Content uploaded by Xu Chen
Author content
All content in this area was uploaded by Xu Chen on Dec 04, 2018
Content may be subject to copyright.
⇤
⇤
Rejecting fast narrow-band disturbances with slow sensor feedback for quality beam steering in selective laser sintering
Abstract
A fundamental problem arises in feedback control when the system is subject to fast disturbances but can only get slowly updated sensor feedback. The problem is particularly challenging when the disturbances have frequency components near or beyond the sensor's Nyquist sampling frequency. Such difficulties occur to selective laser sintering, an additive manufacturing process that employs galvo scanners to steer high-power laser beams and relies on non-contact, slow sensing such as visual feedback to enhance the product quality. In pursuit of addressing the fundamental challenge in quality control under slow sensor feedback, this paper introduces a multi-rate control scheme to compensate beyond-Nyquist disturbances with application to selective laser sintering. This is achieved by designing a special bandpass filter with tailored frequency response beyond the slow Nyquist frequency of the sensor, along with integrating model-based predictor that reconstructs signals from limited sensor data. Verification of the algorithm is conducted by both simulation and experimentation on a galvo scanner that directs the energy beam in the additive manufacturing process.
... • tracking a high-frequency sinusoid in regulating AC power current to a prespecified frequency (particularly in micro-grid systems), • rejection of high-frequency disturbance generated by disk rotation in hard-disk drives [3], [30], or • laser sintering manufacturing systems [9], [20], vision-guided high-speed controls [17], etc. Due to the limited resolution in time, such objectives have been regarded as either impossible or at least ill posed [27]. However, if we examine the sampling theorem, it is clear that the band-limitation below the Nyquist frequency is only a sufficient condition for perfect signal reconstruction. ...
... A related study concerning multiple signals was also given in [21] in a different setting. We also note that the recent article [20] has proposed a multirate control scheme to reject the disturbance beyond the Nyquist frequency in a mechatronic system. However, the optimized intersample behavior and the robustness are not addressed there. ...
This paper studies the problem of signal tracking and disturbance rejection for sampled-data control systems, where the pertinent signals can reside beyond the so-called Nyquist frequency. In light of the sampling theorem, it is generally understood that manipulating signals beyond the Nyquist frequency is either impossible or at least very difficult. On the other hand, such control objectives often arise in practice, and control of such signals is much desired. This paper examines the basic underlying assumptions in the sampling theorem and pertinent sampled-data control schemes, and shows that the limitation above can be removed by assuming a suitable analog signal generator model. Detailed analysis of multirate closed-loop systems, zeros and poles are given, which gives rise to tracking or rejection conditions. Robustness of the new scheme is fully characterized; it is shown that there is a close relationship between tracking/rejection frequencies and the delay length introduced for allowing better performance. Examples are discussed to illustrate the effectiveness of the proposed method here.
... For example, following a repetitive trajectory, the galvo scanner used in SLS directs a high-energy laser beam onto the surface of a powder bed to form a crosssection layer of a part. The laser-material interaction here happens in a short time scale (the laser beam moves at meters per second on the powder bed), and the scanning accuracy relates directly to the part quality [21]. In practice, however, various disturbance sources exist in the optical path, including, for example, mechanical vibrations of the platform and thermal fluctuations due to smoke and circulation of the inert gas in the process chamber. ...
... loop, and Q(z), the disturbance compensating filter. With the disturbance frequency information known, one can design Q(z) with the procedure provided in [21]. Our model-based information recovery (the MR block in Fig. 9) is applied to recover a fast disturbance estimated[n] using sparsely sampled disturbance estimatesd M [n] andd N [n]. ...
This paper considers the real-time recovery of a fast time series by using sparsely sampled measurements from sensors whose sampling speeds are prohibitively slow originally. Specifically, when the fast signal is an autoregressive process, we propose an online information recovery algorithm that reconstructs the dense underlying temporal dynamics fully by systematically modulating two slow sensors, and by exploiting a model-based fusion of the sparsely collected data. We provide the design of collaborative sensing and model-based information recovery algorithm, impacts of parameter choosing and model singularity, and methods to reduce computational complexity and increase prediction robustness. The proposed method is experimentally verified in an optical beam steering platform for additive manufacturing. Application to a closed-loop disturbance rejection problem reveals the feasibility to eliminate fast disturbance signals with the slow and not fully aligned sensor pair in real time, and in particular, the rejection of narrow-band disturbances whose frequencies are much higher than the Nyquist frequencies of the sensors.
