Dither Signal Research Articles

Loop gain stabilizing with an all-digital automatic-gain-control method for high-precision fiber-optic gyroscope.

For a fiber-optic gyroscope (FOG) using electronic dithers to suppress the dead zone, without a fixed loop gain, the deterministic compensation for the dither signals in the control loop of the FOG cannot remain accurate, resulting in the dither residuals in the FOG rotation rate output and the navigation errors in the inertial navigation system. An all-digital automatic-gain-control method for stabilizing the loop gain of the FOG is proposed. By using a perturbation square wave to measure the loop gain of the FOG and adding an automatic gain control loop in the conventional control loop of the FOG, we successfully obtain the actual loop gain and make the loop gain converge to the reference value. The experimental results show that in the case of 20% variation in the loop gain, the dither residuals are successfully eliminated and the standard deviation of the FOG sampling outputs is decreased from 2.00 deg/h to 0.62 deg/h (sampling period 2.5 ms, 10 points smoothing). With this method, the loop gain of the FOG can be stabilized over the operation temperature range and in the long-time application, which provides a solid foundation for the engineering applications of the high-precision FOG.

A Novel Architecture of Pseudorandom Dithered MASH Digital Delta-Sigma Modulator with Lower Spur

A Digital Delta Sigma Modulator (DDSM) is a Finite State Machine (FSM); it is implemented using finite precision arithmetic units and the number of available states is finite. The DDSM always produces a periodic output signal when the input is constant. This paper proposes a novel method of applying periodic dither to a DDSM in order to obtain minimized spurious tones. The effects of adding the pseudorandom dither signal in different stages within the proposed Multi-Stage noise Shaping (MASH) modulator are expressed in the equations, and the results are compared. We present results regarding the periodicity of the quantization noise produced by a MASH modulator with a constant input and a pseudorandom dither signal. The performance is confirmed mathematically, and by simulation.

Parameter tuning method for dither compensation of a pneumatic proportional valve with friction

In the practical application of pneumatic control devices, the nonlinearity of a pneumatic control valve become the main factor affecting the control effect, which comes mainly from the dynamic friction force. The dynamic friction inside the valve may cause hysteresis and a dead zone. In this paper, a dither compensation mechanism is proposed to reduce negative effects on the basis of analyzing the mechanism of friction force. The specific dither signal (using a sinusoidal signal) was superimposed on the control signal of the valve. Based on the relationship between the parameters of the dither signal and the inherent characteristics of the proportional servo valve, a parameter tuning method was proposed, which uses a displacement sensor to measure the maximum static friction inside the valve. According to the experimental results, the proper amplitude ranges are determined for different pressures. In order to get the optimal parameters of the dither signal, some dither compensation experiments have been carried out on different signal amplitude and gas pressure conditions. Optimal parameters are determined under two kinds of pressure conditions. Using tuning parameters the valve spool displacement experiment has been taken. From the experiment results, hysteresis of the proportional servo valve is significantly reduced. And through simulation and experiments, the cut-off frequency of the proportional valve has also been widened. Therefore after adding the dither signal, the static and dynamic characteristics of the proportional valve are both improved to a certain degree. This research proposes a parameter tuning method of dither signal, and the validity of the method is verified experimentally.

Dither in a rolling airframe flight vehicle with a two-position actuator: An amplitude distribution approach

Rolling airframe manoeuvring is a type of manoeuvre in which the missile provides continuous roll during flight. Cross-coupling between the angle of attack and sideslip in rolling airframe missiles (RAMs) yields a coning motion around the flight path. As the pitch and yaw cross-coupling effect decreases, the radius of this coning motion decreases and the accuracy of the control system increases. Two-position (on–off) actuators are used in most RAMs. The presence of a two-position actuator in a feedback system makes its characteristics non-linear. A high-frequency signal so-called dither is applied to compensate for the non-linearity effect of the actuator characteristic in the feedback system and to stabilize the coning motion. The amplitude distribution function (ADF) method in dither analysis shows that the smoothed non-linearity characteristic can be computed as the convolution of the original non-linearity and the ADF of the dither signal. According to the four-degrees-of-freedom (4-DOF) equations of RAMs in a non-rolling frame and regarding various dither signals through the ADF approach on a two-position actuator, an analytical condition for dither amplitude in coning motion stability of RAMs is derived. It was shown that the triangular signal with specified amplitude and high enough frequency led to a smoother response of two-position actuators. Finally, by applying beam-riding guidance to a RAM, the performance of dithers for decreasing the distance of the missile from the centre of the beam is validated through simulations. It is illustrated that applying the triangular dither resulted in minimal error.

