Periodic Dither Research Articles

Adaptive Optimization With Decaying Periodic Dither Signals

Real-time optimization in cyber–physical network systems with unknown system parameters must integrate optimization and parameter estimation, leading to adaptive optimization problems. Such problems encounter fundamental conflict between optimization and system identifiability. Recently, a new method of employing a stochastic or periodic dither has been introduced to resolve this conflict and achieve convergence toward optimal solutions. However, adding a dither introduces persistent disturbances to the optimal solution, resulting in an essential tradeoff between convergence rate and steady-state error. This article introduces a method of adding decaying periodic dither signals into the cyber–physical system, which can still provide sufficient excitations for estimating the unknown parameters and, at the same time, asymptotically reduce optimality errors down to zero without affecting negatively on identifiability. The convergence properties of parameter estimation and optimization updates are provided simultaneously, first for noise-free and model uncertain free cases, followed by general systems that include observation noise and modeling errors. A simulation example is used to illustrate the adaptive optimization algorithms and the main properties.

Sideband Vibro-Acoustic Responses and Improvements With Different Pulsewidth Modulation Strategies in Permanent Magnet Synchronous Motor for Electric Vehicle

This article presents a comprehensive investigation into the sideband vibro-acoustics with continuous and discontinuous pulsewidth modulation (PWM) strategies in permanent magnet synchronous motor (PMSM). The primary motivation for the evaluation reveals the frequency distributions of the sideband components and the magnitudes suppression with the space-vector PWM (SVPWM) and the discontinuous PWM (DPWM). The principle and implementation of the conventional SVPWM and six basic DPWM modes are firstly presented. The sideband harmonic components are provided by the analytical derivations, in which the frequency distributions are established by coupling the temporal features between the current harmonics and radial electromagnetic force. To evaluate and compare the sideband current harmonics and vibro-acoustic responses among the PWM schemes, the experimental tests are presented in a study case of 12/10 PMSM. Significant deterioration is observed in each of the basic DPWMs compared with that in SVPWM. Developed with periodic dithering modulation, notable sideband harmonics suppression and vibro-acoustic improvements in DPWM schemes are observed. This work is expected to provide a guidance for a hybrid modulation strategy in electric vehicles (EVs).

Evaluation and comparison of sideband harmonics and acoustic responses with continuous and discontinuous PWM strategies in permanent magnet synchronous motor for electric vehicles

High-frequency vibro-acoustics, introduced by voltage source inverter (VSI) and control strategies, are the critical features affecting the noise, vibration and harshness (NVH) performances of electric vehicles (EVs). In this paper, a comprehensive evaluation and comparison into sideband current harmonics and high-frequency vibro-acoustic responses has been studied with different control strategies in the study case of permanent magnet synchronous motor (PMSM). At first, the principles and implementation of continuous and discontinuous pulse-width modulations (PWM) techniques are explored. Then, the features of the sideband current harmonic and radial electromagnetic forces are deduced with analytical derivations, in which the frequency characteristics are also presented. Furthermore, all PWM schemes have been improved by a standard periodic dithering modulation with square signal-based to reduce the sideband harmonics. The experimental results show that the sideband current harmonics and vibro-acoustics are generally clustered around the carrier frequency and have a particular orders and spectral distributions. The overall level of the obtained DPWM schemes present a slight deterioration compared to the SVPWM ones. With the periodisation of the carrier frequency, the sideband components show a significant suppression, which is above 15 dBA reduced in the acoustic noise responses.

Adaptive Optimization with Periodic Dither Signals

Adaptive Optimization with Periodic Dither Signals

Probabilistic Guaranteed Gradient Learning-Based Spark Advance Self-Optimizing Control for Spark-Ignited Engines.