This paper studies the problem of signal tracking and disturbance rejection for sampled-data control systems, where the pertinent signals can reside beyond the so-called Nyquist frequency. In light of the sampling theorem, it is generally understood that manipulating signals beyond the Nyquist frequency is either impossible or at least very difficult. On the other hand, such control objectives often arise in practice, and control of such signals is much desired. This paper examines the basic underlying assumptions in the sampling theorem and pertinent sampled-data control schemes, and shows that the limitation above can be removed by assuming a suitable analog signal generator model. Detailed analysis of multirate closed-loop systems, zeros and poles are given, which gives rise to tracking or rejection conditions. Robustness of the new scheme is fully characterized; it is shown that there is a close relationship between tracking/rejection frequencies and the delay length introduced for allowing better performance. Examples are discussed to illustrate the effectiveness of the proposed method here.
This paper discusses fractional-order repetitive control (RC) to advance the quality of periodic energy deposition in laser-based additive manufacturing (AM). It addresses an intrinsic RC limitation when the exogenous signal frequency cannot divide the sampling frequency of the sensor, e.g., in imaging-based control of fast laser-material interaction in AM. Three RC designs are proposed to address such fractional-order repetitive processes. In particular, a new multirate RC provides superior performance gains by generating high-gain control exactly at the fundamental and harmonic frequencies of exogenous signals. Experimentation on a galvo laser scanner in AM validates effectiveness of the designs.
In many laser processing applications, galvanometer scanners are integrated into a larger system that creates external disturbances to the actual laser-material interaction. To reject such disturbance with feedback-based control schemes, the sampling of the output needs to be fast enough to capture all major frequency components of the disturbance. In some applications, however, the sensor’s sampling speed is limited,
such that the disturbance is beyond the sampler’s Nyquist frequency. This paper introduces a multi-rate control scheme to fully reject narrow-band beyond-Nyquist disturbances in galvanometer scanner systems. The proposed algorithm consists
of a special bandpass filter with tailored frequency response, and a model-based predictor that reconstructs signals from limited sensor data. Verification of this algorithm is conducted by both simulated and experimental results on a commercial galvanometer scanner testbed.
Galvanometer scanners (GSs) are the most utilized optomechatronic systems for laser scanning. A GS consists of an oscillatory element (which includes the galvomirror) in a motor structure equipped with a positioning servo-system built usually in a closed-loop structure and controlled by different algorithms. Such structures have to provide speed and accuracy in the positioning of the laser beam or for raster scanning. Although tackled by numerous studies, on different aspects, this is still an open problem. The aim of this study is to approach it in a simple way and to provide a low cost solution to increasing accuracy by developing a structure which is more immune to disturbances than the classical one. In order to do this, a basic closed-loop GS which consists of a proportional-derivative (PD-L1) controller and a servo-motor is considered first. The mathematical model and the GS parameters are identified using a theoretical approach followed by experimental identifications. The extended control solution is developed starting from this basic GS structure by introducing a proportional-integrative (PI) controller in series with the PD-L1 controller of the GS; further on, a P-L1 reference filter is added to this new structure. In the absence of disturbances, both the basic and the extended control solutions show good tracking performances, but the basic solution is faster. In the presence of constant disturbances which can affect the servo-system, the latter structure (extended and filtered) has the best dynamical and tracking performances.
