Nonlinear Compensation Research Articles

Experimental results on nonlinear distortion compensation using photonic reservoir computing with a single set of weights for different wavelengths

Photonics-based computing approaches in combination with wavelength division multiplexing offer a potential solution to modern data and bandwidth needs. This paper experimentally takes an important step towards wavelength division multiplexing in an integrated waveguide-based photonic reservoir computing platform by using a single set of readout weights for up to at least 3 ITU-T channels to efficiently scale the data bandwidth when processing a nonlinear signal equalization task on a 28 Gbps modulated on-off keying signal. Using multiple-wavelength training, we obtain bit error rates well below that of the 1.5×10-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1.5 \ imes \\,10^{-2}$$\\end{document} forward error correction limit at high fiber input powers of 18 dBm, which result in high nonlinear distortion. The results of the reservoir chip are compared to a tapped delay line filter and clearly show that the system performs nonlinear equalization. This was achieved using only limited post processing which in future work can be implemented in optical hardware as well.

Fault-Tolerant Six-Axis FBG Force/Moment Sensing for Robotic Interventions

A fiber Bragg grating (FBG) based six-axis force/moment ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</i> / <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> ) tactile sensor with the capability of nonlinear decoupling, fault-tolerant, and temperature compensation (TC) is developed for robot-assisted minimally invasive surgery. Eight tightly suspended FBGs have been fixed inside a small three-dimensional printed flexure with a diameter of 10 mm to form the force-sensitive unit of the sensor. Considering the suspended FBG fracture risk, an optimized back propagation neural network (BPNN) algorithm has been proposed to eliminate the nonlinear crosstalk effect of the six-axis <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</i> / <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> outputs, diagnose and modify the fault response of the sensor under several FBGs fractures and eliminate the temperature-induce errors. Experimental results indicate that the Type I and Type II errors are within 5% using the BPNN nonlinear decoupling model. The force resolutions can reach 2.73 mN, 2.21 mN, and 28.39 mN within ±4 N, and the moment resolutions can reach 0.36 mN·mm, 0.96 mN·mm, and 47.5 mN·mm within ±20 N·mm. Moreover, the Type I errors in the six-axis can be modified within 8%, the Type II errors can be modified within 10%, even with one and two FBGs fractures. After TC, the maximum temperature-induced errors can be modified within 0.061 N and 0.127 N·mm for force and moment components, respectively. Combining the robot-assisted scanning and the BPNN, the positions of the buried vessels in a phantom can be effectively identified by the designed sensor, even two FBGs fracture. Such merits validate the dependability and robustness of the designed sensor with FBGs fracture.

Complex principal component analysis-based complex-valued fully connected NN equalizer for optical fibre communications

An increasing number of scholars have proposed many schemes to mitigate the Kerr nonlinearity effect restricting the transmission capacity of optical fibres. In this paper, we proposed a complex principal component analysis-based complex-valued fully connected neural network (P-CFNN) model aided by perturbation theory and demonstrated it experimentally on a dual-polarization 64-quadrature-amplitude modulation coherent optical communication system. What we believe to be a novel complex principal component analysis (CPCA) algorithm applied to complex-valued fully connected neural network (CFNN) is designed to further reduce the computational complexity of the model. Meanwhile, an equivalent real-valued fully connected neural network (RFNN) with the same time complexity as a CFNN is proposed for fair performance comparison. Under all launched optical powers, the performance of the P-CFNN equalizer is the best among all comparison algorithms, and the maximum ΔQ-factor compared to without employing the nonlinear compensation algorithm reaches 3.94 dB. In addition, under the constraint of the same Q-factor, we confirmed that the proposed P-CFNN obtained a 40% reduction in time complexity and a 70% reduction in space complexity compared with the PCA-based RFNN, which also proved the very large application prospect of the P-CFNN equalizer in optical fibre communication systems.

Low-complexity fiber nonlinearity compensation based on operator learning over 12075 km single model fiber

Low-complexity fiber nonlinearity compensation based on operator learning over 12075 km single model fiber

Self-supervised learning for neural-network-based perturbative fiber nonlinearity compensation

Self-supervised learning for neural-network-based perturbative fiber nonlinearity compensation

Long-range photonics-aided 17.6 Gbit/s D-band PS-64QAM transmission using gate recurrent unit algorithm with a complex QAM input.

