RMS Tracking Error Research Articles

Three-Dimensional Skin Deformation as Force Substitution: Wearable Device Design and Performance During Haptic Exploration of Virtual Environments.

Virtual reality systems would benefit from a compelling force sensory substitute when workspace or stability limitations prevent the use of kinesthetic force feedback systems. We present a wearable fingertip haptic device with the ability to make and break contact in addition to rendering both shear and normal skin deformation to the fingerpad. A delta mechanism with novel bias spring and tether actuator relocation method enables the use of high-end motors and encoders, allowing precise device control: 10 Hz bandwidth and 0.255 mm RMS tracking error were achieved during testing. In the first of two experiments, participants determined the orientation of a stiff region in a surrounding compliant virtual surface with an average angular error of 7.6 degree, similar to that found in previous studies using traditional force feedback. In the second experiment, we evaluated participants' ability to interpret differences in friction. The Just Noticeable Difference (JND) of surface friction coefficient discrimination using our skin deformation device was 0.20, corresponding with a reference friction coefficient of 0.5. While higher than that found using kinesthetic feedback, this demonstrates that users can perceive differences in surface friction without world-grounded kinesthetic forces. These experiments show that three DoF skin deformation enables both stiffness and friction discrimination capability in the absence of kinesthetic force feedback.

Heart rate control during treadmill exercise using input-sensitivity shaping for disturbance rejection of very-low-frequency heart rate variability

Abstract Background Automatic and accurate control of heart rate (HR) during treadmill exercise is important for prescription and implementation of training protocols. The principal design issue for feedback control of HR is to achieve disturbance rejection of very-low-frequency heart rate variability (VLF-HRV) with a level of control signal activity (treadmill speed) which is sufficiently smooth and acceptable to the runner. This work aimed to develop a new method for feedback control of heart rate during treadmill exercise based on shaping of the input sensitivity function, and to empirically evaluate quantitative performance outcomes in an experimental study. Methods Thirty healthy male subjects participated. 20 subjects were included in a preceding study to determine an approximate, average nominal model of heart rate dynamics, and 10 were not. The design method guarantees that the input sensitivity function gain monotonically decreases with frequency, is therefore devoid of peaking, and has a pre-specified value at a chosen critical frequency, thus avoiding unwanted amplification of HRV disturbances in the very-low-frequency band. Controllers were designed using the existing approximate nominal plant model which was not specific to any of the subjects tested. Results Accurate, stable and robust overall performance was observed for all 30 subjects, with a mean RMS tracking error of 2.96 beats/min and a smooth, low-power control signal. There were no significant differences in tracking accuracy or control signal power between the 10 subjects who were not in the preceding identification study and a matched subgroup of subjects who were (respectively: mean RMSE 2.69 vs. 3.28 beats/min, p = 0.24; mean control signal power 15.62 vs. 16.31 × 10 −4 m 2 /s 2 , p = 0.37). Substantial and significant reductions over time in RMS tracking error and average control signal power were observed. Conclusions The input-sensitivity-shaping method provides a direct way to address the principal design challenge for HR control, namely disturbance rejection in relation to VLF-HRV, and delivered robust and accurate tracking with a smooth, low-power control signal. Issues of parametric and structural plant uncertainty are secondary because a simple approximate plant model, not specific to any of the subjects tested, was sufficient to achieve accurate, stable and robust heart rate control performance.

Comparison of linear and nonlinear feedback control of heart rate for treadmill running

ABSTRACTHeart rate can be used to define exercise intensity; feedback control systems for treadmills which automatically adjust speed to track arbitrary heart rate target profiles are therefore of interest. The aim of this study was to compare linear (L) and nonlinear (NL) controllers using quantitative performance measures. Sixteen healthy male subjects participated in the experimental L vs. NL comparison. The linear controller was calculated using a direct analytical design that employed an existing approximate plant model. The nonlinear controller had the same linear component, but it was augmented using static plant-nonlinearity compensation. At moderate-to-vigorous intensities, no significant differences were found between the linear and nonlinear controllers in mean RMS tracking error (2.34 vs. 2.25 bpm [L vs. NL], p=0.26) and average control signal power (51.7 vs. m2/s2, p=0.16), but dispersion of the latter was substantially higher for NL (range 45.2 to 56.8 vs. 30.7 to m2/s2, L vs. NL). At low speed, RMS tracking errors were similar, but average control signal power was substantially and significantly higher for NL (28.1 vs. m2/s2 [L vs. NL], p<0.001). The performance outcomes for linear and nonlinear control were not significantly different for moderate-to-vigorous intensities, but NL control was overly sensitive at low running speed. Accurate, stable and robust overall performance was achieved for all 16 subjects with the linear controller. This points to disturbance rejection of very-low-frequency heart rate variability as the overriding challenge for design of heart rate controllers.

