Will Increasing Jet Size Improve A Deadspot

Dead-Zone Dynamics and Modeling

Jing Na , ... Xuemei Ren , in Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics, 2018

7.four Conclusion

This chapter introduces the dead-zone dynamics then briefly presents several well-known expressionless-zone models, which will exist used in the command designs to exist presented in this book. Linear dead-zone model is originally developed to show the dominant dead-zone behaviors, while the recently reported not-linear expressionless-zone model is able to represent more realistic not-linear dynamics in the expressionless-zone input of actuators. Both of these two models can be reformulated every bit a combination of a linear term (with fourth dimension-varying proceeds) and a disturbance-like term, which is suitable for adaptive control designs.

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Transform Coding

R.L. de Queiroz , Thousand.R. Rao , in Handbook of Visual Communications, 1995

seven.five.3 Quantizer Design Bug

The dead-zone quantizer just has iii parameters to design: the step size Δ, and the beginning and terminal decision levels, t ₁ and t_q . Since we are assuming symmetric quantizers, t _–1 and t_–q follow immediately, as well every bit the number of quantization levels. The compatible quantizer is achieved when t _i = Δ/2. Generally, q is set to a value such that $\left(q-\frac{1}{2}\right)\mathrm{\Delta }$ lies close to the maximum range of the coefficients, for a value of Δ that is expected to be most usually used. Thus, in a uniform quantizer, the footstep size is the but parameter to be varied and it tin control the charge per unit and distortion of the coder, since larger Δ means more than distortion and less entropy of the output symbols. The dead-zone is used most commonly to command buffers in entropy coding to match the bit charge per unit produced by the coder and the bit rate the channel supports [27].

The nonuniform quantizer can be designed in a way to minimize the mean squared baloney produced by the quantizer, which is divers as

(vii.26) $D_Q={\displaystyle \sum _{\ell =-q}^q{\displaystyle {\int }_{I_{{}_{{}_{\mathrm{fifty}}}}}{\left(x-r_{\ell }\right)}^2}}f\left(x\right)d\mathrm{10}\text{.}$

The well-known Lloyd-Max design method provides an iterative way to specify the decision and reconstruction values, which will minimize D_q for a given PDF f(x) [12,13]. In this case, at that place is no concern with the rate by which the quantizer output symbols would be coded. Another method involves the brake that the output symbols should exist field of study to a given entropy [28]. This is called the entropy-constrained blueprint method. In this, the number of levels is not given as a parameter, merely found from the design algorithm. The other parameters given are the entropy of the output set of symbols and the PDF is assumed. In both methods we can presume a unit of measurement-variance input PDF. Hence, X has to be scaled by its standard deviation to plow it into a unit of measurement-variance signal, earlier quantization.

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Turbulent dispersion in natural systems

Hubert Chanson ME, ENSHM Grenoble, INSTN, PhD (Cant), DEng (Qld) Eur Ing, MIEAust, MIAHR , in Environmental Hydraulics of Open up Channel Flows, 2004

9.2.1 Introduction

In natural rivers, there are regions of secondary currents and flow recirculations. Recirculation and stagnant waters may be associated with irregularities of the river bed and banks. They are known as peripheral expressionless zones, and they tin can trap and release some water and tracer volumes. In natural channels, dead zones may exist found forth the banks and at the bed ( Fig. ix.ii(a)). Examples of bed dead zones include large obstacles, trees, wooden droppings, large rocks and bed forms (Fig. 9.3). Effigy 9.3 illustrates examples of streams with expressionless zones, predominantly along the banks. Lateral expressionless zones may be caused past riparian vegetation, by groynes for river banking concern stabilization, by submerged trees in flood plains, and by houses and cars in flooded townships (Fig. nine.3(a) and (c)). Figure 9.iii(d) and (east) presents bogus dead zones, introduced to assist in river habitat restoration.

