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Optimal Decoupled Disturbance Observers for Dual-Input Single-Output Systems
Abstract and Figures
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 ...
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 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). ...
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. ...
This paper presents a disturbance observer (DOB) design methodology, which is applicable to both multi-input-multi-output (MIMO) and non-minimum phase systems. The DOB is designed via minimizing H∞ norm of closed-loop dynamics from disturbance to its estimation error. This proposed design methodology returns the optimal stable plant inverse and Q filter with guaranteed closed loop stability for a given baseline feedback system, which is more efficient than manual design and tunning that involves lots of effort for either MIMO or non-minimum phase systems. Furthermore, it utilizes well-established H∞ synthesis in robust control theory, and can be further transformed to a convex optimization problem with linear matrix inequality (LMI) constraints and solved efficiently using existing software thereafter. This design methodology unifies all cases of single-input-single-output (SISO) and MIMO systems, as well as minimum-phase and non-minimum-phase systems into one design framework, which lays theoretical fundamental for developing potential DOB design toolbox for a general system. This paper also considers measurement noise, which may severely decrease the DOB's performance. To address this issue, besides the original control channel from disturbance to its estimation error, this paper adds an additional channel when formulating the H∞ optimization problem. This design methodology is comprehensively analyzed, and applied to a tail-sitter UAV platform that possesses a non-minimum phase angular rate dynamics. Both simulation and experiment show that the designed DOB successfully estimates and suppresses external disturbances in the presence of measurement noise.
Processes with multiple inputs and a single output are usual in industries. These processes present more than one actuator driving a single process variable. Analyzing a Two- Input Single-Output (TISO) process that is composed of two actuators to achieve a single process variable. Recent literature presents a Single-Input Two-Output (SITO) controller strategy, based on the Proportional (P) and Integral (I) control actions separated and paired individually, thus changing the nature of a PI-SISO (Single-Input Single-Output) to a PI-SITO. However, in the literature, it was not justified the choice of the pairing of the control actions, it was possible to observe the literature it was adopted a bias for the Proportional action, but it was not demonstrated how to choose the value of the bias. In this sense, the present study explains the matching of control actions and proposes a systematic methodology for bias selection. This adopted analyses utilizing mathematical deductions and experiments, employing computer simulations. The present study delivers the justification for the pairing of control actions proposed in the literature and a precept of the bias choice enabling an achievable implementation of the PI-SITO controller.
Disturbance-observer-based control is a well-known technique for the rejection of unmeasurable disturbances. The application of disturbance-observer-based control is well established for single-input and single-output systems but presents two challenges when applied to multivariable systems with time delays. The first challenge is the calculation of the inverse of the nominal model. The second challenge is the optimal synthesis of the disturbance observer filter to obtain a trade-off between the disturbance rejection and measurement noise attenuation. In this paper, we propose strategies to address these two challenges. To facilitate the design and implementation of the disturbance observer, we propose to approximate the inverse of the nominal model by employing the concept of equivalent transfer function. The equivalent transfer function approximates the inverse of a multivariable model by a matrix whose elements are the inverse of first-order plus time delay transfer functions, that are simpler to deal with. To tackle the second challenge, we propose a synthesis formulation based on a multi-objective optimization problem. Through a multi-objective evolutionary optimization algorithm, it is possible to obtain a set of efficient solutions with different trade-offs between the two objectives. We apply the proposed strategies to two well-known problems in the field of process control to demonstrate its efficiency. We verify that the use of the equivalent transfer function presents the best results in comparison to other methodologies considering the three control objectives: tracking of reference signals, rejection of disturbances, and attenuation of measurement noises.
In preview-based vehicle suspension applications, the preview of the road profile is highly dependent on the preview sensors. In some scenarios such as heavy traffic situations, the preview of road profile can only be estimated by other vehicles because the view of the preview sensors may be blocked by other vehicles. The estimated preview road information can contain errors, which thus requires the controller to have a good robust performance. In this paper, an incremental model predictive control strategy for active suspension systems along with a road profile estimator using preview information from a lead vehicle is proposed. The efficacy of the proposed strategy is experimentally validated on two active suspension stations with comparison to two conventional active suspension control approaches.