Improving the positioning bandwidth of the Integral Resonant Control Scheme through strategic zero placement.

Integral Resonant Control (IRC) is a simple and robust control scheme for vibration damping. Combined with an integral tracking controller, the IRC has been shown to improve the performance of a wide range of nanopositioners. However, the overall improvement in positioning performance is limited by the pole induced by the IRC. Through selective zero placement, the induced pole can be placed near origin. A structured PI tracking controller, where the PI gains are selected to place a zero at a specific location, is used to cancel the pole. This effectively reduces the order of the system by one. For this system, controller gains are derived analytically in order to maximize tracking bandwidth. Simulation results for one axis of a nanopositioner are provided for both standard and modified IRC schemes. Compared to the standard IRC scheme, the modified IRC scheme is found to provide a 55% increase in the ±1 dB bandwidth and a reduction of both maximum and rms tracking errors.

Sigmoid-based hysteresis modeling and high-speed tracking control of SMA-artificial muscle

This paper presents a novel compact shape memory alloy (SMA) based artificial muscle (AM) with self-sensing, silent operation and high force-to-weight ratio functions. The AM has great potential to develop light and compact active ankle–foot orthosis (AAFO) for ankle–foot rehabilitation. However, its performance is severely limited by SMA's slow-speed response and hysteresis properties. Firstly, an effective forced vessel cooling method is introduced to improve the AM response speed without compromising its compactness. Then SMA hysteresis properties are deeply explored and modeled under different stress and driving frequency conditions, whereby the hysteresis is well compensated when the hysteresis model based feedforward controller is proposed to the AM. Finally, a newly AM actuated AAFO is proposed to demonstrate the actuating capability of the AM. Experimental results show that the AM response speed and accuracy are greatly improved with tracking frequency increased from 0.08 to 1Hz, RMS tracking errors reduced by up to 82%, which basically satisfies the initial ankle–foot rehabilitation application.

Large dynamic range nanopositioning using iterative learning control

Abstract This paper presents the control system design and tracking performance for a large range single-axis nanopositioning system that is based on a moving magnet actuator and a flexure bearing. While the physical system is designed to be free of friction and backlash, the nonlinearities in the electromagnetic actuator as well as the harmonic distortion in the drive amplifier degrade the tracking performance for dynamic commands. It is shown that linear feedback and feedforward proves to be inadequate to overcome these nonlinearities. This is due to the low open-loop bandwidth of the physical system, which limits the achievable closed-loop bandwidth given actuator saturation concerns. For periodic commands, like those used in scanning applications, the component of the tracking error due to the system nonlinearities exhibits a deterministic pattern and repeats every period. Therefore, a phase lead type iterative learning controller (ILC) is designed and implemented in conjunction with linear feedback and feedforward to reduce this periodic tracking error by more than two orders of magnitude. Experimental results demonstrate the effectiveness of ILC in achieving 10 nm RMS tracking error over 8 mm motion range in response to a 2 Hz band-limited triangular command. This corresponds to a dynamic range of more than 10 5 for speeds up to 32 mm/s, one of the highest reported in the literature so far, for a cost-effective desktop-sized single-axis motion system.