Fig. ix.2. River systems with expressionless zones. (a) Sketch of idealized dead zones. (b) Longitudinal model in a river with dead zones. (c) Aggregated dead zone (ADZ) model: 2-cell model.

Dead zones are thought to explain long tails of tracer observed in natural rivers. The existence of dead zones implies that the turbulence is not homogeneous beyond the river, and that the time taken for contaminant particles to sample the entire flow is significantly enhanced (i.east. the length of the initial zone is increased).

Notes

ane.

Dead zones increase the length of the initial zone and the longitudinal dispersion coefficient.

2.

The length of the initial zone (i.e. advective zone) is the distance for complete mixing from a centreline or side belch (Chapters seven and 8). In the presence of dead zones, the initial zone may be enlarged significantly, although there are different interpretations (e.m. Fischer et al. 1979, Rutherford 1994).

three.

Equation (8.8) may underestimate dispersion coefficients in river systems with dead zones by a factor of ii–x, or even more. Relevant discussions include Valentine and Wood (1979a, b) and Rutherford (1994, p. 202).

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Adaptive Neural Dynamic Surface Command of Strict-Feedback Systems With Non-linear Dead-Zone

Jing Na , ... Xuemei Ren , in Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics, 2018

9.1 Introduction

Autonomously from dead-zone dynamics presented in the previous capacity, fourth dimension-delays are also unavoidable in the control systems, such as process control and teleoperation, which could bring phase lag and thus may trigger instability in the control systems. To address the issue of fourth dimension-delays in the control systems, Lyapunov-Krasovskii functions have been utilized [one–3] to bargain with delays in the system states. A novel integral Lyapunov function was introduced to avoid the control singularity in [i,4]. For systems with unknown control coefficients and time-delays, Nussbaum type functions were effectively used [5] to guarantee the mistake convergence.

On the other paw, backstepping [6,seven] has been proved to exist a powerful technique to pattern controllers for various systems, e.k., strict-feedback systems, pure-feedback systems, or triangular systems, etc. The over-parameterized problem was also overcome by introducing tuning functions [7]. Nonetheless, in the backstepping pattern, the "explosion of complexity" caused past the repeated differentiation of virtual control functions, as pointed in [eight], becomes more significant as the order of the system increases. A novel idea named equally dynamic surface control (DSC) [eight,nine] has later been investigated by introducing a first-order filter at each recursive pace of the backstepping design procedure. Moreover, to address the unknown non-linearities, neural networks (NNs) accept been incorporated into the control design [10–13]. Nonetheless, in virtually of bachelor adaptive neural backstepping (or DSC) controllers, the number of adaptive parameters to be tuned online, i.e., the NN weight as a vector or matrix, will rapidly grow with the dimension of functions to be approximated [2].

This chapter focuses on adaptive neural tracking control for a grade of not-linear systems with an unknown non-linear dead-zone input and multiple fourth dimension-varying delays. The mean-value theorem is offset applied to derive a formulation of the perturbed non-linear dead-zone, such that it can be taken into account together with other system non-linearities. The DSC pattern is then extended to this general non-linear time-filibuster system such that the differentiation calculation of the virtual command and the respective "explosion of complexity" can be avoided. At each recursive footstep, novel high-order neural networks (HONNs) with a simpler construction and less adaptive parameters are established to approximate unknown non-linear functions. Moreover, the control singularity problem and unknown time-delays are handled by introducing an improved Lyapunov-Krasovskii function including an exponential term. The salient features of the proposed control are that, start, the conventional dead-zone inverse model compensation is not needed to avoid the expressionless-zone identification [14]; second, merely two scalar parameters, independent of the number of NN hidden nodes, are updated online at each step, and thus the computational burden of the algorithm tin drastically be reduced; tertiary, some design difficulties (due east.g., control singularity, discontinuous control) are resolved without using the data on the premises of delayed functions and control functions. Numerical simulations are given to verify above claims.

