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The disturbance observer (DOB) has been a popular robust control approach for servo enhancement in single-input single-output systems. This paper presents a new extension of the DOB idea to dual-and multi-input single-output systems, and discusses an optimal filter design technique for the related loop-shaping. The proposed decoupled disturbance observer (DDOB) provides the flexibility to use the most suitable actuators for compensating disturbances with different spectral characteristics. Such a generalization is helpful, e. g., for modern dual-stage hard disk drives, where enhanced servo design is becoming more and more essential in the presence of vibration disturbances.
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... A narrow notch in the error-rejection function can no longer provide sufficient attenuation; yet a wide notch tends to cause undesired amplification at other frequencies due to the fundamental waterbed limitation of feedback control [16]- [18]. In view of such challenges, the authors proposed an infinite-impulseresponse (IIR) filter design in DOB to control the waterbed effect manually [15], [19] and optimally [20]; such a design also benefits narrow-band disturbance rejection, and underpins first-tier results [21], [22] in an international benchmark on adaptive regulation [12]. [23] provides additional comparison of the DOB framework with peak filter algorithms. ...
... It balances the preferred disturbance attenuation and undesired amplification with minimum position errors. As an extension to our previous work [18]- [20], [24]- [26], this paper contributes in three aspects: (i) the adaptive controller design covers both single and dual-stage HDDs; (ii) wide-band disturbances with the important extension to multiple spectral peaks are addressed; and (iii) experimental verification on a Voice-Coil-Driven Flexible Positioner (VCFP) system is performed. ...
... where T is the nominal complementary sensitivity function satisfying T = 1 − S. After substituting in (3), (20) becomes ...
Article
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Closed-loop disturbance rejection without sacrificing overall system performance is a fundamental issue in a wide range of applications from precision motion control, active noise cancellation, to advanced manufacturing. The core of rejecting band-limited disturbances is the shaping of feedback loops to actively and flexibly respond to different disturbance spectra. However, such strong and flexible local loop shaping (LLS) has remained underdeveloped for systems with nonminimum-phase zeros due to challenges to invert the system dynamics. This article proposes an LLS with prescribed performance requirements in systems with nonminimum-phase zeros. Pioneering an integration of the interpolation theory with a model-based parameterization of the closed loop, the proposed solution provides a filter design to match the inverse plant dynamics locally and, as a result, creates a highly effective framework for controlling both narrowband and wideband vibrations. From there, we discuss methods to control the fundamental waterbed limitation, verify the algorithm on a laser beam steering platform in selective laser sintering additive manufacturing, and compare the benefits and tradeoffs over the conventional direct inverse-based loop-shaping method. The results are supported by both simulation and experimentation.
... The control scheme in Fig. 2 can be easily extended to dual-stage HDD systems using the decoupled DOB technique as in [19]. Fig. 4 shows one example design for the dual-stage case, where P i (z −1 ) and C i (z −1 ) (i = 1, 2) represent the two actuators (voice coil motor for the first stage and piezoelectric actuator for the second) and the corresponding baseline feedback controllers, respectively. ...
... and the sensitivity function satisfies [19] S ...
... Suppose that d(k) generates vibrations with n unknown wide spectral peaks, then based on (19), (21) suggests that e(k) is also a function of parameters in θ = [cos ω 1 , . . . , cos ω n , α l 1 , . . . ...
... The control scheme in Fig. 2 can be easily extended to dual-stage HDD systems using the decoupled DOB technique as in [19]. Fig. 4 shows one example design for the dual-stage case, where P i (z −1 ) and C i (z −1 ) (i = 1, 2) represent the two actuators (voice coil motor for the first stage and piezoelectric actuator for the second) and the corresponding baseline feedback controllers, respectively. ...
... and the sensitivity function satisfies [19] S ...
... Suppose that d(k) generates vibrations with n unknown wide spectral peaks, then based on (19), (21) suggests that e(k) is also a function of parameters in θ = [cos ω 1 , . . . , cos ω n , α l 1 , . . . ...