D-band fiber-wireless technique that overcomes the bandwidth bottleneck of electrical devices has been popularized, but long-range D-band wireless transmission is still limited by the large absorption loss. So, the exploration of m-QAM formats is essential for the D-band long distance wireless transmission due to their different spectrum efficiency and SNR requirement. Moreover, nonlinearity in photonics-aided millimeter-wave (mm-wave) system is also a significant problem caused by fiber, photoelectrical devices and power amplifiers. So it is critical to employ a machine learning-based nonlinear compensation algorithm especially for long-distance D-band wireless delivery. A novel Gate Recurrent Unit (GRU) algorithm with a complex QAM input is proposed to further improve the receiver sensitivity of coherent D-band receiver, which effectively preserves the relative relationship between I/Q components of QAM signals and has memory capabilities with a better precision. We mainly discuss three learners with a complex QAM input, including complex-valued neural network (CVNN), single-lane Long Short-Term Memory (SL-LSTM) and single-lane Gate Recurrent Unit (SL-GRU). Thanks to these adaptive deep learning methods, we successfully realize 135 GHz 4Gbaud QPSK and PS-64QAM signal wireless transmission over 4.6 km, respectively. Considering the aspects of transmission capacity and recovery precision, CVNN equalizer is suitable for QPSK recovery, SL-GRU would be the best choice for PS-64QAM over D-band long range wireless transmission link up to km magnitude. The effective data rate can be achieved up to 17.6 Gbit/s. Therefore, we believe that the combination of high-order modulation and NN supervised algorithms with a complex input has an application prospect for the future 6 G mobile communication.

Deep photonic reservoir computer based on frequency multiplexing with fully analog connection between layers

Reservoir computers (RCs) are randomized recurrent neural networks well adapted to process time series, performing tasks such as nonlinear distortion compensation or prediction of chaotic dynamics. Deep reservoir computers (deep-RCs), in which the output of one reservoir is used as the input for another one, can lead to improved performance because, as in other deep artificial neural networks, the successive layers represent the data in more and more abstract ways. We present a fiber-based photonic implementation of a two-layer deep-RC based on frequency multiplexing. The two RC layers are encoded in two frequency combs propagating in the same experimental setup. The connection between the layers is fully analog and does not require any digital processing. We find that the deep-RC outperforms a traditional RC by up to two orders of magnitude on two benchmark tasks. This work paves the way towards using fully analog photonic neuromorphic computing for complex processing of time series, while avoiding costly analog-to-digital and digital-to-analog conversions.

Design and Nonlinear Error Compensation of a Multi-Segment Soft Continuum Robot for Pulmonary Intervention

Design and Nonlinear Error Compensation of a Multi-Segment Soft Continuum Robot for Pulmonary Intervention

Compensating Chromatic Dispersion and Phase Noise using Parallel AFB-MBPS For FBMC-OQAM Optical Communication System

Filter Bank Multi-Carrier Offset-QAM (FBMC-OQAM) is one of the hottest topics in research for 5G multi-carrier methods because of its high efficiency in the spectrum, minimal leakage in the side lobes, zero cyclic prefix (CP), and multiphase filter design. Large-scale subcarrier configurations in optical fiber networks need the use of FBMC-OQAM. Chromatic dispersion is critical in optical fiber transmission because it causes different spectral waves (color beams) to travel at different rates. Laser phase noise, which arises when the phase of the laser output drifts with time, is a major barrier that lowers throughput in fiber-optic communication systems. This deterioration may be closely related among channels that share lasers in multichannel fiber-optic systems using methods like wavelength-division multiplexing with frequency combs or space-division multiplexing. In this research, we use parallel Analysis Filter Bank (AFB) equalizers in the receiver part of the FBMC OQAM Optical Communication system to compensate for chromatic dispersion (CD) and phase noise (PN). Following the equalization of CD compensation, the phase of the carriers in the received signal is tracked and compensated using Modified Blind Phase Search (MBPS). The CD and PN compensation techniques are simulated and analyzed numerically and graphically to determine their efficacy. To evaluate the FBMC's efficiency across various equalizers, 16-OQAM is taken into account. Bit Error Rate (BER), Optical Signal-to-Noise Ratio (OSNR), Q-Factor, and Mean Square Error (MSE) were the primary metrics we utilized to evaluate performance. Single-tap equalizer, multi-tap equalizer (N=3), ISDF equalizer with suggested Parallel Analysis Filter Banks (AFBs) (K=3), and MBPS were all set aside for comparison. When compared to other forms of Nonlinear compensation (NLC), the CD and PN tolerance attained by Parallel AFB equalization with MBPS is the greatest.