A robust extremum seeking scheme for dynamic systems with uncertainties and disturbances

This paper studies a numerical optimization-based extremum seeking scheme for systems with unmodeled dynamics and unknown disturbances without using dither signals. The robust extremum seeking scheme is composed of a numerical gradient estimator, a numerical optimizer and an extended-state observer based state regulator. A conjugate gradient method is adopted to achieve extremum seeking. A nonlinear extended-state observer based state regulator is proposed to regulate the states. The robust extremum seeker is based on the numerical optimization based extremum seeking framework. Sufficient conditions are derived to ensure the convergence of the overall extremum seeking scheme. The ultimate convergence bound is quantified for a class of strongly convex functions. A numerical example is presented to verify the proposed method.

A novel structure of dithered nested digital delta sigma modulator with low-complexity low-spur for fractional frequency synthesizers

Purpose – Digital Delta Sigma Modulator (DDSM) is used widely in electronic circuits including Radars, class-D power amplifiers and fractional frequency synthesizers. The purpose of this paper is to propose an implementation for MASH DDSMs named as Multi Modulus Reduced Complexity (MMRC) architecture. Design/methodology/approach – This architecture will use a very simple pseudorandom Linear Feedback Shift Register (LFSR) dither signal with period N_d to randomize the digital MMRC modulator used for fractional frequency synthesizers. Using error masking methodology, the MMRC modulator can decrease the hardware consumption and increase accuracy of the fractional frequency synthesizer. Rules for selecting the appropriate word lengths of the constituent MMRC modulator are derived. Findings – This paper contains three modulators. The first stage modulator is a variable modulus First Order Error Feedback Modulator and has a programmable modulus M1 that is not a power of two. The second and third stage modulators are the first order pseudorandom LFSR dithered MASH 1-1 and modified MASH 1-1-1, which have conventional modulo M2, M3, respectively. With optimum selection modulus M1, the new structure can synthesize the desired frequency exactly. Simulation results confirm the theoretical predictions. Also the results of circuit implementation proposed method reports 13 per cent reduction in hardware. Originality/value – This paper for the first time proposes a nested sigma delta modulator with a pseudorandom shaped dither signal which reduced hardware complexity and increased the period of output signal. This modulator is exploited in the fractional frequency synthesizer to the output frequency can be set more accurately.

Nonlinear Dynamics and Control in an Automotive Brake System

Brake squeal is a manifestation of friction-induced self-excited instability in disc brake systems. This study investigated non-smooth bifurcations and chaotic dynamics in disc brake systems and elucidated a chaotic control system. Decreasing squeal noise which is dependent on chaos, increases passengers comfort; consequently, suppressing chaos is crucial. First, synchronization was used to estimate the largest Lyapunov exponent to identify periodic and chaotic motions. Next, complex nonlinear behaviors were thoroughly observed for a range of parameter values in the bifurcation diagram. Rich dynamics of the disc brake system were studied using a bifurcation diagram, phase portraits, a Poincare map, frequency spectra, and Lyapunov exponents. Finally, the proposed technique was applied to a chaotic disc brake system through the addition of an external input that is a dither signal. Simulation results demonstrated the feasibility of the proposed approach.

Spectral Shape Impact of Nonlinear Compensator Signal in LTE RoF System

In this letter, a large scale investigation is carried out, utilizing several spectral shapes as the source for direct modulation based frequency dithering (DMFD). DMFD mitigates the nonlinear effect of long term evolution (LTE) radio-over-fiber (RoF) systems. The dithering signal shapes are; sine, square, saw, sinc and Gaussian with different spectral width characteristics. We show that by varying the dithering signal with increasing spectral width, no additional distortion is introduced in the linear and optimum optical launch power regions, which are dominated by the frequency chirp and chromatic dispersion (CD). Additionally, it is revealed herein that introducing dithering signals with varying spectral widths does not change the nonlinear compensator characteristic towards suppression of nonlinearity. The reason for this is that as long as the optical source linewidth is larger than stimulated Brillouin scattering (SBS) linewidth, the proposed method completely suppresses SBS. Finally, the degree of freedom for the dithering signal is infinite, with an optical power budget improvement of up to 8 dB at an optical launch power of 10 dBm, which can in turn be used towards connecting multiple relay nodes (RNs).

