机械专业毕业论文外文翻译--三轴工作台铣床及运用先进现代控制算法(编辑修改稿)

机械专业毕业论文外文翻译--三轴工作台铣床及运用先进现代控制算法(编辑修改稿)内容摘要：

s, an averaged frequency response wasputed and a nominal continuoustime plant model was fitted. Fig. 6 shows the averaged frequency response and a nominal openloop plant model. A second order plant model was obtained from the curve fit. The identified openloop plant model G(s) forthe zaxis was We can see that the zaxis has a plex pole pair at around . When a PIDtype controller in a typical digital form of where u(k) is controller output, e(k) is error signal, T is samplingperiod, and z is a delay, is applied to the plant, it turns out that a high gain PID can easily excite the oscillatory mode of the plant. To avoid socalled derivative kick, the derivative gain Kd was forced to act on the derivative of the actual position, not on the derivative of the position error, . Kd (1z1)/T is multiplied by the negative position feedback, –y(k) instead of e(k) at Eq. (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。 5 μm over all areas. A feedforward controller such as ZPETC (ZeroPhase Error Tracking Control) takes approximately an inversion of plant dynamics and it requires an accurate plant model. In the yaxis, the feedforward controller was inserted to reduce the error peak at around 0 degree, where the air cylinder counteracting gravity force change its moving direction. It seems that the plant model of yaxis did not capture well the nonlinear characteristics of the air cylinder espe。