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For safe and efficient planning and control in autonomous driving, we need a driving policy which can achieve desirable driving quality in long-term horizon with guaranteed safety and feasibility. Optimization-based approaches, such as Model Predictive Control (MPC), can provide such optimal policies, but their computational complexity is generally unacceptable for real-time implementation. To address this problem, we propose a fast integrated planning and control framework that combines learning- and optimization-based approaches in a two-layer hierarchical structure. The first layer, defined as the "policy layer", is established by a neural network which learns the long-term optimal driving policy generated by MPC. The second layer, called the "execution layer", is a short-term optimization-based controller that tracks the reference trajecotries given by the "policy layer" with guaranteed short-term safety and feasibility. Moreover, with efficient and highly-representative features, a small-size neural network is sufficient in the "policy layer" to handle many complicated driving scenarios. This renders online imitation learning with Dataset Aggregation (DAgger) so that the performance of the "policy layer" can be improved rapidly and continuously online. Several exampled driving scenarios are demonstrated to verify the effectiveness and efficiency of the proposed framework.
... However, this introduced plant modeling errors and the stability was difficult to guarantee. An alternative method proposed in [18] first decoupled the system using the nominal model of the plant and then followed the conventional DOB design procedure for SISO systems. These techniques did not mitigate the issue of designing a good plant inverse in the DOB design. ...
... The weighting filters W v (z) and W m (z) are designed based on the frequency characteristics of the disturbance in both the VCM and the PZT loops. Similar to the assumption made in [18], it is assumed that the disturbance in the VCM loop focuses around 1000 Hz and that the disturbance in the PZT loop focuses around 2500 Hz. Therefore, W v (z) and W m (z) are designed as band-pass filters or peak filters centered around 1000 Hz and 2500 Hz respectively. ...
... The DOB design for MIMO systems is not an easy process either. DOBs for MIMO systems have been designed either by (1) ignoring the coupling effect of different input-output channels of the plant (e.g., [18]), or by (2) decoupling the plant using the nominal model and then following the standard DOB design procedure for SISO systems (e.g., [19]). Most of these DOB design techniques for MIMO systems are only applicable to the systems with the same input and output dimensions (i.e., square systems). ...
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This paper presents a generalized disturbance observer (DOB) design framework that is applicable to both multi-input-multi-output (MIMO) and non-minimum phase systems. The design framework removes conventional DOB's structure constraint, which allows minimizing the H-infinity norm of the dynamics from disturbance to its estimation error over a larger feasible set. The design procedure does not require explicit plant inverse, which is usually challenging to obtain for MIMO or non-minimum phase systems. Furthermore, the generalized DOB is augmented by a learning scheme, which is motivated by iterative learning control, to further enhance disturbance estimation and suppression. Both numerical and experimental studies are performed to validate the proposed learning-based DOB design framework.
... To address this problem, X. Chen et. al [6] consider a class of multiinput-single-output (MISO) system and first decouple the nominal system plant model into a form that no cross-channel coupling presents. DOB design on the decoupled system then follow the conventional DOB design procedure for SISO systems. ...
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The hard disk drive is one of the finest examples of the precision control of mechatronics, with tolerances less than one micrometer achieved while operating at high speed. Increasing demand for higher data density as well as disturbance-prone operating environments continue to test designers’ mettle. Explore the challenges presented by modern hard disk drives and learn how to overcome them with Hard Disk Drive: Mechatronics and Control. Beginning with an overview of hard disk drive history, components, operating principles, and industry trends, the authors thoroughly examine the design and manufacturing challenges. They start with the head positioning servomechanism followed by the design of the actuator servo controller, the critical aspects of spindle motor control, and finally, the servo track writer, a critical technology in hard disk drive manufacturing. By comparing various design approaches for both single- and dual-stage servomechanisms, the book shows the relative pros and cons of each approach. Numerous examples and figures clarify and illustrate the discussion. Exploring practical issues such as models for plants, noise reduction, disturbances, and common problems with spindle motors, Hard Disk Drive: Mechatronics and Control avoids heavy theory in favor of providing hands-on insight into real issues facing designers every day.
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