Spread-Spectrum Continuous-Phase-Modulated Signals for Satellite Navigation

Spread-spectrum continuous-phase-modulated (SS-CPM) signals are investigated with application to satellite navigation. In particular, focus is devoted to the special subclasses of SS-CPM with semi-integer modulation index h greater than one. This constitutes a novelty with respect to traditional navigation signal design on one hand (which is based on direct-sequence spread-spectrum (DS-SS) signals with rectangular pulse) and with traditional communication SS-CPM with h>;1 on the other. Main output is that setting the modulation index h<;1 to semi-integer values allows the SS-CPM signals to behave like having subcarriers, exactly in the same way as it happens for the binary offset carrier (BOC) modulation. The main advantage is that CPM ensures a constant envelope at the transmission side, thus being appealing when these features are required at the system level. After a description of signal properties, focus is devoted to ranging code synchronization, by exploitation of the theory on time-delay estimation (TDE). A few delay-lock loop schemes are also presented, based on an offset quadrature phase-shift keying (OQPSK) approximation of the signal at the receiver side, achieved by Laurent's decomposition at the receiver side. Proposed loops performance are analyzed in terms of Cramer-Rao bound (CRB), rms tracking error, and multipath robustness. An application of SS-CPM for a two-rate-service scheme is proposed.

SU‐E‐J‐146: Gold Nanoparticles as a Contrast Agent for In‐Treatment Tumor Tracking

Purpose: There has been recent interest in gold nanoparticles as vascular disruptive agents when combined with megavoltage x‐ray irradiation. In addition to the therapeutic benefits, the gold nanoparticles may also have a role as an alternative to implanted fiducials for improving localization for IGRT and real‐time tumor tracking. We demonstrate the feasibility of tracking a gold nanoparticle solution of moderate concentration with kV x‐ray fluoroscopy. Methods: A 2.0 mg/ml solution of polymer coated gold nanoparticles was injected into 0.5 cm clinical bolus material. Additional build up with solid water was used to create a more realistic radiological scenario. A cylindrical gold fiducial (3 mm × 1 mm) was placed nearby to act as a reference surrogate. The phantom was set in sinusoidal motion with 2 cm amplitude and 4.0 s period. Images were acquired at 30 frames/sec with the kV on‐board imaging system of a Varian IX Clinac. The ratio of the image intensity in each target versus background was measured. Target tracking was performed using a single template matching approach and non‐clinical research software. Tracking error was quantified as the difference in location of each track point from the input sine function. Results: The intensity ratio in a single image of a sequence was 1.3 for the gold fiducial and 1.2 for the 2.0 mg/ml gold nanoparticle solution. Tracking was maintained throughout the 25 seconds of target motion. RMS tracking error was 0.4 mm for the gold fiducial and 0.6 mm for the gold nanoparticles. The tracking score was smaller for the nanoparticles (mean: 0.63 +/− 0.02) than for the fiducial (mean: 0.89 +/− 0.6). Conclusions: Target tracking in kV fluoroscopy can be enabled by gold nanoparticles. A solution of 2.0 mg/ml can be tracked in a phantom with an accuracy similar to tracking a gold fiducial.

An analytical model of code-tracking performance for next-generation GNSS modulations

Precorrelation bandlimiting, sampling, and quantization (BSQ) are three fundamental functions of receivers for global navigation satellite system (GNSS) signal processing. Analytical models have been developed to evaluate the implementation losses due to different combinations of these parameters for legacy modulations such as BPSK. However, the performance metric was losses of effective carrier-to-noise ratio in dB, instead of performance degradation of a delay-locked loop (DLL) used for code-tracking. This paper proposes an analytical model to predict the DLL performance with the loss of RMS tracking error in meters as the performance metrics. The signal model & assumptions and canonical form of DLL are first introduced. Then, analytical model is derived for DLL tracking accuracy and the performance metrics, tracking loss is defined. Finally, simulation results of two next-generation modulations for GPS and Galileo, namely CBOC and TMBOC, are presented.

