41的輸出信號間之偏差。Further, in the present embodiment, the current limiter 34 is configured to be capable of outputting a current limit. Further, the integrator 23 is input with a deviation between the speed feedforward V ff outputted from the velocity model 21 and the output signal of the changeover switch 41.
模型補正部40係與位置控制器31同樣以從積分器23輸出的位置前饋Xff 與以位置檢測器14檢測出的實際位置X間之偏差(誤差信號)為輸入,輸出對該偏差乘上預先設定好的模型補正增益Wm而得的模型補正信號。所輸出的模型補正信號係輸入至切換開關41。Similarly to the position controller 31, the model correcting unit 40 takes the deviation (error signal) between the position feedforward X ff output from the integrator 23 and the actual position X detected by the position detector 14 as an input, and outputs the multiplication of the deviation. The model correction signal obtained by correcting the gain Wm with the model set in advance. The output model correction signal is input to the changeover switch 41.
切換開關41乃係依電流限制器34輸出的電流限制之有無而成為接通或無接通之構成。當電流限制器34中發生電流限制時,切換開關41成為接通,當未發生電流限制時,切換開關41成為無接通。換言之,切換開關41係當電流指令U的大小超過限制電流值時成為接通,當電流指令U的大小為限制電流值以下時成為無接通。The changeover switch 41 is configured to be turned on or off depending on the presence or absence of the current limit output from the current limiter 34. When the current limit occurs in the current limiter 34, the changeover switch 41 is turned on, and when the current limit does not occur, the changeover switch 41 is turned off. In other words, the changeover switch 41 is turned on when the magnitude of the current command U exceeds the limit current value, and is turned off when the magnitude of the current command U is equal to or less than the limit current value.
當切換開關41為接通狀態時,切換開關41的輸出為模型補正信號,當切換開關41為無接通狀態時,切換開關41的輸出為0。When the changeover switch 41 is in the ON state, the output of the changeover switch 41 is a model correction signal, and when the changeover switch 41 is in the non-on state, the output of the changeover switch 41 is zero.
藉由切換開關41的輸出,積分器23係對速度前饋Vff 與模型補正信號間之偏差進行積分,輸出位置前饋Xff 。By switching the output of the switch 41, the integrator 23 integrates the deviation between the speed feedforward V ff and the model correction signal, and outputs the position feedforward X ff .
接著,說明實施形態3的馬達控制裝置的動作。Next, the operation of the motor control device of the third embodiment will be described.
首先,當設定離現在的實際位置X夠遠的目標位置Xr ,如在實施形態2中參照式(19)之說明,速度指令算出部22係輸出最大速度Vmax ,速度指令Vr 係從0切換為Vmax ,馬達11的實際速度V係加速至最大速度Vmax 。First, when the target position X r far enough from the current actual position X is set, as described with reference to the formula (19) in the second embodiment, the speed command calculation unit 22 outputs the maximum speed V max , and the speed command V r is derived from 0 is switched to V max , and the actual speed V of the motor 11 is accelerated to the maximum speed V max .
此時,若於加速中發生電流飽和,切換開關41便會變為接通狀態,積分器23、模型補正部40及切換開關41形成回饋迴路(feedback loop)。此回饋迴路的狀態方程式係以下式(21)表 示。At this time, if current saturation occurs during acceleration, the changeover switch 41 is turned on, and the integrator 23, the model correcting unit 40, and the changeover switch 41 form a feedback loop. The equation of state for this feedback loop is the following equation (21) Show.
若設模型補正增益Wm為觀測器增益(observer gain),上述式(21)便變為與狀態觀測器(observer)的式子相同,由積分器23、模型補正部40及切換開關41形成的回饋迴路係以使位置前饋Xff 與實際位置X間之誤差減少之方式補正位置前饋Xff 。When the model correction gain Wm is the observer gain, the above equation (21) is the same as that of the state observer (observer), and is formed by the integrator 23, the model correction unit 40, and the changeover switch 41. The feedback loop compensates for the position feedforward X ff by reducing the error between the position feedforward X ff and the actual position X.
如實施形態2所說明過,在第6圖所示的馬達控制裝置中,當電流飽和發生時,會藉由變化量係數α 補正速度模型21的動作。當如此補正速度模型21的動作,位置模型2與控制對象1a間的響應之背離便獲得抑制,從而即使發生電流飽和仍能夠獲得良好的響應。As described in the second embodiment, in the motor control device shown in Fig. 6, when the current saturation occurs, the operation of the speed model 21 is corrected by the variation coefficient α . When the action of the velocity model 21 is corrected in this way, the deviation of the response between the position model 2 and the control object 1a is suppressed, so that a good response can be obtained even if current saturation occurs.
在本實施形態的第9圖中所示的馬達控制裝置中,亦藉由模型補正部40補正位置前饋Xff 與實際位置X間之誤差,因此更進一步抑制電流飽和發生時位置模型與控制對象1a間的響應之背離。因此,對於電流飽和能夠實現比實施形態2更為強健的控制。In the motor control device shown in Fig. 9 of the present embodiment, the model correction unit 40 corrects the error between the position feedforward X ff and the actual position X, thereby further suppressing the position model and control when current saturation occurs. The deviation of the response between objects 1a. Therefore, it is possible to achieve more robust control than the second embodiment for current saturation.
此外,於電流未飽和的狀況下,切換開關41係成為無接通狀態,因此與以稱為一般性模型追隨控制的控制方式所進行的位置控制一致,從而能夠實現對於控制對象的變異和外部干擾強健的控制。Further, in the case where the current is not saturated, the changeover switch 41 is in the non-on state, and thus the position control performed by the control method called the general model follow control can be realized, and variation and externality to the control target can be realized. Interfere with robust controls.