In the ground-based astronomical telescope, the imaging quality is usually affected by tip-tilt vibrations induced by the telescope structure. Long exposure time of the image sensor is usually required for a good signal-to-noise ratio, which brings the amount of time delays into the control loop of the tip-tilt mirror. Thus, a low control bandwidth is insufficient to compensate telescope vibrations. In this paper, an improved disturbance observer (DOB) control based on only the image sensor is proposed to reject structural vibrations. This new DOB controller is added into the original loop in the tip-tilt mirror control system, so the closed-loop performance can be optimized by designing an appropriate Q-filter. An improved Q-filter is presented to reject large-magnitude vibrations and also to reduce amplifications induced by this controller at nondisturbance frequencies. This proposed controller can achieve a satisfying result in vibration mitigations when vibration frequencies are provided to design the Q-filter. Furthermore, in the tilt-tilt mirror control system, this improved DOB is not restricted by an accurate model such that noise in the loop cannot provide serious influence on vibration mitigation. Both simulations and extensive experiments are carried out to demonstrate that the DOB can earn an extra improvement on the control performance in comparisons with the conventional feedback controller.
Many servo systems require micro/nano-level positioning accuracy. This requirement sets a number of challenges from the viewpoint of sensing, actuation, and control algorithms. This article considers control algorithms for precision positioning. We examine how prior knowledge about the parameterization of control structure and the disturbance spectrum should be utilized in the design of control algorithms. An outer-loop inverse-based Youla–Kucera parameterization is built in the article. The presented algorithms are evaluated on a tutorial example of a galvo scanner system.
This paper presents an overview of a linear matrix inequality
(LMI) approach to the multiobjective synthesis of linear output-feedback
controllers. The design objectives can be a mix of H∞
performance, H2 performance, passivity, asymptotic
disturbance rejection, time-domain constraints, and constraints on the
closed-loop pole location. In addition, these objectives can be
specified on different channels of the closed-loop system. When all
objectives are formulated in terms of a common Lyapunov function,
controller design amounts to solving a system of linear matrix
inequalities. The validity of this approach is illustrated by a
realistic design example
The disturbance observer (DOB) has been one effective robust control approach for servo enhancement in single-input-single-output systems. This paper presents a new extension of the DOB idea to dual-input-single-output systems, and discusses an optimal Q-filter design. The proposed decoupled disturbance observer (DDOB) provides a flexible approach to use the most suitable actuators for compensating disturbances at different frequencies. Such a scheme 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 audio vibrations.
In this paper, an adaptive control scheme is developed to reject unknown multiple narrow-band disturbances in a hard disk drive. An adaptive notch filter is developed to efficiently estimate the frequencies of the disturbance. Based on the correctly estimated parameters, a disturbance observer with a newly designed multiple band-pass filter is constructed to achieve asymptotic perfect rejection of the disturbance. Evaluation of the control scheme is performed on a benchmark problem for HDD track following.
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.
This paper proposes a path-tracking algorithm to compensate for path deviation due to torque limits. The algorithm uses a disturbance observer with an additional saturation element at each joint of n degrees of freedom (DOF) manipulator to obtain a simple equivalent robot dynamic (SERD) model. This model is represented as an n independent double integrator system and is designed to ensure stability under input saturation. For an arbitrary trajectory generated for a given path in Cartesian space whenever any of the actuators is saturated, the desired acceleration of the nominal trajectory in Cartesian space is modified on-line by using SERD. An integral action with respect to the difference between the nominal and modified trajectories is utilized in the nonsaturated region of actuators to reduce the path error. To verify the effectiveness of the proposed algorithms, real experiments were performed for a two DOF SCARA-type direct-drive arm.
This paper discusses the design and implementation of two track-following controllers for dual-stage hard disk drive servo systems. The first controller is designed by combining an outer loop sensitivity-decoupling (SD) controller with an inner loop disturbance observer (DOB). The second is designed by combining mixed H2/H∞ synthesis techniques with an add-on integral action. The designed controllers were implemented and evaluated on a disk drive with a PZT-actuated suspension-based dual-stage servo system. Position error signal (PES) for the servo system was obtained by measuring the slider displacement with an LDV and injecting a simulated track runout.
In this paper the disturbance attenuation and rejection problem is investigated for a class of MIMO nonlinear systems in the disturbance-observer-based control (DOBC) framework. The unknown external disturbances are supposed to be generated by an exogenous system, where some classic assumptions on disturbances can be removed. Two kinds of nonlinear dynamics in the plants are considered, respectively, which correspond to the known and unknown functions. Design schemes are presented for both the full-order and reduced-order disturbance observers via LMI-based algorithms. For the plants with known nonlinearity, it is shown that the full-order observer can be constructed by augmenting the estimation of disturbances into the full-state estimation, and the reduced-order ones can be designed by using of the separation principle. For the uncertain nonlinearity, the problem can be reduced to a robust observer design problem. By integrating the disturbance observers with conventional control laws, the disturbances can be rejected and the desired dynamic performances can be guaranteed. If the disturbance also has perturbations, it is shown that the proposed approaches are infeasible and further research is required in the future. Finally, simulations for a flight control system is given to demonstrate the effectiveness of the results. Copyright © 2005 John Wiley & Sons, Ltd.