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Adaptive Prescribed Performance Control of Strict-Feedback Systems With Non-linear Expressionless-Zone

Jing Na , ... Xuemei Ren , in Adaptive Identification and Control of Uncertain Systems with Non-polish Dynamics, 2018

10.1 Introduction

As presented in the previous chapters, dead-zone is ane of commonly encountered actuator not-linearities in practical systems, e.g., hydraulic servo valves, electronic motors, which can be descried by a not-polish function characterizing no output for a range of control inputs [one]. To accost the command pattern for systems with unknown expressionless-zone dynamics, several techniques have been presented in the past decades, e.thousand., [one–x] and amongst others. Apart from the classical inverse dead-zone model control designs (suitable for linear expressionless-zone dynamics), contempo research focuses on changed model contained adaptive control designs. The previous chapters have introduced a recently reported idea to reformulate non-linear dead-zone as a fourth dimension-varying organization. Affiliate 9 also develops a dynamic surface control (DSC) design for strict-feedback systems with time-delays and expressionless-zone input, which remedies the "explosion of complexity" in the backstepping designs. In fact, there have been many adaptive control schemes of uncertain not-linear time-delay systems (meet [11–xix] and references therein).

However, in standard adaptive control designs with function approximation, eastward.yard., neural networks (NNs) and fuzzy logic systems (FLSs), the online learning process may be sluggish before it achieves convergence. This sluggish online learning process may pb to poor transient control response (east.g., overshoot, convergence rate, and even steady-state error). In item, for not-linear systems with both dead-zone input and fourth dimension-delays, our piece of work presented in the previous affiliate and [20] can guarantee the uniform ultimate boundedness of the closed-loop system. Yet, the transient performance of this DSC command (e.chiliad., overshoot, undershoot, and convergence charge per unit) can not be strictly guaranteed and prescribed. Moreover, the above mentioned adaptive control designs all presume that the input gain functions $g(x)$ are strictly positive or negative. Hence, these methods are not suitable for systems with unknown control gain directions.

This chapter focuses on the adaptive tracking command design for a course of non-linear systems with an unknown non-linear expressionless-zone input and time-delays. The main idea is to farther tailor the principle of prescribed performance command (PPC) that has been introduced in the previous affiliate of this book for the studied systems. After representing the not-linear expressionless-zone as a linear time-varying system with a bounded disturbance term, we can lump the expressionless-zone dynamics into unknown system dynamics. The unknown command directions and not-linear dead-zone are also handled past ways of Nussbaum-type function [nineteen]. By employing a prescribed operation function (PPF) as [21,22], an output error transformed system is and so derived. Consequently, the tracking error convergence within prescribed spring of the original organisation can be guaranteed provided the transformed error system is stable. To reach this, an adaptive control derived based on backstepping is designed and so that both the transient and steady-country tracking fault operation including the convergence rate and maximum overshoot of original organisation are all ensured. To accommodate unknown non-linearities, high-order neural networks (HONNs) [23] with a simpler structure are established, where only a scalar parameter, independent of the number of hidden nodes in the neural network [xv], is updated online.

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Mixing in estuaries

Hubert Chanson ME, ENSHM Grenoble, INSTN, PhD (Cant), DEng (Qld) Eur Ing, MIEAust, MIAHR , in Environmental Hydraulics of Open up Channel Flows, 2004

Tidal trapping

Estuaries, like rivers, are afflicted by 'dead zones'. The function of such zones are enhanced by tidal activeness. The propagation of the tide in an estuary is a balance between the inertia of the h2o mass, the pressure level strength due to the slope of the h2o surface and the retarding force of bottom friction. As the tide changes, pocket-sized dead zones have little momentum and the flow direction volition change equally before long every bit the h2o level begins to drop. In contrast, the menstruum in the chief channel has an initial momentum and the current will continue to menstruation against the opposing pressure slope. This process will raise longitudinal dispersion induced by the dead zones.

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Draining of Hoppers and Silos: Stresses and Flow Rate

Jean-Paul Duroudier , in Divided Solids Mechanics, 2016

3.4 Flow with expressionless zone

iii.4.i Dead zones: features and disadvantages

If the angle θ crosses the limit θ_Mp , a dead zone appears between the wall and the withdrawal opening.

Figure 3.four. Master profile of the dead zone (wide hopper)

The vertical tiptop of the dead zone increases proportionately with the cohesion of the product – at the expense of the renewable volume. And then the more a product possesses cohesion, the more the volume of the sacrificed capacity in the dead zone increases. If the cohesion is cipher, the internal surface of the dead zone reduces to that of a crater whose bending with the horizontal is approximately equal to the angle of repose.

The presence of a expressionless zone has the post-obit drawbacks:

–

equally we accept just seen, a reduction in the net volume, that is the renewable volume;

–

difficult precise changes in the dead volume and, consequently, of the net volume;

–

ho-hum change always possible and even the degradation of the production with time in the stationary zone;

–

during complete elimination, the derived product can plow out to be heterogeneous either because it has changed in the dead book, or because the heterogeneity was created in the form of loading jetwise.

In fact, during the loading in a jet, the product constitutes a heap on the slopes of which the granules flow easily and announced on the periphery while the fine products percolate vertically across the grains and find themselves at the center of the hopper or silo.

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SYNTOM II: A NEW PHASED ARRAY ULTRASONIC INSPECTION Arrangement

F. Boggiani , ... 1000. Mozzoni , in Not-Destructive Testing 1989, 1989

SYSTEM CHARACTERIZATION

Concerning probe characterization, L-and Due south-moving ridge dead zones, angular and lateral beam spread have been measured as functions of altitude and deflection angle. Typical values for the 0° L-wave beam are: expressionless zone = 25 mm, farfield athwart resolution (-3dB) ≈ 4°. Range resolution is near three mm, largely independent of angle and distance but probe dependent. As to prove + arrangement label, L-and South-moving ridge profiles of audio-visual pressure maxima have been measured as functions of deflection angle in transport-receive functioning (reflection from hemicylindrical steel blocks of different radii). Focused an unfocused reflected beam aamplitude profiles take likewise been determined every bit functions of defle ction angle, for side-drilled holes located at unlike distances and angles from the probe (L-and S-waves).

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Vat photopolymerization methods in condiment manufacturing

Ali Davoudinejad , in Additive Manufacturing, 2021

5.2.4 Continuous liquid interface product

Clip relies on the inhibition of free radical photopolymerization in the presence of atmospheric oxygen. The dead zone created above the window maintains a liquid interface beneath the advancing part. Consequently, an oxygen-permeable build window results in the formation of a dead zone, or a region of uncured liquid resin, which allows the continuous fabrication of features. Fig. five.8 shows the schematic of a button-up CLIP 3D-press process. The Clip-process is very similar to DLP but differs by the compages of the transparent window in the lesser of the resin container. By using an oxygen-permeable and UV-transparent window beneath the resin vat, oxygen can travel through the window and mix into the liquid polymer resin. Therefore, the build plate does not move up and down for each layer, and there is a continuous growth of the role. The part is considered layer less, and the traditional trade-off between speed and layer thickness is eliminated with this continuous growth of the features. The resolution in the build direction is non determined by the layer thickness but is limited to the slicing conditions of the part and the optical assimilation-elevation of the resin [14].

Figure 5.viii. Schematic of the continuous liquid interface production applied science with bottom-up projection method.

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Adaptive Dynamic Surface Output Feedback Command of Pure-Feedback Systems With Non-linear Dead-Zone

Jing Na , ... Xuemei Ren , in Adaptive Identification and Control of Uncertain Systems with Not-smooth Dynamics, 2018

xi.four.three Stability Analysis

This section will prove the stability and tracking operation of the proposed control system. It is proved that all signals of the overall airtight-loop organisation are uniformly ultimately bounded (UUB) and the tracking errors converge to an arbitrarily modest residue set.

Theorem 11.1

Consider the closed-loop system consisting of the institute (xi.1) , unknown expressionless-zone non-linearities (11.2) , the non-linear ESO (eleven.15) , the TDs (xi.24) , (11.30) , (xi.39) , the virtual control (11.28) , (xi.35) , and the actual control (11.42) . Then,

ane)

All signals in the closed-loop system are UUB for whatever given initial conditions $x_i(0),{\xi }_j(0),{\hat{\iota }}_i(0)$ , $i=1,\cdots ,\mathrm{due\; north}$ , $j=\mathrm{ane},\cdots ,\mathrm{northward}+\mathrm{one}$ .

ii)

The tracking errors ${\mathrm{east}}_i,i=1,\cdots ,\mathrm{due\; north}$ , converge to a meaty prepare effectually zero defined by (eleven.53) .

Proof

Divers the following Lyapunov role every bit

(eleven.45) $\begin{array}{ccc}\hfill V(t)& \hfill =\hfill & \sum _{i=\mathrm{ane}}^n{\mathrm{Five}}_i(t)+V_e(t)+\sum _{i=\mathrm{i}}^n\frac{{\tilde{\iota }}_i{(t)}^2}{2{\theta }_i}\hfill \end{array}$

where $V_e(t)={\eta }^{T}P\eta$ , for $\eta ={[{\eta }_{\mathrm{i}},\dots ,{\eta }_{\mathrm{northward}+1}]}^T$ .

From (11.29), (11.36), and (11.44), the derivative of V satisfies

(11.46) $\begin{array}{ccc}\hfill \dot{5}& \hfill ⩽\hfill & -\sum _{i=1}^{\mathrm{northward}}{c}_i{\mathrm{eastward}}_i^2+{\mathrm{eastward}}_{\mathrm{north}}(F-{\xi }_{n+1})+\sum _{i=\mathrm{one}}^n{\iota }_i(e_i-e_i\tanh (\frac{0.2785{\hat{\iota }}_i{e}_i}{\omega }))+{\dot{V}}_{\mathrm{eastward}}\hfill \\ \hfill & \hfill \hfill & -\sum _{i=\mathrm{one}}^n{\sigma }_i{\tilde{\iota }}_i{\hat{\iota }}_i+\sum _{i=\mathrm{i}}^n{\hat{\iota }}_i{e}_i\tanh (\frac{0.2785{\hat{\iota }}_i{e}_i}{\omega })\hfill \\ \hfill & \hfill ⩽\hfill & -\sum _{i=\mathrm{i}}^{\mathrm{north}}{c}_i{e}_i^2+e_n(F-{\xi }_{n+1})+\sum _{i=1}^{\mathrm{northward}}{\iota }_i({\mathrm{due\; east}}_i-e_i\tanh (\frac{0.2785{\hat{\iota }}_i{\mathrm{eastward}}_i}{\omega }))\hfill \\ \hfill & \hfill \hfill & +{\eta }^T(A_o^{T}P+P{A}_o)\eta -\sum _{i=1}^n{\sigma }_i{\tilde{\iota }}_i{\hat{\iota }}_i+\sum _{i=\mathrm{ane}}^{\mathrm{due\; north}}{\hat{\iota }}_i{e}_i\tanh (\frac{0.2785{\hat{\iota }}_i{\mathrm{eastward}}_i}{\omega })\hfill \end{array}$

Then, by using the fact that

(11.47) $\begin{array}{ccc}\hfill |e_i|-e_i\tanh (\frac{0.2785{\hat{\iota }}_i{\mathrm{eastward}}_i}{\omega })& \hfill ⩽\hfill & 0.2785\omega \hfill \\ \hfill -{\sigma }_i{\tilde{\iota }}_i{\hat{\iota }}_i& \hfill ⩽\hfill & -\frac{{\sigma }_i{\tilde{\iota }}_i^2}{\mathrm{ii}}+\frac{{\sigma }_i{\iota }_i^{\mathrm{ii}}}{2}.\hfill \end{array}$

The inequality (11.46) tin can be rewritten equally

(eleven.48) $\begin{array}{ccc}\hfill \dot{V}& \hfill ⩽\hfill & -\sum _{i=1}^{\mathrm{north}}{c}_i{e}_i^2+{\eta }^T(A_o^{T}P+P{A}_o)\eta -\sum _{i=1}^{\mathrm{north}}\frac{{\sigma }_i{\tilde{\iota }}_i^2}{2}+\sum _{i=1}^n\frac{{\sigma }_i{{\iota }_i}^2}{2}+0.2785\omega \mathrm{north}\iota \hfill \\ \hfill & \hfill \hfill & +\sum _{i=1}^{\mathrm{northward}}|{\hat{\iota }}_i{e}_i|+\frac{{\mathrm{due\; east}}_n^{\mathrm{two}}}{2{\alpha }_{\mathrm{eastward}}}+\frac{{\alpha }_{\mathrm{eastward}}\iota }{2}\hfill \\ \hfill & \hfill ⩽\hfill & -\sum _{i=\mathrm{i}}^{\mathrm{due\; north}-\mathrm{i}}{c}_i{e}_i^2-(c_{\mathrm{northward}}-\frac{1}{\mathrm{ii}{\alpha }_e})e_{\mathrm{due\; north}}^{\mathrm{two}}-\frac{1}{{\lambda }_{\max }(P)}{V}_{\mathrm{due\; east}}+\varsigma \hfill \end{array}$

where $\varsigma =\sum _{i=1}^n\frac{{\sigma }_i{\iota }^2}{\mathrm{ii}}+0.2785\omega \mathrm{due\; north}\iota +\sum _{i=1}^{\mathrm{due\; north}}|{\hat{\iota }}_i{\mathrm{due\; east}}_i|+\frac{{\alpha }_e\iota }{2}$ .

Letting

(11.49) $\begin{array}{ccc}\hfill {\rho }_5& \hfill ={\min }_{\mathrm{i}⩽i⩽n}\hfill & \{c_i,c_n-\frac{\mathrm{ane}}{\mathrm{two}{\alpha }_e},\frac{1}{{\lambda }_{\max }(P)},\frac{1}{2}{\theta }_i{\sigma }_i\}\hfill \end{array}$

we have the following inequality

(11.50) $\dot{5}⩽-2{\rho }_{5}5+\varsigma .$

Solving the inequality (11.50) yields

(xi.51) $\begin{array}{ccc}\hfill 0& \hfill ⩽V(t)\hfill & ⩽\frac{\varsigma }{\mathrm{ii}{\rho }_5}+(V(0)-\frac{\varsigma }{\mathrm{two}{\rho }_5})e^{-\mathrm{ii}{\rho }_{v}t}.\hfill \end{array}$

The above inequality implies that $\mathrm{Five}(t)$ is eventually divisional by $\varsigma /2{\rho }_v$ . Consequently, all signals in the closed-loop system including $e_i(t),{\eta }_i(t),i=1,\cdots ,n$ are ultimately uniformly bounded. Furthermore, it follows from (11.51) that

(11.52) $\begin{array}{ccc}\hfill \underset{t\to \infty }{\lim }V(t)& \hfill ⩽\hfill & \frac{\varsigma }{2{\rho }_v}\triangleq {\mu }_{\infty }\hfill \end{array}$

which means that the tracking errors ${\mathrm{eastward}}_i,i=1,\cdots ,n$ , can converge to a compact gear up effectually zero defined past

(11.53) $\begin{array}{ccc}\hfill {\mathrm{\Omega }}_{\infty }& \hfill \triangleq \hfill & \{{\mathrm{eastward}}_i:|e_i|⩽\sqrt{\mathrm{two}{\mu }_{\infty }}\}.\hfill \end{array}$

This completes the proof. □

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Will Increasing Jet Size Improve A Deadspot,

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