【正文】 time was where S(s) is the sensitivity function, T(s) is the plementary sensitivity function, K(s) is the desired H∞ controller, 1/|wp(s)|, 1/|wt(s)| and 1/|wu(s)| put upper bounds on the magnitude of S(s) (for performance), T(s) (for noise attenuation) and K(s) S(s) (to penalize large inputs), respectively. The H∞ optimal controller was obtained by solving the problem2 Fig. 7 shows other design parameters used in the zaxis control design and the final sensitivity function from the puted H∞ controller. The final sensitivity function S(s) clearly shows that the H∞ controller has double integral action in low frequency range as intended with the shape of 1/|wp(s)|. The designed H∞ controller was converted to a discretetime controller K(z) for a 2 kHz sample and hold rate and implemented on a DSP board for tests. The final H∞ controller K(z) was a 5th order controller. The classical feedback sensitivity function S(s) is the transfer function from the reference signal r(t) to the control error signal e(t), . e(t) = S(s)? r(t). To pare tracking performance between the designed H∞ controller and PID controller, a fixedamplitude sine wave of varying frequencies was injected as a mand signal and the corresponding error signal was measured and the ratio of their magnitude versus frequency was plotted in Fig. 8. Thus it is an empirical sensitivity function plot and we can estimate the level of tracking performance from this plot. The H∞ controller shows % tracking error for 1 Hz sine mand, but 10% from PID controller in this particular design. It is due to the intended double integral action from H∞ control design. Similarly other H∞ controllers were designed for the x and yaxes but the tracking performance from H∞ control was similar to that from PID control in the x and yaxes which have voice coil motors and LM guides. A circular reference trajectory of mm in radius in yz plane was given to the y and zaxis servo as a mand with a feedrate of 25 mm/sec and its contour errors are pared in Fig. 9. Note that the contour errors are different from the tracking errors. A tracking controller attempts to minimize the difference between the reference trajectory, which is specified as a function of time, and the output of the controlled plant. On the other hand, a contouring controller attempts to minimize the difference between the spatial trajectory of the reference and the spatial trajectory traced by theoutput of the controlled plant. The contour error from two axes servo motion takes into account only the spatial trajectories and large tracking error does not necessarily mean large contour error. If one axis is in great synchronization with the other axis although it has large tracking error due to time delay, then the final contour error may be small in the sense that the output of the controlled plant matches well the manded reference trajectory with same amount of time delay from both axes. If two axes have good tracking performance then they will show good contour error. In Fig. 9, the yaxis servo motion is drawn horizontally and the zaxis servo motion is drawn vertically. The blue circle in the middle of the figure