Dynamic MLC tracking of moving targets with a single kV imager for 3D conformal and IMRT treatments

Background. Tumor motion during radiotherapy is a major challenge for accurate dose delivery, in particular for hypofractionation and dose painting. The motion may be compensated by dynamic multileaf collimator (DMLC) tracking. Previous work has demonstrated that a single kV imager can accurately localize moving targets for DMLC tracking during rotational delivery, however this method has not been investigated for the static gantry geometry used for conformal and IMRT treatments. In this study we investigate the accuracy of single kV-imager based DMLC tracking for static-gantry delivery. Material and methods. A 5-field treatment plan with circular field shape and 200 MU per field was delivered in 20 s per field to a moving phantom with an embedded gold marker. Fluoroscopic kV images were acquired at 5 Hz perpendicular to the treatment beam axis during a 120° pre-treatment gantry rotation, during treatment delivery, and during inter-field gantry rotations. The three-dimensional marker position was estimated from the kV images and used for MLC adaptation. Experiments included 12 thoracic/abdominal tumor trajectories and five prostate trajectories selected from databases with 160 and 548 trajectories, respectively. The tracking error was determined as the mismatch between the marker position and the MLC aperture center in portal images. Simulations extended the study to all trajectories in the databases and to treatments with prolonged duration of 60 s per field. Results. In the experiments, the mean root-mean-square (rms) tracking error was 0.9 mm (perpendicular to MLC) and 1.1 mm (parallel to MLC) for thoracic/abdominal tumor trajectories and 0.6 mm (perpendicular) and 0.5 mm (parallel) for prostate trajectories. Simulations of these experiments agreed to within 0.1 mm. Simulations of all trajectories in the databases resulted in mean rms tracking errors of 0.6 mm (perpendicular) and 0.9 mm (parallel) for thorax/abdomen tumors and 0.4 mm (perpendicular) and 0.2 mm (parallel) for prostate for both 20 s and 60 s per field. Conclusion. Single kV imager DMLC tracking, which is fully compatible with IMRT, was demonstrated for static fields. The mean tracking error was sub-2 mm for most tumor trajectories with respiratory motions and sub-1 mm for most prostate trajectories.

SU‐FF‐J‐72: Markerless Fluoroscopic Tracking of Lung Tumors Based On 4D CT

Purpose: To develop a markerless fluoroscopic lung tumor tracking algorithm based on 4D CT generated reference templates. Method and Materials: Fluoroscopic images were acquired at a sampling rate of 15Hz using an on‐board X‐ray imaging (OBI) system. Each fluoroscopic image has a resolution of 768 by 1024, where each pixel represents a physical size of 0.26 mm. 4D CT was obtained from phase sorting based on internal anatomic features. DRRs were generated from 10 phases of the 4D CT, of which inhale and exhale DRRs were shifted to cover a greater motion range. These DRRs served as the reference templates for tracking purposes. GTV contours from the 4D CT give the reference tumor positions in the templates. Motion enhancement was applied to both DRR templates and fluoroscopic images. Pearson's correlation was calculated between each fluoroscopic image and each template in a given ROI. The tracking output is the weighted average of the tumor positions in those templates with largest correlation scores, weighted by the corresponding correlation scores. Results: RMS tracking error ranges between 0.65mm and 0.77mm. Absolute error at 95th percentile ranges between 1.41mm and 1.58mm. These values are well within the error bounds obtained from earlier studies, which require human‐marked tumor positions in the fluoroscopic images for training. Conclusion: This work demonstrates the feasibility of tracking lung tumor fluoroscopically based on 4D CT templates. Future work involves more sophisticated image processing and computer vision techniques to obtain more robust tracking results.

A Modified Decorrelated Delay Lock Loop for Synchronous DS-CDMA Systems

This paper presents a modified decorrelated delay lock loop (MD-DLL) for synchronous direct-sequence code-division multiple-access (DS-CDMA) systems under multiuser environments. The structure of the MD-DLL is similar to that of a traditional delay lock loop (T-DLL), aside from the fact that the despreading signals in T-DLL are replaced by a linear combination of all the users' code sequences with various weightings and timing offsets. The basic principles of MD-DLL are given as follows: 1) to use the decorrelating technique of a multiuser detector to remove the multiple-access interference at the on-time code position instant and 2) to choose a proper timing offset for the code sequences to reduce the weighting imbalance between the two arms of the tracking loop and suppress noise enhancement. The proposed MD-DLL scheme solves the tracking bias problems in a decorrelated delay lock loop under a low-signal-to-noise-ratio (SNR) condition. Computer simulations based on Gold code sequences are used to verify the findings. It is shown that MD-DLL achieves a better and stable S-curve with negligible tracking bias, better rms tracking error and mean-time-to-lose-lock performance under high-SNR conditions, and stronger near-far resistance than T-DLL.

