Pulse-width Modulated Systems Research Articles

Averaging for switched impulsive systems with pulse width modulation

Linear switched impulsive systems (SIS) are characterized by ordinary differential equations as modes dynamics and state jumps at the switching time instants. The presence of possible jumps in the state makes nontrivial the application of classical averaging techniques. In this paper we consider SIS with pulse width modulation (PWM) and we propose an averaged model whose solution approximates the moving average of the SIS solution with an error which decreases with the multiple of the switching period and by decreasing the PWM period. The averaging result requires milder assumptions on the system matrices with respect to those needed by the previous averaging techniques for SIS. The interest of the proposed model is strengthened by the fact that it reduces to the classical averaged model for PWM systems when there are no jumps in the state. The theoretical results are verified through simulations obtained by considering a switched capacitor electrical circuit.

The Effect of Nozzle Body Volume on Pressure Dynamics in a PWM Sprayer System

Highlights The variability in damping ratio between different sized nozzle tips was reduced with an increase in nozzle body volume, indicating that the previous works using pressure-sensing manifolds in PWM systems may have underestimated the nozzle pressure fluctuations. Pressure sensors installed at the nozzle body and the manifolds tested exhibited a different damping ratio, suggesting a slight change in sensor location might yield different measurements of transient pressure characteristics. A minimally invasive instrumented pressure sensor at the nozzle body is needed to accurately measure nozzle pressure dynamics. Abstract. Nozzle pressure measurements in agricultural sprayers are commonly conducted by adding a manifold between the nozzle body and nozzle tip. The additional component substantially increases the internal volume of the nozzle body, which affects nozzle pressure dynamics. This research focused on the effect of nozzle body volume on pressure dynamics when operating a spray nozzle under pulse-width-modulation control. A nozzle body and two manifolds of different volumes were instrumented with embedded pressure sensors. In a static test environment, pressure data were collected at 345 kPa nominal pressure at 50% duty cycle with a variety of nozzle orifice sizes. A second-order transfer function was used to model a portion of the dynamic pressure data. The damping ratio generally decreased as the volume of the nozzle body increased due to the addition of a manifold. The variability in damping ratio with respect to nozzle orifice size was reduced when adding a manifold. The lower damping ratios when a manifold was present generally resulted in more overshoot and slower settling time. Results also showed a slightly higher damping ratio at the nozzle body than at the manifold when either manifold was added. The differences in nozzle pressure dynamics with and without the addition of a pressure sensing manifold suggest that previous studies using instrumented nozzle bodies under PWM control may have underestimated the amplitude of pressure oscillations and the time to reach equilibrium. Keywords: Agricultural Sprayers, Measurement Accuracy, Nozzle Body Volume, Pressure Dynamics, Pulse Width Modulation (PWM).

Multilevel Fixed Pulse Pattern Control for Medium-Voltage High-Frequency Inverter

To satisfy the demand for more compact medium-voltage motor drive systems, it is desirable to increase the frequency of the cascaded H-bridge inverters used in high-speed motor systems. However, in asynchronous pulse width modulation (PWM) systems, as the output frequency increases, the command voltage and triangular wave carrier frequencies get closer, making it impossible to accurately output the command voltage. This manifest itself as increased current harmonics, increased surge voltage at the motor terminals, and increased low-frequency ripple current due to the asynchronous nature of the system. In this study, we adopt a fixed pulse pattern modulation method to address these problems. In our method, a low-distortion output voltage is compiled in advance into a table, and subsequently output in synchronization with the fundamental voltage phase. We were able to confirm the effectiveness of the proposed method in simulations at fundamental wave frequencies of 700 Hz and 1000 Hz.

Application of Led on Plant Growth Unit in Tomato Cultivation

Effects of Light Emitting Diode (LED) lamps on plant growth with different modulations on the tomato plant were investigated by applying under actual conditions in the greenhouses. Thus, four different pulse width modulation (PWM) systems from red and blue LEDS at different wavelengths were designed. Trials were performed by using direct current (Mode1), 5Khz-φ = 0o (Mode2), 5Khz-φ = 180o (Mode3) and 1Khz-φ = 0o (Mode4) and the tomato grown under the sun at the same conditions were compared for controlling purposes. Stomata movements and total chlorophyll content of the tomatoes were examined, and the results were compared to the tomatoes that were grown under sun. The custom developed artificial four light source system, a treatment of Mode 2 produced the highest yield, while each treatment played its special role in regulating plant morphology and physiology. Bangladesh J. Bot. 50(3): 523-529, 2021 (September)