represents the 0 μm error line, . The controlled plant output exactly matches the spatial reference trajectory. When a PID controller is applied to the yaxis, it shows approximately 30 μm error at around 0 degree, but 50 μm error appears from the H∞ controller at the same position. This error is caused by the air cylinder counteracting gravity force for the feedforward controller is inserted in an attempt to reduce the error in the yaxis at around 0 degree, but the feedforward controller does not show any noticeable improvement. At other areas except 0 and 180 degree regions the error from the H∞ controller is still better than the PID controller in the yaxis. The H∞ controller in the zaxis clearly shows better performance than PID. The tracking error from H∞ controller in the zaxis is within 177。 本文中 ,我們描述了一種微型三軸銑床及其數(shù)控系統(tǒng)。這兩部分通過一個(gè)雙向 RAM（隨機(jī)讀取存儲(chǔ)器）傳遞信息，兩部分的工作分配在這里進(jìn)行詳細(xì)的討論。為了估計(jì)微型機(jī)床基本的機(jī)械加工性能和剛度 ,我們?cè)O(shè)計(jì)了一個(gè)微型三軸銑床并將其作為測試機(jī)床。當(dāng)把 10N的力加載到 Z方向的加工位置處時(shí)， 數(shù)值計(jì)算結(jié)果表明 ,工作臺(tái)處位移改變量大約為 ,而背面的 Z方向偏差 小于 。 PC 部分用 MSWindows 和用戶輸入。目前，可供執(zhí)行的 G指令和 M指令有 G00（快速移動(dòng) ),G01(直線運(yùn)動(dòng) ),G02(順時(shí)針圓弧運(yùn)動(dòng)）、 G03（逆時(shí)針圓弧運(yùn)動(dòng)）、 G04（暫停）、 G17（選擇 x y平面 ),G18(選擇 ZX平面 ),G19(選擇 YZ平面）、 M21（輪廓開啟）、 M22（輪廓關(guān)閉）、 M30（程序結(jié)束和重置）。 DPRAM中的。成一個(gè)單一的平滑的運(yùn)動(dòng)不間斷地每一個(gè)終端。這表明所設(shè)計(jì)的微型三軸銑床擁有比傳統(tǒng)機(jī)床更高的固有頻率。 圖 1 三軸銑床及其參數(shù) 圖 2 三軸銑床圖 本文運(yùn)用了有限元模型對(duì)設(shè)計(jì)的三軸銑床進(jìn)行了有限元分析用以研究其靜態(tài)和動(dòng)態(tài)性能，如圖 3所示。第五部分給出結(jié)論。 數(shù)控系統(tǒng)用于操作三軸工作臺(tái)銑床，它包括一個(gè) G指令譯碼器，能實(shí)時(shí)編輯基本的 G指令和 M指令。 用于微型機(jī)械加工系統(tǒng)主要的技術(shù)單元有高速主軸系統(tǒng)、高精度進(jìn)給系統(tǒng)、協(xié)調(diào)運(yùn)動(dòng)控制系統(tǒng)、工裝和 chucking系統(tǒng)、框架設(shè)計(jì)以及基于高剛度優(yōu)化的模塊分配系統(tǒng)。 微型工廠是一個(gè)小型柔性制造系統(tǒng)，它所用的空間和能量相對(duì)傳統(tǒng)工廠要小得多，而且它適宜生產(chǎn) IT、 BT 和 NT產(chǎn)業(yè)中所需的微型 /中型尺寸的機(jī)械部件。這臺(tái)三軸銑床在真實(shí)加工試驗(yàn)中成功的現(xiàn)實(shí)了其加工性能。第四部分討論了一些現(xiàn)代控制方法如 H∞控制、成型控制、擾動(dòng)觀測器和非門控制的優(yōu)缺點(diǎn)。圖 2為三軸銑床的圖片。 XY軸的固有頻率大約為 400710 Hz，且其背部結(jié)構(gòu)大約為 440640 Hz。它顯示當(dāng)用戶界面程序讀取 G指令文件時(shí) G指令所描述的刀具路徑，當(dāng)前刀具位置也以小紅點(diǎn)的形式出現(xiàn)在屏幕上，所以數(shù)控用戶可以方便的判斷加工程序執(zhí)行到 G指令文件的哪個(gè)位置，用戶也可以使用線性輪廓功能 ,并將線段和弧的切線或近似切線合成為在每 個(gè)終點(diǎn)不間斷的單一平滑運(yùn)動(dòng)。 所有的預(yù)程序信息輸入 DPRAM然后遞給了 DSP程序。 圖 5 CNC系統(tǒng)的用戶界面 當(dāng)用戶點(diǎn)擊 G指令開啟 按鈕時(shí)，完整的 G指令文件讀取并保存在內(nèi)存區(qū)，然后 G指令出現(xiàn)在左下角列表框。 DSP部分每秒接受成千上萬的時(shí)鐘脈沖，譯成實(shí)時(shí)指令用于機(jī)床的每個(gè)軸并執(zhí)行伺服控制循環(huán)。它表明三軸銑床具有良好的剛度與其良好的結(jié)構(gòu)設(shè)計(jì)和一對(duì)支撐 X軸和 Y軸的 LM引導(dǎo)有關(guān)。圖 1顯示了該三軸銑床及其規(guī)格。 為了提高三軸銑床數(shù)控系統(tǒng)優(yōu)于傳統(tǒng) PID型控制方式的性能，我們對(duì)三軸銑床進(jìn)行了不同的控制方法的研究，包括 H∞控制、輸入成型控制、擾動(dòng)觀察器和非門控制器。這個(gè)三軸銑床作為一個(gè)微型工廠模塊用來生產(chǎn)高精度零件。 中文 6512 字 出處： International Journal of Precision Engineering and Manufacturing, 2020, 11(1): 3947 Development of a 3axis Desktop Milling Machine and a CNC System Using Advanced Modern Control Algorithms Kim B S, Ro S K, Park J K 1. Introduction As new fields such as IT(Information Technology), BT(Bio Technology) and NT(Nano Technology) emerge as a driving force in the industry, the interests in microfac