Tracking Control of a Piezoceramic Actuator With Hysteresis Compensation Using Inverse Preisach Model

This paper presents the classical Preisach hysteresis modeling and tracking control of a curved pre-stressed piezoceramic patch actuator system with severe hysteresis. The actuator is also flexible with very small inherent damping. It has potential applications in active antennas. A series of tests are conducted to study the hysteresis properties of the piezoceramic actuator system. The numerical expressions of the classical Preisach model for different input variations are presented. The classical Preisach model is applied to simulate the static hysteresis behavior of the system. Higher order hysteresis reversal curves predicted by the classical Preisach model are verified experimentally. The good agreement found between the measured and predicted curves showed that the classical Preisach model is an effective mean for modeling the hysteresis of the piezoceramic actuator system. Subsequently, the inverse classical Preisach model is established and applied to cancel the hysteresis the piezoceramic actuator system for the real-time microposition tracking control. In order to improve the control accuracy and to increase damping of the actuator system, a cascaded PD/lead-lag feedback controller is designed with consideration of the dynamics of the actuator. In the experiments, two cases are considered, control with major loop hysteresis compensation, and control with minor loop hysteresis compensation. Experimental results show that RMS tracking errors are reduced by 50% to 70% if the hysteresis compensation is added in the feedforward path in both cases. Therefore, hysteresis compensation with the feedback controller greatly improves the tracking control accuracy of the piezoceramic actuator.

Performance of laser tracking of small targets during turbulence and beam jitter

Small target detection and tracking are important for laser radars in many applications such as laser weapons, directed infrared countermeasures (DIRCM), fire control, target recognition, and free-space laser communications. The detection and tracking performance depends on the mode of detection, SNR, target signal statistics, beam jitter, and turbulence induced irradiance variations. We show results of the root mean square (rms) tracking error versus SNR primarily for direct detection systems using a strong glint return. For the general case of a certain signal and noise probability density functions (pdf) it is hard to obtain analytical solutions for the mean and variances of the estimates for the rms tracking error. We have therefore used numerical simulations to illustrate how the pdf and SNR will affect the tracking accuracy. Gamma functions and other pdf's can be used to characterize the signal distributions to get a first hand on tracking performance. The results are presented as tracking errors versus the angular spot size of the laser beam in the tracking detector plane. We also investigate the beam optimization problem for target detection and "power in bucket," which is maximizing the laser energy at the target. We find that there are optimum beam sizes (w) versus the rms jitter () and that optimum w/ (minimizing the false alarm rate for a given detection probability Pd) typically fall in regions 1 to 3 depending on probability of detection and the representative pdf for the application in mind.

ULTRA‐FINE TRACKING CONTROL ON PIEZOELECTRIC ACTUATED MOTION STAGE USING PIEZOELECTRIC HYSTERETIC MODEL

ABSTRACTThe tracking control accuracy of the piezoelectric actuator (PEA) is limited due to its inherent hysteresis nonlinearity. A new piezoelectric‐actuator model is synthesized based on two first‐order transfer systems in parallel with two tuned parameters determined from one experiment. Two open‐loop tracking controllers are implemented with the proposed model to compensate the hysteresis of linear positioning. Numerical simulations and experimental tests on the tracking of sinusoidal and triangular waveforms with signal frequencies ranging from 1Hz to 30 Hz are revisited and compared with the conventional Bouc‐Wen and Duhem models. Experimental results reveal that the RMS tracking error can be reduced to less than 2% of the maximum traveling distance without any feedback sensor. When a piezoelectric actuated on a two Degree‐Of‐Freedom (DOF) monolithic motion stage was employed, the RMS tracking error was 50 nm within the measured sensor accuracy.

