【正文】 q. (2). For the zaxis, using the derivative of position instead of that of position error allowed more aggressive PID gains. Based on the plant model at Eq. (1), the control loop employed an H∞ robust controller at 2 kHz sampling frequency. A mixed sensitivity problem was solved to design an H∞ controller in continuoustime and the resulting continuous time controller was converted to a discretetime model. The mixed sensitivity specification for H∞ control design in continuoustime 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。 微型工廠是一個小型柔性制造系統(tǒng)，它所用的空間和能量相對傳統(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。研究人員一直在試圖將微型技術(shù)與構(gòu)建生產(chǎn)微型 /中型精準(zhǔn)件的微型工廠系統(tǒng)結(jié)合起來滿足制造業(yè)的需求。這個三軸銑床作為一個微型工廠模塊用來生產(chǎn)高精度零件。從有限元分析和沖擊錘測試中，我們已經(jīng)證實了它有很好的結(jié)構(gòu)剛度和高的固有頻率。這臺三軸銑床在真實加工試驗中成功的現(xiàn)實了其加工性能。該數(shù)控系統(tǒng)由兩部分組成，一個是在 Windows系統(tǒng)下的用戶界面，另一個是可加入指令并執(zhí)行實時伺服控制的 DSP 程序。 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、擾動觀察器和非門控制器。這部分給出了通過沖擊錘測試得到的有限元分析和固有頻率的結(jié)果。第四部分討論了一些現(xiàn)代控制方法如 H∞控制、成型控制、擾動觀測器和非門控制的優(yōu)缺點。 2. 三軸銑床設(shè)計 微型機(jī)床要求具有很高的加工精度，同時要提供足夠的剛度。圖 1顯示了該三軸銑床及其規(guī)格。垂直方向的 XY軸由電機(jī)驅(qū)動， Z軸由 磁力預(yù)緊空氣軸承和 直流電機(jī)控制，空氣主軸轉(zhuǎn) 速可達(dá) 160,000rpm，足以用于高精度加工。圖 2為三軸銑床的圖片。 計算結(jié)果表明 ,由于其自身重量撓度微不足道。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)計和一對支撐 X軸和 Y軸的 LM引導(dǎo)有關(guān)。測得的固有頻率并不與計算所得完全一致，但是指定的頻率范圍從沖擊錘測試的有限元 模態(tài)分析來看是類似的。 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。 圖 4 沖擊錘測試下的頻率響應(yīng)函數(shù) 表 1 沖擊錘測試下的固有頻率 3 數(shù)控系統(tǒng) 圖形用戶界面程序 基于 PC的數(shù)控系統(tǒng)用于三軸銑床，該數(shù)控系統(tǒng)由兩部分組成， PC中的圖形用戶界面程序和 DSP中的 DSP程序。 DSP部分每秒接受成千上萬的時鐘脈沖，譯成實時指令用于機(jī)床的每個軸并執(zhí)行伺服控制循環(huán)。 圖 5為數(shù)控系統(tǒng)的圖形用戶界面及其簡要解釋。它顯示當(dāng)用戶界面程序讀取 G指令文件時 G指令所描述的刀具路徑，當(dāng)前刀具位置也以小紅點的形式出現(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終點不間斷的單一平滑運動?？刂瓶梢栽诔绦蜻\行時手工開啟或關(guān)閉，或者可以運用程序中 M21和 M22指令來控制開啟和關(guān)閉。 圖 5 CNC系統(tǒng)的用戶 界面 當(dāng)用戶點擊 G指令開啟按鈕時，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。在執(zhí)行 G指令行期間，用戶界面程序開始計算、平面運動、驅(qū)動軸、 允許的最大速度和加速度 ,起始位置的減速、方向余弦定理。 所有的預(yù)程序信息輸入 DPRAM然后遞給了 DSP程序。 當(dāng)用戶界面程序發(fā)現(xiàn) DSP程序執(zhí)行完畢 G指令并空出空間時，它將按照順序把新的預(yù)程序 G指令填入緩沖