In spark-ignited (SI) engines, the spark advance (SA) controls the combustion phase that has a significant impact on the efficiency. Online self-optimizing control (SOC) of SA to maximize the indicated fuel conversion efficiency (IFCE) forms a stochastic optimization problem for a static map due to the stochasticity of combustion. Gradient-based optimization algorithms using periodic dithers are effective methods of dealing with such problems. However, decision sequences corrupted by periodic dithers are undesirable in SA online SOC. To choose a proper decision sequence for this problem, a gradient descent-based dither-free SOC scheme iteratively updates the decision based on probabilistic guaranteed gradient learning (PGGL). The PGGL approach uses the statistical distribution of the past samples to approximate the gradient on which the sample size can be adaptively adjusted to achieve the probabilistic target. The proposed scheme not only guarantees the accuracy of gradient learning but also adaptively adjusts the sample size in the learning process, achieving a tradeoff between a rapid response and a stable decision sequence. Moreover, the convergence performance of the obtained decision sequence is analyzed with respect to the probability distribution. Finally, experimental validations performed on an SI engine test bench show that the proposed PGGL-based SOC scheme successfully manages engine operation around the optimal IFCE with a fast response and stable SA behavior, under both steady and mild transient conditions.

An extremum-seeking control method driven by input–output correlation

This paper presents a new extremum-seeking controller (ESC) derived from a statistical interpretation of conventional ESC. The proposed ESC replaces the gradient feedback variable with a normalized correlation coefficient. The algorithm, as presented, can be fully configured with knowledge of only the open-loop response time of the system being optimized and the amplitude of the dither signal. Simulation tests show that the new algorithm has fast convergence times compared with other types of ESC algorithms. The paper also shows that the proposed method is not limited to a periodic dither signal and that it can also utilize a stochastic signal to similar efficacy. The purpose of the paper is to describe the new algorithm and present a practical implementation along with results from simulation tests.

Improving Digital-to-Analog Converter Linearity by Large High-Frequency Dithering

A new method for reducing harmonic distortion due to element mismatch in digital-to-analog converters is described. This is achieved by using a large high-frequency periodic dither. The reduction in nonlinearity is due to the smoothing effect this dither has on the nonlinearity, which is only dependent on the amplitude distribution function of the dither. Since the high-frequency dither is unwanted in the output of the digital-to-analog converter, the dither is removed by an output filter. The fundamental frequency component of the dither is attenuated by a passive notch filter and the remaining fundamental component and harmonic components are attenuated by the low-pass reconstruction filter. Two methods that further improve performance are also presented. By reproducing the dither on a second channel and subtracting it using a differential amplifier, additional dither attenuation is achieved; and by averaging several channels, the noise-floor of the output is improved. Experimental results demonstrate more than 10 dB improvement in the signal-to-noise-and-distortion ratio.

Interplay between turbulence, neoclassical and zonal flows during the transition from low to high confinement mode at ASDEX Upgrade

The spatio-temporal interplay between turbulence, mean and zonal flows has been investigated at the L–H and H–L transitions in the edge region of the ASDEX Upgrade tokamak. Close to both transitions, an intermediate phase (I-phase) characterized by ‘limit cycle like oscillations’ (LCOs) is observed in which periodic bursts of turbulence correlate with flow reduction and relaxation of gradients. During the I-phase, the velocity is dominated by the mean flows indicating that turbulence driven flows are small. Periodic dithers between L-mode and the phases with LCOs are also observed just before the H-mode onset where the edge density and temperature profile gradients evolve on similar timescale as the flows. Thus connection between mean and flows holds during the all evolution from L-mode to H-mode demonstrating the fundamental role of the neoclassical flows in the L–H transition physics.

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.

Discrimination of steady state and transient state of dither extremum seeking control via sinusoidal detection

A major class of extremum seeking control (ESC) is based on the use of periodic dither perturbation of plant input for extracting the gradient information. Presence of the dither input into the steady state operation is undesirable in practice due to the possible excessive wear of actuators. It is thus beneficial to stop the dithering action after the ESC reaches its steady state. In this paper, we propose a method for automatically discriminating between the steady state and the transient state modes of extremum seeking control process using the sinusoidal detection techniques. Some design guidelines are proposed for the parameter selection of the relevant sinusoidal detection scheme. The proposed scheme is validated with simulation study on dynamic virtual plant of two building HVAC systems.