Iterative learning control and repetitive control for engineering practice

This paper discusses linear iterative learning and repetitive control, presenting general purpose control laws with only a few parameters to tune. The method of tuning them is straightforward, making tuning easy for the practicing control engineer. The approach can then serve the same function for learning/repetitive control, as PID controllers do in classical control. Anytime one has a controller that is to perform the same tacking command repeatedly, one simply uses such a law to adjust the command given to an existing feedback controller and achieves a substantial decrease in tracking error. Experiments with the method show that decreases by a factor between 100 and 1000 in the RMS tracking error on a commercial robot, performing a high speed trajectory can easily be obtained in 8 to 12 trials for learning. It is shown that in engineering practice, the same design criteria apply to learning control as apply to repetitive control. Although the conditions for stability are very different for the two problems, one must impose a good transient condition, and once such a condition is formulated, it is likely to be the same for both learning and repetitive control.

Half-sine and triangular despreading chip waveforms for coherent delay-locked tracking in DS/SS systems

The performance of a coherent delay-locked tracking scheme for direct-sequence/spread-spectrum systems using half-sine or triangular chip waveforms for early and late despreading sequences is analyzed. The effect of band-limiting on the received signals is considered. Mean time to lose lock (MTLL) and root mean square (rms) tracking error of the delay-locked loop (DLL) are compared with that of a conventional DLL which uses rectangular chip despreading waveforms. Linear and nonlinear (based on the renewal process approach) analyses are employed to evaluate the performance of the DLL. Results show that the use of either the half-sine or triangular chip waveform reduces the rms tracking error and increases the MTLL considerably when the early-late spacing is approximately between 0.7-1.3 chip times. The results apply in particular to the commonly used DLL using one chip early-late spacing. Computer simulation for band-limited signals confirms the analytical results. The use of these despreading chip waveforms also reduces tracking offset in multipath environments.

Control of Linear Motors for Machine Tool Feed Drives: Experimental Investigation of Optimal Feedforward Tracking Control

This paper investigates the use of optimal l1 and H∞ model reference optimal feedforward control to enhance the tracking performance of a linear motor drive. Experimental work is presented which studies the effects of signal preview, tracking constraint, and reference model choice on tracking performance. Suboptimal l1 control where the closed-loop system has a zero on the unit circle due to integral action in the feedback controller is given special attention, and is seen to give near optimal performance for the system under study here. For the specific trajectory employed here, the best performing feedforward controllers were experimentally seen to reduce by more than half the maximum and rms tracking errors of the H∞ optimal feedback closed-loop systems.

Comparison and combination of learning controllers - Computational enhancement and experiments

Five discrete-frequency linear learning-control laws are compared and experimentally tested. These include simple integral-control-based learning using a single learning gain, phase-cancellation learning control, a contractionmapping learning-control law with monotonic decay of the error norm, and learning controllers that invert the system model and the observer model. The inversion designs converge the fastest initially, but phase cancellation with identification updates and the contraction-mapping method with model updates have better stability robustness properties. The learning control approaches are combined to obtain the advantages of each, by using inversion methods for the first few repetitions, followed by a more robust method. It is demonstrated that the computation of the learning action can be made in the frequency domain using fast Fourier transform methods, with as much as 94% reduction in computarion time. In experiments on a Robotics Research Corporation robot, the learningcontrol laws result in a reduced rms tracking errors for all joints, by a factor of close to 3 orders of magnitude.

Adaptive fuzzy proportional integral power control for a cellular CDMA system with time delay

We investigate the use of fuzzy logic control techniques for adaptive power control in a direct-sequence code-division multiple-access (DS/CDMA) cellular system over the mobile fading radio channels with propagation time delay. A fuzzy PI (proportional-plus-integral) control whose input variables are the received power error and error change is introduced to determine each user transmitting power in order to simultaneously equalize all users' signal powers received at the base station and achieve better system stability and control performance. This control strategy can ensure long loop transmission delays without causing the system to become unstable. According to the well-known phase-plane method, the derivation of the fuzzy PI control has been carried out by analyzing the response areas, cross-over, and extreme points of the system step response with apriori knowledge of the dynamics of the CDMA mobile fading channels. For a long time-delay fading process, a methodology is developed to modify the rule base to contain the delay information for reducing the deadtime effects of the process. Moreover, the additional advantages of fuzzy PI control over conventional control theories are: increased robustness in spite of interference and the ability to handle the time-delay process whose parameters are not accurately known. Simulation results show that a good performance can be achieved both in RMS tracking error and traffic capacity by use of fuzzy PI power control, especially in poor interuser interference and long time delay conditions.