A Maximum Power Tracking Technique for Grid-Connected DFIG-Based Wind Turbines

In this paper, a maximum power tracking technique is presented for doubly fed induction generator-based wind turbines. The presented technique is a novel version of the conventional method, i.e., the electrical torque is proportional to the square of the rotor speed, in which the proportional coefficient is adaptively adjusted in real-time through three control laws. The first control law calculates the desired electrical torque using feedback linearization, assuming that the power capture coefficient and the desired rotor speed are instantaneously identified. The second control law estimates the real-time values of the power capture coefficient from a Lyapunov-based analysis, and the third control law provides the desired rotor speed. These control laws cause the turbine to adaptively adjust the rotor speed toward a desired speed in which the operating point moves in the direction of increasing the power capture coefficient. The proposed maximum power tracking method differs distinctly from the perturb-and-observe scheme by eliminating a need for adding a dither or perturbation signal, and robustly tracks the trajectory of maximum power points even in the event of a sudden wind speed change that can cause the perturb-and-observe technique to fail. In this paper, the National Renewal Energy Laboratory 5-MW reference wind turbine model is used to demonstrate the validity and robustness of the proposed method.

Ditherless Extremum Seeking for Hydrogen Minimization in PEM Fuel Cells

This paper presents a nonsmooth adaptive extremum seeker that minimizes the hydrogen consumption in a fuel-cell system. The extremum seeker operates by estimating the gradient of the objective function but, unlike other seekers, it does not require a dither signal to produce such estimate. The absence of a dither signal simplifies the choice of parameter values for the seeker, and more importantly, it allows it to converge to the optimal value exactly, not only to a small neighborhood. The proper functioning of the proposed scheme is proved using nonsmooth Lyapunov analysis. The strategy is tested on the input–output map of a real polymer electrolyte fuel cell.

Dither Re-Use in Nash Equilibrium Seeking

Nash equilibrium seeking (NES) scheme consists of a number of decentralized extremum-seeking (ES) “agents”, each controlling an input such that an associated (selfish) cost is regulated to its steady-state Nash equilibrium. A non-local stability result for the NES scheme is provided which allows two agents to use the same dither signal if the effect of each agent on the other's steady-state cost function is sufficiently weak. Its application to plants with quadratic cost functions is presented as an example. It is then demonstrated in simulation that, by reducing the number of distinct dither signals, the proposed scheme still has acceptable convergence properties, while design effort is reduced.

Spurious tones in digital delta-sigma modulators resulting from pseudorandom dither

Digital delta-sigma modulators (DDSMs) are finite state machines; their spectra are characterized by strong periodic tones (so-called spurs) when they cycle repeatedly in time through a small number of states. This happens when the input is constant or periodic. Pseudorandom dither generators are widely used to break up periodic cycles in DDSMs in order to eliminate spurs produced by underlying periodic behavior. Unfortunately, pseudorandom dither signals are themselves periodic and therefore can have limited effectiveness. This paper addresses the fundamental limitations of using pseudorandom dither signals that are inherently periodic. We clarify some common misunderstandings in the DDSM literature. We present rigorous mathematical analysis, case studies to illustrate the issues, and insights which can prove useful in design.

PWM and PFM for visual servoing in fully decoupled approaches

In this paper, novel visual servoing techniques based on Pulse Width Modulation (PWM) and Pulse Frequency Modulation (PFM) are presented. In order to apply previous pulse modulations, a fully decoupled position based visual servoing approach (i.e. with block-diagonal interaction matrix) is considered, controlling independently translational and rotational camera motions. These techniques, working at high frequency, could be considered to address the sensor latency problem inherent in visual servoing systems. The expected appearance of ripple due to the concentration of the control action in pulses is quantified and analyzed under simulated scenario. This high frequency ripple does not affect the system performance since it is filtered by the manipulator dynamics. On the contrary it can be seen as a dither signal to minimize the impact of friction and overcome back-lashing.

Security Analysis of Scalar Costa Scheme Against Known Message Attack in DCT-Domain Image Watermarking

This paper proposes an accurate information-theoretic security analysis of Scalar Costa Scheme (SCS) when the SCS is employed in the embedding layer of digital image watermarking. For this purpose, Discrete Cosine Transform (DCT) coefficients are extracted from the cover images. Then, the SCS is used to embed watermarking messages into mid-frequency DCT coefficients. To prevent unauthorized embedding and/or decoding, the SCS codebook is randomized using the pseudorandom dither signal which plays the role of the secret key. A passive attacker applies Known Message Attack (KMA) on the watermarked messages to practically estimate the secret key. The security level is measured using residual entropy (equivocation) of the secret key provided that the attacker’s observations are available. It can be seen that the practical security level of the SCS depends on the host statistics which has contradiction with previous theoretical result. Furthermore, the practical security analysis of the SCS leads to the different values of the residual entropy in comparison with previous theoretical equation. It will be shown that these differences are mainly due to existence of uniform regions in images that cannot be captured by previous theoretical analysis. Another source of such differences is ignoring the dependencies between the observations of non-uniform regions in previous theoretical analysis. To provide an accurate reformulation, the theoretical equation for the uniform regions and the empirical equation for the non-uniform regions are proposed. Then, by combining these equations a new equation is presented for the whole image which considers both host statistics and observations dependencies. Finally, accuracy of the proposed formulations is examined through exhaustive simulations.