An Effective Dithering Method for Electromagnetic Interference (EMI) Reduction in Single-Phase DC/AC Inverters

A comprehensive method of electromagnetic emission interference (EMI) reduction in dc/ac inverters through periodic dithering of the pulse-width modulated (PWM) switching frequency is presented in this paper. The periodic dithering is the process of changing the switching frequency of the PWM signal that drives the switches of the power electronics inverter. The effects of the various parameters involved in the PWM dithering process have been analyzed in this paper. The important parameters involved in the dithering process are the frequency range used for dithering, the periodic time of the dithering signal, and the phase of the dithering signal. The effect of each of these parameters has been studied to determine their values that minimize the EMI. Additionally, analytical expressions for theoretical prediction of the EMI levels at different frequencies have been derived for performance analysis during the design stage. The theoretical predictions for the dithering signals have been found to accurately correlate with both the simulation and experimental results.

Effect of waveform on the effectiveness of tangential dither forces to cancel friction-induced oscillations

High-frequency dither forces are often used to reduce unwanted vibration in frictional systems. This paper examines how the effectiveness of these dither-cancellation techniques is influenced by the nature of periodic signal employed. The paper investigates a single-degree-of-freedom (sdof) system consisting of a mass in frictional contact with a translating belt using two different models of friction. Prior work by the authors focused on sinusoidal dither waveforms. This paper extends this analysis to general, periodic dither forces. Using an averaging technique, the optimal waveforms are determined among periodic signals having either unit-amplitude or unit-rms value. For unit-amplitude dither signals, it is found that square waveforms are able to quench self-excited oscillations with the smallest amplitude of all waveforms of equal strength at every belt speed. Among unit-rms dither waveforms, square waves are best for low belt speeds, but sinusoidal dither is revealed to be best in higher ranges of belt speed. After studying generic waveforms, the results are specialized for three specific examples: sinusoidal, triangular, and square. In particular, the relative performance of the three waveforms is studied using an averaging technique as well as direct time integration.

The influence of noise on output of Ring Laser Gyroscope

Although the effect of lock-in in Ring Laser Gyroscope (RLG) can be reduced sharply by introducing mechanical dither into the input of RLG, there is still much large RLG readout error, which is unacceptable for medium/high-precision inertial navigation, due to the appearance of dynamic lock-ins. Superimposing noise on periodic dither signal can reduce the influence of dynamic lock-ins further. The relationships of RLG output's deviation from mean and dispersion coefficient with noise intensity are analyzed with the inputs of both single noise and compound dither (periodic dither superimposed with noise), respectively. The results show that single noise is less practical than compound dither.

Spur-reduced digital sinusoid synthesis

This paper presents and analyzes a technique for reducing the spurious signal content in digital sinusoid synthesis. Spur reduction is accomplished through dithering amplitude and phase values prior to wordlength reduction. The analytical approach developed for analog quantization is used to produce new bounds on spur performance in these dithered systems. Amplitude dithering allows output wordlength reduction without introducing additional spurs. Effects of periodic dither similar to that produced by a pseudo-noise (PN) generator are analyzed. This phase dithering method provides a spur reduction of 6(M+1) dB per phase bit when the dither consists of M uniform variates. While the spur reduction is at the expense of an increase in system noise, the noise can be made white, making the noise power spectral density small. This technique permits the use of a smaller number of phase bits addressing sinusoid look-up tables, resulting in an exponential decrease in system complexity. Amplitude dithering allows the use of less complicated multipliers and narrower data paths in purely digital applications, as well as the use of coarse-resolution, highly-linear digital-to-analog converters (DAC's) to obtain spur performance limited by the DAC linearity rather than its resolution.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>