Field assessment of a pulse width modulation\xa0(PWM) spray system applying different spray volumes: duty cycle and forward speed effects on vines spray coverage

The pulse width modulation (PWM) spray system is the most advanced technology to obtain variable rate spray application without varying the operative sprayer parameters (e.g. spray pressure, nozzle size). According to the precision agriculture principles, PWM is the prime technology that allows to spray the required amount where needed without varying the droplet size spectra which benefits both the uniformity of spray quality and the spray drift reduction. However, some concerns related to the effect of on–off solenoid valves and the alternating on/off action of adjacent nozzles on final uneven spray coverage (SC) have arisen. Further evaluations of PWM systems used for spraying 3D crops under field conditions are welcomed. A tower-shaped airblast sprayer equipped with a PWM was tested in a vineyard. Twelve configurations, combining duty cycles (DC: 30, 50, 70, 100%) and forward speeds (FS: 4, 6, 8 km h−1), were tested. Two methodologies, namely field-standardized and real field conditions, were adopted to evaluate the effect of DC and FS on (1) SC variability (CV%) along both the sprayer travel direction and the vertical spray profile using long water sensitive papers (WSP), and (2) SC uniformity (IU, index value) within the canopy at different depths and heights, respectively. Furthermore, the SC (%) and deposit density (Nst, no stains cm−2), determined using short WSP, were used to evaluate the spray application performances taking into account the spray volumes applied. Under field-controlled conditions, the pulsing of the PWM system affects both the SC variability measured along the sprayer travel direction and along the vertical spray profile. In contrast, under real field conditions, the PWM system does not affect the uniformity of SC measured within the canopy. The relationship between SC and Nst allowed identification of the ranges of 200–250 and 300–370 l ha−1 as the most suitable spray volumes to be applied for insecticide and fungicide plant protection products, respectively.

Field Performance Evaluation of Pulse-Width Modulation and Pressure-Controlled, Fixed-Orifice Application Systems for Sensor-Based Nitrogen Applications

HighlightsComparison of PC system and PWM system in-field performance indicated that the PWM system made sensor-based N applications more accurately than the PC system.The turndown ratio calculated from the aggregate application instances was 6.2:1.For both the PWM system and the PC system, applications were made more accurately when 28% UAN was applied rather than 32% UAN. Abstract. Sensor-based nitrogen (N) applications have shown promise for improving N use efficiency, but present significant challenges for application rate control due to highly variable and frequently changing target rates. If applications are to be made precisely, equipment systems used for sensor-based N applications must be designed to meet system demands. Pulse-width modulation (PWM) equipped systems have emerged as a technological advancement over traditional pressure-controlled (PC) systems for improving variable rate N application accuracy. Little research, however, has been done to assess the performance of PWM systems during sensor-based N applications in-field. This work analyzed as-applied data collected from in-field sensor-based N applications with pressure-controlled (PC) and PWM systems in Nebraska between 2015 and 2017 to quantify system requirements, assess system performance, and determine performance impacting operational variables. It was found that systems should be capable of 1-s rate changes of ±71.1 L ha-1 (7.6 gpa), 1-s flow rate changes of ±11.4 L min-1 (3 gpm), and turndown ratios of at least 6:1. PWM systems achieved application rates within 10% of the target rate 10% more often than PC systems, and showed less variability in application error. However, PWM systems still demonstrated significant application errors with an observed RMSE of 44.9 L ha-1 (4.8 gpa). Speed change magnitude was found to be most associated with increases in percent application error. These findings substantiate that PWM systems effectively improve sensor-based N application accuracy versus traditional PC systems. However, collaborative efforts toward greater cohesion between sensor-based application expectations and application equipment capabilities are necessary for maximizing the effectiveness of sensor-based N applications. Keywords: Precision agriculture, Rate controllers, Site-specific crop management, Sprayer, Turndown ratio.

Research of modular multilevel converter with phase-shifted pulse-width modulation

The work is devoted to the study of performance of a multilevel electric energy converter using phase-shifted pulse-width modulation. Equations describing the state of a dynamic system multilevel converter - load are investigated and a mathematical model of the system in Matlab / Simulink environment has been constructed. Variants of implementation of phase-shifted pulse-width modulation systems from the point of view of influence on harmonics of output voltage and magnitude of circulating current in the converter are investigated.

An analytical method of switching waveform design for selective harmonic elimination

The paper proposes an analytical approach to the design of switching waveforms to eliminate harmonics and thereby improve THD (Total Harmonic Distortion) in power converters. Generally, numerical solutions are used to obtain the switching angles to eliminate targeted harmonics and the solution requires guessing of an initial value and a valid modulation index, m (a ratio of the fundamental to the dc input). Both of these values affect solution convergence whereas, such difficulties do not arise in analytical solutions. The closed-form solutions obtained through the analytical approach also determine the valid range of m. Due to the closed form, this method is suitable for real-time applications where a microcontroller can be programmed, thus making it attractive for low-cost applications. A PWM (Pulse Width Modulation) signal with even–odd symmetry has been selected to minimize the complexity of the solution. The approach requires the solution of transcendental equations associated with Fourier coefficients of a periodic waveform. Chebyshev expansion is used to convert the transcendental equations to power-sum non-linear polynomials. A successive polynomial simplification method has been used that lead to a set of elementary functions in closed-form, which are used to generate a polynomial and its roots are the desired optimal switching angles. In this paper, the proposed approach has been examined through a fourth-order, three-phase system for bipolar and multistep waveforms. The approach is equally applicable to other types of PWM systems. Simulation results verify the harmonic cancellations.

Autonomous Event Driven Model of Second Order Voltage Switched Charge Pump PLL

The charge-pump Phase-Locked Loop (CP-PLL) is a widely used subsystem in wireless communication and smart system applications to perform the function of frequency synthesizer. Since the CP-PLL is a mixed-signal system, it is more complex to analyze the system behavior, especially when a voltage switched charge-pump-PLL (VSCP-PLL) is used. A more robust approach is required for such a non-linear pulse width modulated system, where the overall gain of the loop is varying due to non-constant pump current. To analyze the sampled behavior of a VSCP-PLL, the Event Driven (ED) model based on discrete-time phase equations is one of the powerful and resource efficient tool. In this brief, an autonomous ED model (time-independent and linear to fixed point) is developed for a second order VSCP-PLL by modifying the ED approach. The developed Autonomous ED-model is validated using the ED simulations in the locked state.

Droplet size and nozzle tip pressure from a pulse-width modulation sprayer

Pulse-width modulation (PWM) sprayers can improve application accuracy through flow control, turn compensation, and high-resolution overlap control by pulsing an electronically-actuated solenoid valve which controls the relative proportion of time each solenoid valve is open (duty cycle). The objective of this experiment was to identify the droplet size distribution and nozzle tip pressure when influenced by PWM duty cycle, nozzle technology, and gauge pressure to provide PWM guidelines. The experiment was conducted in a low-speed wind tunnel at the Pesticide Application Technology Laboratory using a SharpShooter® PWM system. In general, for non-venturi nozzles, as duty cycle decreased, droplet size slightly increased between 40 and 100% duty cycles. Conversely, venturi nozzles did not always follow this trend. The lowest duty cycle evaluated (20%) negatively impacted droplet size and caused inconsistencies for all nozzle by pressure combinations. The addition of a solenoid valve lowered nozzle tip pressure while gauge pressure remained constant indicating a restriction is present within the solenoid valve. Greater orifice sizes increased the pressure loss observed. Duty cycle minimally impacted nozzle tip pressure trends which were similar to the electrical square wave PWM signals. However, venturi nozzles deviated from this trend, specifically twin-fan, single pre-orifice venturi nozzles. In conclusion, venturi nozzles are not recommended for PWM systems as they may lead to inconsistent applications, specifically in regards to droplet size generation and nozzle tip pressures. Spray pressures of 276 kPa or greater and PWM duty cycles of 40% or greater are recommended to ensure proper PWM operation.

Analyzing the Nozzle Spray Fan Pattern of an Agricultural Sprayer Using Pulse Width Modulation Technology to Generate an On-Ground Coverage Map

Chemical application is an integral part of crop care. Today, advanced sprayers automatically control individual boom sections and nozzles to accommodate increased machine sizes and travel speeds, yet automatic control of flow-based systems raises concerns regarding coverage accuracy and uniformity during changes in travel speed and spray swath width. New commercial systems apply product at a constant pressure using varied duty cycles of pulse width modulated (PWM) solenoids to maintain a constant application rate. However, concerns exist regarding the dynamic effect of solenoid on/off latency on spray fan pattern and spray coverage. The objectives of this study were to investigate the on/off latency in PWM nozzles, determine if active nozzles affect spray fan pattern latency, and develop flow characteristics to simulate dynamic spray coverage. A PWM system and flow rate controller were installed on a 6.6 m three-section boom sprayer with 13 nozzles. A Raven Viper 4 controller regulated the product flow rate and pressure, while a Capstan Pinpoint controller was used to set the system pressure, nozzle on/off configuration, and duty cycle. The results indicated that the PWM spray system maintained the pressure within ±5% of the target value and applied an accurate amount of flow per pulse regardless of the number of nozzles activated. There was a 20 ms delay in nozzle pressure development during each cycle, and the delay was constant regardless of the number of nozzles activated. After de-energizing the solenoid, the nozzle continued spraying at system pressure for 10 ms. Static spray droplet distribution proved that the system applied the correct volume per pulse. In addition, PWM duty cycles of 100%, 80%, 60%, and 40% provided spray coverage within ±10% of the target rate for 100%, 94%, 77%, and 67% of the time, respectively. Greater signal overlap between odd and even nozzles increased the application coverage. Dynamic spray simulations showed that as-applied application error may vary beyond ±10% of the target rate. As such, while the PWM system provided the desired amount of product per pulse, the spray coverage results indicated that the on-ground coverage could result in areas with under- or over-application.

Compact pulse width modulation circuitry for silicon photomultiplier readout

The adoption of solid-state photodetectors for positron emission tomography (PET) system design and the interest in 3D interaction information from PET detectors has lead to an increasing number of readout channels in PET systems. To handle these additional readout channels, PET readout electronics should be simplified to reduce the power consumption, cost, and size of the electronics for a single channel. Pulse-width modulation (PWM), where detector pulses are converted to digital pulses with width proportional to the detected photon energy, promises to simplify PET readout by converting the signals to digital form at the beginning of the processing chain, and allowing a single time-to-digital converter to perform the data acquisition for many channels rather than routing many analogue channels and digitizing in the back end. Integrator based PWM systems, also known as charge-to-time converters (QTCs), are especially compact, reducing the front-end electronics to an op-amp integrator with a resistor discharge, and a comparator. QTCs, however, have a long dead-time during which dark count noise is integrated, reducing the output signal-to-noise ratio. This work presents a QTC based PWM circuit with a gated integrator that shows performance improvements over existing QTC based PWM. By opening and closing an analogue switch on the input of the integrator, the circuit can be controlled to integrate only the portions of the signal with a high signal-to-noise ratio. It also allows for multiplexing different detectors into the same PWM circuit while avoiding uncorrelated noise propagation between photodetector channels. Four gated integrator PWM circuits were built to readout the spatial channels of two position sensitive solid-state photomultiplier (PS-SSPM). Results show a 4 × 4 array 0.9 mm × 0.9 mm × 15 mm of LYSO crystals being identified on the 5 mm × 5 mm PS-SSPM at room temperature with no degradation for twofold multiplexing. In principle, much larger multiplexing ratios are possible, limited only by count rate issues.

Analysis and synthesis of discrete-time systems

This paper presents an introduction to the analysis and synthesis of sampled-data (discrete-time) systems, i.e. systems in which some or all signals can change values only at discrete values of time. The description of these systems is presented using state-space concepts. Following an introduction to linear discrete-time systems including systems where two or more samplers operate at different frequencies, here is a brief introduction to non-linear systems including the study of stability using the Second Method of Lyapunov. The latter part of the paper describes pulse-width modulated discrete systems. The final section considers the synthesis of systems designed to reach equilibrium states in the minimum number of sampling periods. The concepts discussed in the paper are illustrated with a large number of examples.

Optimum crossing-point estimation of a sampled analog signal with a periodic carrier

The problem of estimating the crossing points of a continuous-time random process, represented by a sequence of uniformly spaced noisy samples, with a periodic analog carrier signal is of crucial importance in the implementation of pulse-width modulation (PWM) and other event-triggered sampling systems. In this paper, we formally approach this problem from a statistical signal processing perspective under a Bayesian framework. We derive the maximum a posteriori (MAP) estimator of the crossing point from a finite sequence of noisy observations, along with a close approximation based on minimum mean squared error (MMSE) considerations. We also study the Bayesian Cramér–Rao bound (CRB) on attainable mean square estimation error. Finally, simulations of a PWM scenario demonstrate that both the MAP and MMSE estimators approach the CRB and outperform several benchmark estimators. The MMSE is a particularly attractive solution as it offers a computationally efficient approximation to the MAP estimator.

Robust tracking with [formula omitted] performance for PWM systems

Control synthesis for robust tracking is considered for a class of pulse-width modulated systems that appear, for example, in power electronics applications. The control objective is to regulate a high frequency ripple signal to robustly track a constant reference signal in an average sense. To achieve this goal, a new H ∞ control problem with integral action and average sampling is proposed. The solution of this problem involves a hybrid lifting framework which requires a careful elaboration in order to develop an algorithm that allows one to solve the design problem by the standard state space formulas for H ∞ control. The design procedure is verified on a synchronous buck converter.

Harmonic analysis of pulse-width modulated systems

The paper considers the so-called dynamic phasor model as a basis for harmonic analysis of a class of switching systems. The analysis covers both periodically switched systems and non-periodic systems where the switching is controlled by feedback. The dynamic phasor model is a powerful tool for exploring cyclic properties of dynamic systems. It is shown that there is a connection between the dynamic phasor model and the harmonic transfer function of a linear time periodic system and this connection is used to extend the notion of harmonic transfer function to describe periodic solutions of non-periodic systems.

Stability Analysis of a Class of PWM Systems

This note considers stability analysis of a class of pulsewidth modulated (PWM) systems that incorporates several different switched mode dc-dc converters. The systems of the class typically have periodic solutions. A sampled data model is developed and used to prove stability of these solutions. Conditions for global and local exponential stability are derived using quadratic and piecewise quadratic Lyapunov functions. The state space is partitioned and the stability conditions are verified by checking a set of coupled linear matrix inequalities (LMIs).

Naturally sampled triangle carrier PWM bandwidth limit and output spectrum

This paper first presents a general theory predicting harmonic components in naturally sampled pulse-width modulation (PWM) output signals, so that any input signal with a Fourier series representation may be handled. This theory provides a basis for the mathematical analysis of PWM systems, such as converters transmitting a main signal and a broadband of feedback or feedforward signals, or Class D amplifiers. Ultimately, the results of this theory are applied to two concrete problems, and conditions similar to the Nyquist theorem or Carson's rule for FM modulation are derived for the cases of recovery of an input signal consisting of a main signal and a bandwidth of small feedback or feedforward signals and a bandlimited signal consisting of several harmonics of comparable magnitude. A rule of thumb, and conservative estimate of the bandwidth in both cases is one third of the carrier frequency (/spl omega//sub upper/<(1/3)/spl omega//sub c/). This research has been based on the premise that the results obtained will provide valuable insight into the general behavior of PWM systems, and provide a supporting theory for concrete systems utilizing signals of this kind, such as PWM converters whose purpose is to ensure a dominant sinusoidal waveform along with a broadband frequency channel for small feedback signals.

Input to state set stability for pulse width modulated control systems with disturbances

New results on set stability and input-to-state stability in pulse-width modulated (PWM) control systems with disturbances are presented. The results are based on a recent generalization of two time scale stability theory to differential equations with disturbances. In particular, averaging theory for systems with disturbances is used to establish the results. The nonsmooth nature of PWM systems is accommodated by working with upper semicontinuous set-valued maps, locally Lipschitz inflations of these maps, and locally Lipschitz parameterizations of locally Lipschitz set-valued maps.

Transient thermal response of a hot-wire anemometer

The ability of a thermal anemometry system to accurately measure unsteady fluidvelocity depends on the electrical control system as well as the thermal propertiesof the sensor. The present work is a numerical study of the thermal transientresponse of a hot-wire. A conventional constant temperature anemometer with anideal feedback amplifier as well as a pulse width modulated system wereused to model the electrical current supplied to the sensor to maintain anominally constant sensor resistance. The agreement between these twoelectrical models confirmed that the response characteristics are onlydue to thermal effects. The thermal response was tested by providing aknown input function for the cooling velocity, and comparing this with theoutput of the model. The first test used a step input function. It wasfound that the thermal transient effects along the length of the sensorcaused the system to initially under predict the actual velocity increase;this was followed by an exponential increase to the steady state velocity.Secondly, the model was tested with sinusoidal inputs over a wide frequencyrange. The ratio: indicated-velocity/input-velocity, as a function of theinput frequency was used to characterize the ‘thermal frequency response’.