如上述說明,本實施形態的馬達控制裝置係根據位置指令對具備馬達的控制對象進行驅動,該馬達控制裝置係具 備:速度指令算出部,係根據前述位置指令與位置前饋間之偏差,輸出速度指令;速度模型,係根據屬於1個以上變數的第1狀態變數與前述速度指令,算出前述第1狀態變數的變化量並更新前述第1狀態變數,根據更新後的前述第1狀態變數,算出速度前饋及電流前饋並予以輸出;模型補正部,係根據前述馬達的實際位置的與前述位置前饋間之差分,輸出模型補正信號;切換開關,係以前述模型補正信號為輸入,於接通狀態時係輸出前述模型補正信號,於無接通狀態時係輸出零信號;積分器,係對前述速度前饋與前述切換開關的輸出信號間之偏差進行積分,輸出前述位置前饋;位置控制器,係根據前述馬達的實際位置與前述位置前饋間之差分,輸出速度補正量;速度控制器,係根據前述馬達的實際速度、前述速度補正量、前述速度前饋及前述電流前饋,算出屬於1個以上變數的第2狀態變數的變化量並更新前述第2狀態變數,根據前述馬達的前述實際速度、前述速度補正量、前述速度前饋、前述電流前饋及更新後的前述第2狀態變數,算出電流指令並予以輸出;電流限制器,係以前述電流指令為輸入,輸出將前述電流指令的大小限制在限制電流值以下的限制後電流指令;及變化量係數算出部,係根據前述電流指令與前述限制後電流指令,算出屬於前述第1狀態變數與前述第2狀態變數的變化量的補正係數之變化量係數;前述速度模型係在前述第1狀態變數的變化量的算出中,進行乘上前述變化量係數的補正;前述速度控制器係在前述第2狀態變數的變化量的算出中,進行乘上前述變化量係數的補正;前述切換開關係當前述電流指令的大小超過前述限制電流值時成為接通,當前述電流指令的大小為前述限 制電流值以下時成為無接通。As described above, the motor control device according to the present embodiment drives the control target including the motor based on the position command, and the motor control device is provided. The speed command calculation unit outputs a speed command based on a deviation between the position command and the position feedforward, and the speed model calculates the first state variable based on the first state variable belonging to one or more variables and the speed command. The amount of change is updated by the first state variable, and the speed feedforward and current feedforward are calculated and output based on the updated first state variable; the model correction unit is based on the position of the motor and the position feedforward. The difference between the two is outputting the model correction signal; the switch is input with the model correction signal, and the model correction signal is output when the switch is in the on state, and the zero signal is output when the switch is not on; the integrator is The speed feedforward is integrated with the deviation between the output signals of the switch, and the position feed forward is output; the position controller outputs a speed correction amount according to the difference between the actual position of the motor and the position feedforward; the speed controller According to the actual speed of the motor, the speed correction amount, the speed feedforward and the current feedforward Calculating the amount of change of the second state variable belonging to one or more variables and updating the second state variable, based on the actual speed of the motor, the speed correction amount, the speed feedforward, the current feedforward, and the updated The second state variable calculates a current command and outputs the current command, and the current limiter outputs a current command that limits the magnitude of the current command to a current limit or less; and a change coefficient calculation unit. Calculating a variation coefficient of the correction coefficient belonging to the first state variable and the change amount of the second state variable based on the current command and the current command after the restriction; and calculating the amount of change in the first state variable by the velocity model And correcting by multiplying the change coefficient; the speed controller is performing multiplication by the change of the change amount coefficient in the calculation of the change amount of the second state variable; and the switching open relationship is the magnitude of the current command When the current limit value is exceeded, it becomes ON, and when the magnitude of the current command is the aforementioned limit When the current value is lower than the current value, it is turned off.
如上所述,就適用於慣性矩和摩擦之類的負載為未知或負載大小大幅變化的控制對象之馬達控制裝置而言,本發明的馬達控制裝置非常有用。As described above, the motor control device of the present invention is very useful for a motor control device that is suitable for a control object whose inertia and friction are unknown or whose load magnitude greatly changes.
1‧‧‧控制對象1‧‧‧Control object
11‧‧‧馬達11‧‧‧Motor
12‧‧‧機械系統12‧‧‧Mechanical systems
13‧‧‧速度檢測器13‧‧‧Speed detector
21‧‧‧速度模型21‧‧‧Speed model
33‧‧‧速度控制器33‧‧‧Speed controller
34‧‧‧電流限制器34‧‧‧ Current limiter
35‧‧‧電流控制器35‧‧‧ Current controller
36‧‧‧變化量係數算出部36‧‧‧Change coefficient calculation unit
361‧‧‧轉矩常數乘法器361‧‧‧Torque Constant Multiplier
362‧‧‧非線性轉矩模型362‧‧‧Nonlinear Torque Model
363‧‧‧比率演算器363‧‧‧ ratio calculator
i‧‧‧電流I‧‧‧current
T‧‧‧實際轉矩T‧‧‧ actual torque
Tcmd ‧‧‧轉矩指令T cmd ‧‧‧ torque command
U‧‧‧電流指令U‧‧‧current command
Uff ‧‧‧電流前饋U ff ‧‧‧current feedforward
Umax ‧‧‧最大電流指令值U max ‧‧‧Maximum current command value
Usat ‧‧‧限制後電流指令U sat ‧‧‧Restricted current command
V‧‧‧實際速度V‧‧‧ actual speed
Vff ‧‧‧速度前饋V ff ‧‧‧speed feedforward
Vr ‧‧‧速度指令V r ‧‧ ‧ speed command
α ‧‧‧變化量係數variation coefficient α ‧‧‧
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