XPM estimation and compensation in the WDM system based on a low-complexity inner FEC.

In this work, we focus on compensation of inter-channel nonlinearity in optical wavelength division multiplexed (WDM) systems. We consider pre-coding with a high-rate forward error correction (FEC) code and a low-complexity and low-latency decoding and equalization scheme at the receiver. The 2 × 2 multiple-input multiple-output (MIMO) recursive least square (RLS) equalizer is applied to reduce the inter-symbol interference (ISI) caused by the inter-channel nonlinearity, while the decoder improves the quality of the data feedback. Decisions based on feedback reliability have been implemented to prevent error propagation. We demonstrate that our system can readily utilize the inner FEC part of a mainstream concatenated optical FEC designs such as the 400ZR standard FEC. We evaluate the proposed algorithm for the dual-polarization 16QAM and 256QAM optical links. Based on our simulation results, the Q-factor has been increased by 0.36 and 0.67 dB for the 16QAM and 256QAM, respectively. The optimum launch power has been increased by 0.4 dB for both cases.

Simultaneous tuning of multiple PID controllers for multivariable systems using deep reinforcement learning

Traditionally, tuning of PID controllers is based on linear approximation of the dynamics between the manipulated input and the controlled output. The tuning is performed one loop at a time and interaction effects between the multiple single-input-single-output (SISO) feedback control loops is ignored. It is also well-known that if the plant operates over a wide operating range, the dynamic behaviour changes thereby rendering the performance of an initially tuned PID controller unacceptable. The design of PID controllers, in general, is based on linear models that are obtained by linearizing a nonlinear system around a steady state operating point. For example, in peak seeking control, the sign of the process gain changes around the peak value, thereby invalidating the linear model obtained at the other side of the peak. Similarly, at other operating points, the multivariable plant may exhibit new dynamic features such as inverse response. This work proposes to use deep reinforcement learning (DRL) strategies to simultaneously tune multiple SISO PID controllers using a single DRL agent while enforcing interval constraints on the tuning parameter values. This ensures that interaction effects between the loops are directly factored in the tuning. Interval constraints also ensure safety of the plant during training by ensuring that the tuning parameter values are bounded in a stable region. Moreover, a trained agent when deployed, provides operating condition based PID parameters on the fly ensuring nonlinear compensation in the PID design. The methodology is demonstrated on a quadruple tank benchmark system via simulations by simultaneously tuning two PI level controllers. The same methodology is then adopted to tune PI controllers for the operating condition under which the plant exhibits a right half plane multivariable direction zero. Comparisons with PI controllers tuned with standard methods suggest that the proposed method is a viable approach, particularly when simulators are available for the plant dynamics.

Data-Based Shape Self-Sensing of a Cable-Driven Notched Continuum Mechanism Using Multidimensional Intrinsic Force Information for Surgical Robot