A new anti-forensic scheme--hiding the single JPEG compression trace for digital image.

To prevent image forgeries, a number of forensic techniques for digital image have been developed that can detect an image's origin, trace its processing history, and can also locate the position of tampering. Especially, the statistical footprint left by JPEG compression operation can be a valuable source of information for the forensic analyst, and some image forensic algorithm have been raised based on the image statistics in the DCT domain. Recently, it has been shown that footprints can be removed by adding a suitable anti-forensic dithering signal to the image in the DCT domain, this results in invalid for some image forensic algorithms. In this paper, a novel anti-forensic algorithm is proposed, which is capable of concealing the quantization artifacts that left in the single JPEG compressed image. In the scheme, a chaos-based dither is added to an image's DCT coefficients to remove such artifacts. Effectiveness of both the scheme and the loss of image quality are evaluated through the experiments. The simulation results show that the proposed anti-forensic scheme can verify the reliability of the JPEG forensic tools.

A time-varying extremum-seeking control approach

This paper considers the solution of a real-time optimization problem using adaptive extremum seeking control. It is assumed that the equations describing the dynamics of the nonlinear system and the cost function to be minimized are unknown and that the objective function is measured. The main contribution of the paper is to formulate the extremum-seeking problem as a time-varying estimation problem. The proposed approach is shown to avoid the need for averaging results which minimizes the impact of the choice of dither signal on the performance of the extremum seeking control system. Several examples are used to illustrate the effectiveness of the proposed technique.

Design of Adaptive Filter for Laser Gyro

According to the filtering of laser gyro output signal of low precision, slow speed of dynamic response, the research and implementation of a new method of laser gyro filtering process, the scheme using LMS adaptive filtering algorithm, the dither feedback signal as the iterative filter data input, the dither signal, random noise, white noise as the reference signal filter, digital filter and the external control using FPGA, give the filter algorithm and hardware block diagram. Experimental results show that the filtering module with filter with high precision and wide dynamic response range, can meet the requirements of speed and precision of laser gyro demodulation aerospace fields.

A multi-objective extremum-seeking controller design technique

This paper considers the solution of a multi-objective optimisation problem using adaptive extremum-seeking control for a class of uncertain nonlinear systems. It is assumed that the equations describing the dynamics of the nonlinear system and the cost functions to be optimised are unknown and that the objective functions are measured. The proposed extremum-seeking control technique uses a time-varying estimation of the unknown gradients that minimises the impact of the choice of dither signal on the performance of the extremum-seeking control system. The technique guarantees convergence of the system to any point of the set of Pareto optimal solutions. It is adapted to allow the computation of specific desirable Pareto solutions using a utopic formulation. Simulation examples are used to illustrate the effectiveness of the proposed technique.

JPEG Anti-Forensics With Improved Tradeoff Between Forensic Undetectability and Image Quality

This paper proposes a JPEG anti-forensic method, which aims at removing from a given image the footprints left by JPEG compression, in both the spatial domain and DCT domain. With reasonable loss of image quality, the proposed method can defeat existing forensic detectors that attempt to identify traces of the image JPEG compression history or JPEG anti-forensic processing. In our framework, first because of a total variation-based deblocking operation, the partly recovered DCT information is thereafter used to build an adaptive local dithering signal model, which is able to bring the DCT histogram of the processed image close to that of the original one. Then, a perceptual DCT histogram smoothing is carried out by solving a simplified assignment problem, where the cost function is established as the total perceptual quality loss due to the DCT coefficient modification. The second-round deblocking and de-calibration operations successfully bring the image statistics that are used by the JPEG forensic detectors to the normal status. Experimental results show that the proposed method outperforms the state-of-the-art methods in a better tradeoff between the JPEG forensic undetectability and the visual quality of processed images. Moreover, the application of the proposed anti-forensic method in disguising double JPEG compression artifacts is proven to be feasible by experiments.

A Minmax Extremum-Seeking Controller Design Technique

This paper considers the solution of a minmax optimization problem using adaptive extremum seeking control. It is assumed that the equations describing the dynamics of the nonlinear system and the cost function to be minimized are unknown and that the objective function is measured. The appropriate selection of the minimizing and the maximizing inputs is also assumed to be known a priori. The proposed extremum-seeking control technique uses a time-varying estimation of the unknown gradients that minimizes the impact of the choice of dither signal on the performance of the extremum seeking control system. Two examples are used to illustrate the effectiveness of the proposed technique.