高度精度結構控制實驗室對於靜摩擦力和極限精密定位的研究已有多年，而且有不錯的研究成果。因此，希望能在應用到工業上時，能夠更有效率，能自動化鑑別馬達的靜摩擦階段的參數。
在靜摩擦階段，必須先自動鑑別出馬達的阻尼和較大界限(lower bound)的彈簧常數，所以必須使用曲線擬合(curve fitting)的方法來擬合在靜摩擦階段的非線性彈簧力矩對角位移的曲線。首先，使用二階和十階多項式來擬合，發現有反曲點的問題並不符合實際曲線，所以使用Hsieh 和 Pan[1]所提出的曲線方程式來擬合。在尋找最佳彈簧非線性曲線時，使用二分法(binary method)來尋找最佳曲線。
另外，由於受控廠的環境並不是不變的，常常會因為外界的干擾而改變參數，或是一開始所使用的系統參數就是不準確的。因此，必須設計出一套能即時偵測出參數變化的方法，即線上參數鑑別，即時的改變相對應的控制律，使得輸出能達到想要的規格。
所用的方法為，先從離線的參數鑑別所得到的參數當作一開始的預測值，然後從這些參數和其他輸出、輸入來預測下一個取樣時間(sampling time)的輸出。而實際的下一個取樣時間輸出減去預測的下一個取樣時間輸出就是系統參數不準造成的誤差。然後，使用梯度搜尋法(gradient search method)來預測這些參數的誤差，本文使用了正規梯度搜尋法(gradient search method)做線上參數鑑別和加權重梯度搜尋法做線上參數鑑別，並經由模擬和實驗驗證其結果。

For static friction identification, from Hsieh and Pan[1], there is a nonlinear spring in the static friction phase. So, use the equation that is represented by Hsieh and Pan[1] to fit the nonlinear spring curve via binary method.
For on-line identification, Use estimated output and actual output to get error, and use gradient search method with weighting and gradient search method without weighting to improve the motor parameters. If the motor parameters change or the intial motor parameters are wrong, we will find and use on-line identification to decrease the error between the actual parameters and the estimated parameters. With simulation and experiments, verify the above method.

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