Abstract The accurate shape-sensing capability of the continuum mechanism is fundamental to improve and guarantee the motion control accuracy and safety of continuum surgical robots. This paper presents a data-based shape self-sensing method for a cable-driven notched continuum mechanism using its multidimensional intrinsic force information, which mainly includes the multidimensional forces/torques and driving cable tensions. The nonlinear hysteresis compensation and the shape estimation of the notched continuum mechanism play significant roles in its motion control. Calibration compensation of the notched continuum mechanism is performed based on kinematic modeling to improve the accuracy of its preliminary motion control. The hysteresis characteristics of the continuum mechanism are analyzed, modeled, and compensated through considering the abundant dynamic motion experiments, such that a feedforward hysteresis compensation controller is designed to improve the tracking control performance of the continuum mechanism. Based on the kinematic calibration and hysteresis compensation, combined with the motor displacement, driving cable tensions, and six-dimensional forces/torques information of the continuum mechanism, a data-based shape self-sensing method based on particle swarm optimization back propagation neural network (PSO-BPNN) is proposed in this study. Experimental results show that this method can effectively estimate the loaded and unloaded shape of the notched continuum mechanism, which provides a new approach for the shape reconstruction of cable-driven notched continuum surgical robots.

Adaptive fuzzy command–filtered control strategy for electro-hydraulic braking systems of winding hoist with prescribed performance

In the braking control of winding hoisting systems, proper braking strategy is of great significance in reducing the probability of significant hidden dangers and improving the safety and reliability of the system. However, as a typical elastic and variable stiffness system, the winding hoisting systems have large nonlinearity, parameter uncertainties, random disturbances, and so on, which severely restrict the improvement of braking performance. To this end, an adaptive fuzzy command–filtered controller with prescribed performance is developed for electro-hydraulic braking systems of winding hoist in this article. First, the dynamic model of the winding hoisting system is established with consideration of the elasticity of wire rope. Based on the established dynamic model, using the fuzzy logic system, the algebraic loop problem caused by non-strict feed structure is overcome, and the unknown nonlinearities arising from modeling error, parameter uncertainties, and system disturbances are also approximated for the subsequent active unknown nonlinearities compensation. Next, to enhance the convergence rate and guarantee the position tracking error within a prescribed region, a tracking error transformation method based on the prescribed performance function is utilized. Subsequently, the adaptive fuzzy control algorithm is developed with command filters, which can also avoid the complexity explosion issue due to the analytic calculation of the derivatives of stabilizing functions, and the rigorous stability of the close-loop system is proved by the Lyapunov theory. Finally, experimental results are utilized to illustrate the effectiveness of the developed controller.

Perturbation-Aided Fiber Nonlinearity Compensation in Subcarrier-Multiplexing Systems

A perturbation-aided advanced digital backpropagation (P-ADBP) is proposed for subcarrier-multiplexing (SCM) coherent systems. To improve the nonlinearity compensation (NLC) performance, for the first time, the first-order perturbation analysis is introduced into the conventional ADBP. Based on the fact that the perturbation-based self-subcarrier nonlinearity (PSSN) has a similar form as the cross-subcarrier nonlinearity (CSN), we approximate that PSSN and CSN can be calculated in parallel and the compensation of them can be fused together. This compensation fusion scheme saves the computational complexity effectively by sacrificing only a little performance. Furthermore, to realize the best performance, gradient descent is used to jointly optimize the perturbation coefficients and other necessary parameters in P-ADBP. Verified by 9 × 120-GBaud 1600-km wavelength-division multiplexing SCM systems with dual-polarization 16QAM modulation format, 1-Step P-ADBP provides identical Q <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula> improvement as 5-Step ADBP but saves about 72.3% complexity. 5-Step P-ADBP and 10-Step P-ADBP also leapfrog into the NLC level of 10-Step ADBP and 20-Step ADBP, but save about 44.4% and 46.0% complexity, respectively. The proposed algorithm helps achieve an improved performance-complexity trade-off compared to the conventional ADBP and its state-of-the-art modifications.

Modelling and model-based tracking control of soft twisted and coiled actuators

Soft twisted and coiled actuators (STCAs) have promising prospects for application in the field of soft-bodied robots. However, the STCA has a complex energy conversion mechanism and a rate-dependent hysteresis nonlinearity, which brings great difficulties to its modelling and control. To solve these difficulties, this paper proposes modelling and model-based tracking control methods to realize the high-precision output-force tracking control of the STCA. First, a dynamics model framework is constructed, which consists of a thermo-electric model and a thermo-mechanical model, to describe the current-to-force process of the STCA. Among which, the thermo-mechanical model is established by combining the Bouc–Wen model and the linear dynamic system in series, which can accurately describe the rate-dependent hysteresis nonlinearity of the STCA. Then, a double closed-loop control architecture with a hysteresis inverse compensation controller is proposed, which can realize the timely control of the temperature and the compensation for the rate-dependent hysteresis nonlinearity of the STCA. Next, controller parameters are adjusted in the simulation environment to reduce the risk of the damage of the STCA and to obtain a satisfactory control effect. Finally, practical experiments are conducted, and root mean square errors of all experiment results are all less than 5.01%, which verifies the effectiveness of the proposed modelling and control methods.