A fundamental challenge in digital control arises when the controlled plant is subjected to a fast disturbance dynamics but is only equipped with a relatively slow sensor. Such intrinsic difficulties are, however, commonly encountered in many novel applications such as laser- and electron-beam-based additive manufacturing, human–machine interaction, etc. This paper provides a discrete-time regulation scheme for exact sampled-data rejection of disturbances beyond Nyquist frequency. By introducing a model-based multirate predictor and a forward-model disturbance observer, we show that the inter-sample disturbances can be fully attenuated despite the limitations in sampling and sensing. The proposed control scheme offers several advantages in stability assurance and lucid design intuitions. Verification of the algorithm is conducted on a motion control platform that shares the general characteristics in several advanced manufacturing systems.
We study experimentally the effective duty cycle of galvanometer-based scanners (GSs) with regard to three main parameters of the scanning process: theoretical/imposed duty cycle (of the input signal), scan frequency, and scan amplitude. Sawtooth and triangular input signals for the device are considered. The effects of the mechanical inertia of the oscillatory element of the GS are analyzed and their consequences are discussed in the context of optical coherence tomography (OCT) imaging. When the theoretical duty cycle and the scan amplitude are increased to the limit, the saturation of the device is demonstrated for a useful range of scan frequencies by direct measurement of the position of the galvomirror. Investigations of OCT imaging of large samples also validate this saturation, as examplified by the gaps/blurred portions obtained between neighboring images when using both triangular and sawtooth scanning at high scan frequencies. For this latter aspect, the necessary overlap between neighboring B-scans, and therefore between the corresponding volumetric reconstructions of the sample, are evaluated and implemented with regard to the same parameters of the scanning process. OCT images that are free of these artifacts are thus obtained.
Iterative learning control (ILC) for a galvanometer scanner is proposed to achieve high speed, linear, and accurate bidirectional scanning for scanning laser microscopy. A galvanometer scanner, as a low stiffness actuator, is first stabilized with a feedback control compensating for disturbances and nonlinearities at low frequencies, and ILC is applied for the control of the fast scanning motion. For stable inversion of the non-minimum phase zeros, a time delay approximation and a zero phase approximation are used for design of ILC, and their attainable bandwidths are analyzed. Experimental results verify the benefits of ILC of its wide control bandwidth, enabling a faster, more linear, and more accurate scanning without a phase lag and a gain mismatch. At the scan rate of 4112 lines per second, the root mean square (RMS) error of the ILC can be reduced by a factor of 73 in comparison with the feedback controlled galvanometer scanner of the commercial system.
Thermal characteristics such as process temperatures and melt pool sizes offer important information in metal additive manufacturing (AM) technologies such as powder-bed electron beam additive manufacturing (EBAM). In this study, a near infrared (NIR) thermal imager was employed to acquire build surface process temperatures during EBAM fabrications using Ti-6Al-4V powder. Challenges in NIR temperature measurements for EBAM were tackled including compensating temperatures due to the transmission loss and estimating the emissivity of Ti-6Al-4V in its molten state. At a beam speed of about 728 mm/s, a beam current of about 7.2 mA and a diameter of 0.55 mm, the maximum process temperature is on the order of around 2700 °C, and the melt pools have dimensions of about 2.72 mm and 0.72 mm in length and width, respectively.
Due to the aliasing effect produced by the sampling operation, mechanical resonant modes beyond the Nyquist frequency are difficult to be identified using conventional system identification techniques. In this paper, a parametric approach is proposed to identify these resonances. Identification is performed in a closed-loop multirate sampled-data system, where the input is sampled integer times faster than the output. First, the polynomial transformation technique-based recursive least-squares algorithm with a dead-zone is designed to identify the mixed-rate model. Next, the identified mixed-rate model is used to compute the fast-rate model, from which the resonant modes beyond the Nyquist frequency can be extracted. The proposed approach is evaluated on the head-positioning servo control system of a hard disk drive during the track-seeking mode and the effectiveness is verified by both simulation and experimental results. As compared to analog sensors, the proposed approach can potentially be implemented to identify mechanical resonances to arbitrarily high frequencies by increasing the sampling rate of the digital-to-analog converter.
Most AM processes require post-processing after part building to prepare the part for its intended form, fit and/or function. Depending upon the AM technique, the reason for post-processing varies. For purposes of simplicity, this chapter will focus on post-processing techniques which are used to enhance components or overcome AM limitations. These include: