Phase Error Tracking Research Articles

Perfect Tracking Control with Discrete-Time LQR for a Non-Minimum Phase Electro-Hydraulic Actuator System

Abstract This paper presents a perfect tracking control for discrete-time nonminimum phase of electro-hydraulic servo (EHS) system by adopting a combination of feedback and feedforward controller. A linear-quadratic-regulator (LQR) is firstly design as a feedback controller and a feedforward controller is then proposed to eliminate the phase error emerge by the LQR controller during the tracking control. The feedforward controller is develop by implementing the zero phase error tracking control (ZPETC) technique which the main difficulty arises from the non-minimum phase system is have no stable inverse. Subsequently, the controller is applied to EHS system which is represented in discrete-time model where the model is obtained experimentally using system identification method. The proposed controller design using ZPETC is particularly suited to the various positioning control applications that encounter non-minimum phase problem. It is also shows that the controller offers good performance in reducing phase and gain error that typically occur in positioning or tracking systems.

Spiral Servo Writing in Hard Disk Drives Using Iterative Learning Based Tracking Control

AbstractThe servo control in a hard disk drive (HDD) system relies heavily on the position information obtained from the servo sectors. As the tracks-per-inch (TPI) gets higher and higher in HDDs, writing of servo sectors takes a longer and longer time. One way to solve this problem is to use servo track writers to write spiral servo patterns on the disks and then perform self servo writing (SSW) within each HDD unit. The quality of the spirals is the key to achieve high TPI in SSW. This paper discusses high precision tracking control algorithms for the writing of spiral servo patterns. An iterative learning scheme is introduced, which combines a disturbance observer with the zero phase error tracking algorithm, and develops a new way of designing asymptotically optimal feedforward inputs for a general two degree of freedom control systems. In learning control schemes, non-repetitive disturbances have an adverse influence on the tracking performance. The paper analyzes this situation, and develops a robust learning scheme to deal with the problem.

An analysis of delay-locked loop tracking binary Markovian sequence in the presence of multiple access interference and channel noise

This paper presents an analysis of delay-locked loops in direct spreading code division multiple access systems with Markovian spreading sequences. The established analysis with piecewise constant approximation is similar to the mean field analysis which estimates macroscopic characteristics of a spatially-distributed probabilistic system from the local interaction between the elements of the system with low computational complexity. The low complexity makes it possible to analyze the behavior of not only second-order archetype delay-locked loops but also higher-order non-coherent delay-locked loops in the presence of both multiple access interference and channel noise. It is found from the presented analysis that replacing i.i.d. spreading sequences with Markovian spreading sequences with non-vanishing negative autocorrelation reduces the phase tracking error of a non-coherent 1Δ delay-locked loop. The time spent for estimating the error by the presented method is about 1/1000 compared with that by the path integral method.

Enhanced feedforward control of non-minimum phase systems for tracking predefined trajectory

This article proposes a novel feedforward controller for non-minimum phase systems by utilising the preview information of the desired trajectory. The performance of the proposed controller is analysed theoretically and verified through the simulation, including comparison with the optimal zero phase error tracking controller and the preview-based stable inversion. The simulation results show that the proposed controller can gain outstanding performance even if the preview time of the desired trajectory is limited.

Compound Control for Hydraulic Flight Motion Simulator

The design of a compound control is presented for the servo system of hydraulic flight motion simulator, which suffers from highly nonlinear dynamics, large parameter time-variation and severe load coupling among channels. The compound control is composed of a robust feedback controller and a feedforward compensator. The design aim is to achieve high tracking performance even in the presence of considerable uncertainty, external disturbance and load coupling among channels. Toward this aim the feedback controller for rejecting perturbation and disturbance is designed by using μ synthesis optimization technique and the feedforward compensator for compensating time lag of dynamic system is established based on the basic idea of zero phase error tracking. To validate the proposed control strategy, simulations and experiments are implemented, and show that the resulting system is highly robust against model perturbation and possesses excellent capability of suppressing the load coupling and improving the tracking performance.

Closed-Loop Identification and Composed Controller Design for Precise Machining

For a class of three-loop architecture motion control system, two-stage close-loop identification is introduced to estimate the control plant and thus to tune the velocity controller. Based on the estimated model, PID position controller with derivative filter is proposed using pole-zero cancellation and pole assignment. Feed-forward compensators such as Velocity and Acceleration Feed-forward Controller (VAFC), Zero Phase Error Tracking Controller (ZPETC), Zero Magnitude Error Tracking controller (ZMETC) are introduced as well, and their effects are compared.

Efficient Phase-Error Suppression for Multiband OFDM-Based UWB Systems

This paper proposes an efficient phase-error suppression scheme for multiband (MB) orthogonal frequency-division multiplexing (OFDM)-based ultrawideband (UWB) communication systems. The proposed scheme consists of a clock-recovery loop and a common phase-error (CPE) tracking loop. The clock-recovery loop performs estimation of the sampling frequency offset (SFO) and its 2-D (time and frequency) compensation, while the CPE tracking loop estimates and corrects the phase errors caused by residual carrier frequency offset (CFO), residual SFO, and phase noise (PHN). The SFO and CPE estimators employ pilot-tone-based and channel-frequency-response (CFR)-weighted low-complexity approaches, each of which uses a robust error-reduction scheme without using angle calculations or divisions. Analytical results and numerical examples show the effectiveness of the proposed scheme in different multipath fading scenarios and signal-to-noise ratio (SNR) regimes.

Development and Assessment of a Novel Decoupled XY Parallel Micropositioning Platform

This paper presents the development and performance assessment procedures for a new <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">XY</i> parallel micropositioning platform (PMP) aiming at a submicrometer accuracy for microscale manipulation. The uniqueness of the proposed micro-parallel platform lies in that it possesses an uncomplicated structure as well as actuation isolation and output motion decoupling properties, which facilitates the adoption of two single-input-single-output controllers. Based on the matrix method, the kinetostatics models of the PMP are established and verified by finite-element analysis. Via system identification, a digital lag--lead compensator is designed to compensate for the hysteresis of each piezoelectric actuator. A feedforward control is then implemented to construct a zero phase error tracking controller. Positioning performance of the PMP in terms of resolution, accuracy, repeatability, and contouring performances of 1-D and 2-D motions has been evaluated by several experimental studies. Experimental results not only validate the effectiveness of the designed controller but also show that both positioning and contouring of the PMP can achieve a submicrometer precision within a specified velocity range.

Steady-state analysis of delay-locked loops tracking binary Markovian sequences

We analyze stationary phase tracking error of delay-locked loops (DLL) in direct spread code division multiple access (DS-CDMA) using Markovian spreading sequences. The phase tracking error is caused by noise generated inside of DLLs by multiple access interferences. When binary Markovian sequences are used, the noise is not considered as white Gaussian noise. This makes analysis of the tracking error difficult. In this paper, we describe DLLs by stochastic difference equations and derive forward evolutional equations of the probability distribution of the states of DLLs. Applying path integral analysis to the evolutional equations, we obtained stationary distribution. We found from the distribution that Markovian spreading sequences with negative eigenvalue were effective in decreasing stationary phase tracking error of not only a type of DLL in asynchronous CDMA but also DLLs in chip-synchronous CDMA.

4C15 Feed-Forward Robust Controller Design with ZPETC-PDF Method for Seesaw Type Swing Arm Actuator

A micro holographic optical pickup head is designed to miniaturize the optical configuration which provides a better approach for portable application. This optical module is then mounted on the seesaw type swing arm actuator for focusing and tracking operation in small form factor optical disk drive. In high-speed tracking and high track density servo system, the conventional feedback control system, such as Lead-Lag control, is not enough to reduce residual tracking error and reject the disturbance interference. For this reason, we presented a method that using the zero phase error tracking (ZPET) control to improve the system performance such as the transient response and system bandwidth, also combined with Pseudo-Derivative Feedback (PDF) control block to provide stiffness and overcome low frequency disturbances, such as friction.

Robust Feedforward Tracking Control Suppressing Harmonics Disturbance and DC Offset for Optical Disk Recording System

This paper proposes a new robust feedforward tracking control system suppressing tracking error including harmonics disturbance and DC offset for optical disk recording system. The proposed tracking control system consists of triple compensation loops of tracking error which are the robust feedback control loop, a new harmonics disturbance suppression loop based on Zero Phase Error Tracking(ZPET) feedforward control and a new additional DC offset compensation loop. The feedback controller is the most inner loop which is based on the high gain servo system. The harmonics disturbance suppression loop based on ZPET control is the middle loop which suppresses the influence of many periodic disturbances. The final outer loop is a new additional DC offset compensation loop which suppresses the DC offset caused by ZPET feedforward control. The experimental results point out that the proposed system well realizes the fine tracking performance for optical disk recording system.

Quantitative feedback theory and zero phase error tracking control combined robust control for radar truck leveling simulator

Radar leveling system is the key equipment for improving the radar mobility and survival capability. A combined quantitative feedback theory (QFT) controller is designed for the radar truck leveling simulator in this paper, which suffers from strong nonlinearities and system parameter uncertainties. QFT can reduce the plant uncertainties and stabilize the system, but it fails to obtain high-precision tracking. This drawback can be solved by a robust QFT control scheme based on zero phase error tracking control (ZPETC) compensation. The combined controller not only possesses high robustness, but greatly improves the system performance. To verify the effectiveness and the potential of the proposed controller, a series of experiments have been carried out. Experimental results have demonstrated its robustness against a large range of parameters variation and high tracking precision performance, as well as its capability of restraining the load coupling among channels. The combined QFT controller can drive the radar truck leveling platform accurately, quickly and stably.

Nonminimum Phase Dynamic Inversion for Settle Time Applications

Single-track hard disk drive (HDD) seek performance is measured by settle time, ts. In this paper, we show the effective use of feedforward dynamic inversion, coupled with reference trajectory yd generation, to achieve high performance ts. Models of HDD dynamics are typically nonminimum phase (NMP), and it is well known that the exact tracking solution for NMP systems requires noncausal preactuation to maintain bounded internal signals. In the specific HDD operating modes of interest, anticipation of a seek command is unrealistic, and thus preactuation adds to the overall computation of settle time. Unlike many dynamic inversion tracking applications, this negative effect of preactuation leads to interesting trade-offs between preactuation delay, yd tracking accuracy, and achievable settle performance. We investigate multiple single-input single-output (SISO) inversion architectures, and we show that the feedforward closed-loop inverse (FFCLI) achieves superior settle performance to the feedforward plant inverse (FFPI) in our application because FFCLI does not excite the closed-loop dynamics. Using the FFCLI architecture, we further investigate numerous NMP inversion algorithms, including both exact inversion schemes with initial condition preloading and stable approximate NMP inverse techniques. We conclude that the settle performance of the zero-order Taylor series stable NMP approximation matches the best performance of the exact inversion techniques in our application, and does so without the high frequency excitation required by the zero magnitude error tracking controller (ZMETC), or the excessive preactuation required by the zero phase error tracking controller (ZPETC). Minimum energy optimal trajectory generation methods show that the system order n is a limiting factor in settle performance. This confirms that the zero-order series method, which is capable of producing settle times in less than n samples, is on par with optimal approaches yet much simpler to implement. Multiple NMP inversion algorithms are experimentally validated on a servo track writer (STW), which reinforces the general trends observed in ideal simulations.

A DLL With Jitter Reduction Techniques and Quadrature Phase Generation for DRAM Interfaces

A DLL featuring jitter reduction techniques for a noisy environment is described. It controls a loop response mode by monitoring the magnitude of input jitter caused by supply noise. This technique varies the probability of phase error tracking. It reduces the output jitter of the DLL due to a low effective variance of input phase error and a narrow effective loop bandwidth. The DLL is implemented in a 0.13 mum CMOS process. Under noisy environments, the output clock of 1 GHz has 4.58 ps RMS and 29 ps peak-to-peak jitter.

Determining scintillation effects on GPS receivers

Although formulae are available to determine tracking jitter (variance of the phase tracking error at the output of the Global Navigation Satellite Systems receiver phase‐locked loop) resulting from scintillation for GPS/SBAS C/A code processing and semicodeless GPS L1 and L2 Y‐code, these require input of the spectral parameters p (inverse power law of the phase power spectral density (PSD)) and T (spectral strength of the phase PSD at 1 Hz) which will not generally be available. It would certainly be more convenient if tracking jitter could be determined just from scintillation indices (S4 and σϕ) enabling determination when spectral parameters are not readily available and permitting tracking jitter for all the simultaneously observed satellites to be easily determined and used in a scintillation mitigation scheme. The main difficulty is that the Fresnel frequency, fF, which is an important feature of the amplitude PSD, should be known. Here a method is proposed which uses both scintillation indices (σϕ and S4) to give an additional relation to find both p and T. This makes use of the known general fading frequency behavior of the PSD spectrum which is different between amplitude and phase scintillation. This difference is exploited, utilizing approximate models of the PSD for both amplitude and phase, to define equations that can be solved for p and T for any given fF. Even when fF is not known, it is shown that by taking account of the range of physically realistic values of fF, the tracking jitter can generally be determined to a reasonable degree of accuracy.

