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We have many servo systems that require nano/micro level positioning accuracy. This requirement sets a number of interesting challenges from the viewpoint of sensing, actuation, and control algorithms. This paper considers the control aspect for precision positioning. In motion control systems at nano/micro levels, it has been noted that the control algorithm should be customized as much as possible to the spectrum of disturbances. We will examine how prior knowledge about the disturbance spectrum should be utilized in the design of control algorithms and what are advantages of such prior knowledge. The algorithms will be evaluated on a simulated hard disk drive (HDD) benchmark problem and a laboratory setup for a wafer scanner that is equipped with a laser interferometer for position measurement.
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... It is worth noting that in the field of high precision motion control, the concept of disturbance observer (DOB)-based control with internal model principle has been recently explored to reject disturbances with unknown and/or time-varying spectra [7]. For example, a DOB-based algorithm has been formulated and implemented to a wafer-scanning process in lithography [8]. The fundamental idea of DOB control is to conduct an internal disturbance observation using model inversion and then to achieve disturbance cancelation by using an inner feedback control loop. ...
... Recall Eqs. (7) and (8). Based on the internal model principle [13], to asymptotically reject the disturbance, the following equation should be satisfied: ...
... where b 2 ð0; 1Þ. The design of B p ðbz À1 Þ is based on the damped pole-zero pair principle [7,8], which entertains the advantage of controlled waterbed effect in loop shaping. ...
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... Yet, as the attenuation width is increased further, the amplification of intermediate frequencies due to the waterbed effect also increases [23]. Additional design considerations are therefore necessary for achieving better performance, such as the gain scheduling and the use of a damped notch filter [24]. ...
... In the proposed quasi RC, N is designed to be an integer by shifting the fundamental frequency to the least common multiple (LCM) between itself and the sampling frequency, that is, N = f s /LCM f s , f 0 . The stability conditions for the wide-band and quasi RCs are the same as those for the plug-in RC design in [24], that is,P −1 z −1 , Q z −1 , and C z −1 belong to the set of stable, proper, and rational transfer functions. ...
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... DOB is a robust control technique to reject disturbances with guaranteed robust stability for linear system [18]. Moreover, given a stabilizing nominal controller, Q-filter in DOB can be an arbitrary stable filter to make the sensitivity function shaped as desired [19]. It has been applied to robust lateral trajectory tracking and its effectiveness has been verified by experiments [20]. ...
... We design Q as a second-order low-pass filter to reject lowfrequency disturbances, because κ s,ref should have relatively low frequency components for smooth reference trajectory. When modeling errors exist, we can use the robust control theorem to ensure robust stability [19]. However, modeling uncertainty between the linear model and the nonlinear model nonlinear model is involved in our problem, which complicates the analysis. ...
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... Disturbance observers usually update the control input via feedback compensation [5]- [7]. Youla parameterization can be parameterized either as an add-on compensation at the plant input side [8], [9], or a combined compensation at the plant input and controller input [10], [11]. In feedforwardrelated control, iterative learning control (ILC) [12]- [16] and adaptive or sensor-based feedforward compensation [17]- [19] can be configuraed as add-on algorithms either at the plant input or at the reference input. ...
... and Y (s, e i ) are, respectively, the Laplace transforms of the natural transient and the transient due to input discontinuity. Using (9) gives ...
... Inheriting from the plug-in RC design, the stability conditions for the wide-band and quasi RCs are:̂− 1 ( ), ( ), and ( ) belong to the set of stable, proper, and rational transfer functions (Chen & Tomizuka, 2013). ...
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... These error sources are difficult, or infeasible, to eliminate completely by better mechanical designs. For instance, the interference between the galvo mirrors is intrinsic to the beam-steering mechanism; and vibrations in a complex mechanical system is unavoidable [2][3][4]. ...
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... Either for general low-frequency enhancement [5]- [7], or for the extensions to structured disturbance rejection [8]- [10], disturbance observers usually update the commands at the input side of the plant. Youla parameterization can be parameterized either as an add-on compensation at the plant input side [11], [12], or a combined compensation at the plant input and controller input [13], [14]. In feedforward-related control, adaptive or sensorbased feedforward compensation [15]- [17] can be configured Tianyu Jiang (email: tianyu.jiang@uconn.edu) ...
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