Nonlinear disturbance compensator for active suspension systems with actuator saturation

Nonlinear disturbance compensator for active suspension systems with actuator saturation

Nonlinear electromagnetic force analysis and compensation control of electromagnetic linear actuator

Nonlinear electromagnetic force is a common phenomenon in electromagnetic linear actuators (EMLA). This nonlinearity limits the application in high-precision control systems. For facilitating the controller design, the influencing factors of nonlinear electromagnetic force were analyzed, and the quadratic polynomial with unknown weights was designed to approximate the nonlinear relationship among electromagnetic force, excitation current and displacement. An adaptive integral robust control algorithm based on electromagnetic force compensation (AIRC-FC) was designed, which combined the adaptive control law of electromagnetic force nonlinear compensation, stable feedback and error signal continuous integral robust control. The tracking performance and the adaptability of the EMLA with and without compensation control were analyzed under different loads. The results show that AIRC-FC improve the tracking performance of the EMLA effectively, and maintain high control accuracy under different loads.

KRLS post-distorter with adaptive kernel width for visible light communications.

As a viable supplement to the fifth generation wireless communication, visible light communications (VLC) with affluent spectrum resources can cater to the ever-increasing high speed data transmission demand. However, the nonlinear characteristics of light emitting diode (LED) can distort the transmitted signal in the VLC link, which damages the communication quality. To mitigate the nonlinear impairments, a reproducing kernel Hilbert space post-distortion scheme is proposed in this paper, which is based on kernel recursive least squares (KRLS) with adaptive kernel width. In this kernel based method, the kernel width will affect the approximation ability of the model. Therefore, in the recursive process of KRLS, Gauss-Newton (GN) algorithm is adopted to update the kernel width. In addition, combined with the enhanced novelty criterion (ENC), the KRLS-GN post-distorter learns the sparse dictionary adaptively according to the input data, which is beneficial to complete the linearization under the limited memory budget constraints. The performance of the proposed KRLS-GN-ENC scheme is verified by simulations, and the results show that KRLS-GN-ENC can achieve a significant improvement over KRLS-ENC. Compared with the schemes based on classical polynomial filtering, KRLS-GN-ENC exhibits better nonlinear compensation performance and faster convergence speed.

Long-Distance OFDR With High Spatial Resolution Based on Time Division Multiplexing

In this study, a long-distance optical frequency domain reflectometry (OFDR) with high spatial resolution based on time division multiplexing is proposed and experimentally demonstrated. Distributed strain sensing with high spatial resolution over long sensing range can be realized by reconfiguring the system layout in a time-division-multiplexed manner by re-routing the measurement signals for segmented processing with extra circulators and couplers only, rather than any other mechanisms for performance improvement of laser source or algorithms for nonlinear errors compensation. Through time-division-multiplexed reconfiguration, the sensing distance is no longer restricted by the path difference of the auxiliary interferometer which is commonly employed in OFDR systems for compensating laser frequency tuning nonlinearity. Compared with the traditional system layout, the proposed system allows distributed measurement with flexible spatial resolutions in each sub-sensing unit without any crosstalk among them. In experiments, distributed strain sensing with spatial resolution up to 5mm is achieved over an active sensing distance of 225m by the proposed system. Furthermore, the spatial resolution flexibility of the proposed system is further verified by successfully obtaining the strain information with 2 mm spatial resolution at the end of a 235-m-long fiber.

Improve Performance of 1-bit ADC Receiver by Blind Non-Linear Compensation

Improve Performance of 1-bit ADC Receiver by Blind Non-Linear Compensation