Dynamic feed-forward control of a parallel kinematic machine

This paper deals with the dynamic feed-forward control of a 6-UPS parallel kinematic machine (PKM). The control system consists of the closed-loop control subsystem and the dynamic control subsystem. The closed-loop control subsystem is constructed by using the PD control and low-pass filter. Moreover, zero phase error tracking control (ZPETC) is introduced to the closed-loop control subsystem to improve its response capability. Based on the rigid-body dynamic model of the PKM, the dynamic control subsystem is designed by using the computed torque control and feed-forward control. Since the phase lag of the closed-loop control subsystem is almost eliminated by ZPETC and PD control, the motion precision of the closed-loop control subsystem is improved largely. The influence of the dynamic characteristic of the PKM on the motion precision is decreased due to the introduction of rigid-body dynamic model into the control system. As a result, the motion precision of the moving platform is greatly improved.

High-Speed Recording up to 15,000 rpm Using Thin Optical Disks

We propose a high-speed optical disk system using thin flexible optical disks (HS-FOD) recording up to 15,000 rpm. The thin optical disk system is composed of three technical elements: media employing a thin and flexible substrate 0.1 mm thick, a mechanical stabilizer, and a high-speed tracking servo employing a feed-forward control with zero phase error tracking (ZPET-FF control). The HS-FOD system has an optical head with numerical aperture (NA) of 0.85 and is compatible with the optical system of a Blu-ray disc or a broadcast-use optical disk. We have successfully performed disk rotation stably and have performed precisely a focus servo and a tracking servo at 15,000 rpm. We also achieved writing and reading data at 15,000 rpm and recording 252 Mbps of random pattern data and could get small values of jitter below the tolerance. These results are enough to record professional high-definition television (HDTV) video signals in formats such as HD-D5 for broadcast-use.

Full constellation phase detector for carrier recovery in high-order QAM systems

A full constellation phase detector that improves carrier acquisition performance in high-order quadrature amplitude modulation (QAM) is proposed. The weighting function of the phase detector is mathematically derived, and simulated phase detector characteristics are presented for 256QAM. The results of an experimental evaluation are also reported, which show that the carrier recovery loop based on the proposed phase detector has a large frequency acquisition range and low phase tracking error in high-order QAM.

Adaptive two-degree-of-freedom control of feed drive systems

Feed drive systems are widely used in industrial applications, and many efforts for improving their precision control have been made thus far. One of the basic approaches for improving the control accuracy of feed drive systems is to design a controller based on the internal model principle, which states that for a control system to track a reference signal without a steady state error, it needs to include a generator of the reference signal. Feed-forward controllers, such as the zero phase error tracking controller (ZPETC) proposed by Tomizuka, are also employed for improving control performance. However, prior knowledge of plant dynamics and/or reference signal properties is required for both the internal model principle and the feed-forward controller based designs. For precision control, plant dynamics should be identified in real time because feed drive dynamics are affected by varying conditions, such as frictional and thermal effects. This paper presents a new type of adaptive control for arbitrary reference tracking, which requires neither plant dynamics nor reference signal properties for controller design. This type of controller can also reduce the effect of unknown disturbances. The control system is designed using a discrete-time plant model and consists of adaptive feed-forward and feedback controllers. This design is then applied to a feed drive system with a ball screw drive. The effectiveness of the proposed design is demonstrated by simulation and experimental results, which was obtained by applying the proposed control system to an unknown reference signal whose property is varied during control.

High-Speed Tracking Servo Using Zero Phase Error Tracking-Feed-Forward Method for Professional-Use Optical Disks over 10000 rpm

We have realized a high-speed and precise tracking servo using a feed-forward control with the zero phase error tracking method (ZPET-FF control) on an optical disk at the disk rotation speed of 10800 rpm. To realize a high-data-transfer-rate recording of more than 200 Mbps over the entire disk area, the optical head must be controlled with an accuracy of better than 9 nm at the maximum rotation speed of about 10800 rpm for track following on a high-density optical disk. We performed high-speed tracking, and the experimental results show that the ZPET-FF control is more precise than feedback control. The residual tracking error is suppressed to 6.3 nm at a disk rotation speed of 10800 rpm on optical disk drives having an object lens with a numerical aperture (NA) of 0.85 and media with a track pitch of 0.32 µm, such as the Blu-ray disc and broadcast-use optical disk.