Three-state controller

A three-state controller is used to drive either a pair of independent on/off actuators such as heating and cooling valves, or a bidirectional motorized actuator. The controller is actually two on/off controllers, each with deadband, separated by a dead zone. When the controlled variable lies within the dead zone, neither output is energized. This controller can drive a motorized valve to the point where the manipulated variable matches the load, thereby avoiding cychng. 

FIG 5.11. The three-state controller is comprised of two on-off devices separated by a dead zone Z. 

It has been demonstrated that a loop whose gain varies inversely with amplitude is prone to limit-cycle. Any controller with similar characteristics can promote limit cycling in an otherwise linear loop. On-off controllers are in this categoiy. So any nonlinear device that is purpose inserted into a loop for the sake of engendering stability must have the opposite characteristic gain increasing with amplitude. The only stabilizing nonlinear devices discussed up to this point have this property -it was manifested as a dead zone in the three-state controller and as the linear mode in the dual mode system. 

It is possible to create a controller with a continuous nonlinear function whose gain increases with amplitude. In contrast to the three-state controller, its gain in the region of zero error would be greater than zero, with integrating action to avoid offset. But its change in gain with amplitude should be less severe than that of a dual-mode system. Thus it would be more tolerant of inaccuracy in the control parameters. 

A lever is driven by a bidirectional constant-speed motor to a position determined by a three-state controller. The motor has a speed of 10 percent of full stroke per second, and an inertial time constant of 1.0 sec. Differential gap in the controller is 2 percent of full stroke. How wide does the dead zone have to be to prevent limit cycling What would be the period of the cycling ... 

Figure 1. Schematic illustration of two-pathway control in the (a) frequency and (b) time domains. In case (a) the ground state is excited to a coupled continuum by either one photon of frequency CO3 or three photons of frequency C >i. Control is achieved by introducing a phase lag between the two fields. In case (b) a two-pulse sequence has sufficient bandwidth to excite a superposition of two intermediate states. Control is achieved by introducing a delay, At, between the pulses, resulting in a phase difference of to At.

Coherent excitation of quantum systems by external fields is a versatile and powerful tool for application in quantum control. In particular, adiabatic evolution has been widely used to produce population transfer between discrete quantum states. Eor two states the control is by means of a varying detuning (a chirp), while for three states the change is induced, for example, by a pair of pulses, offset in time, that implement stimulated Raman adiabatic passage (STIRAP) [1-3]. STIRAP produces complete population transfer between the two end states 11) and 3) of a chain linked by two fields. In the adiabatic limit, the process places no temporary population in the middle state 2), even though the two driving fields - pump and Stokes-may be on exact resonance with their respective transitions, 1) 2)and... 

Note that each state factor can influence soil carbon storage in two ways by influencing the quantity and quality of plant inputs and by influencing the residence time of organic matter in the soil. Figures 6.2-6.4 show the influence of three state factors on soil C storage. Many of the descriptions of state factors below touch upon the importance of controls on SOM stabilization, and these controls are discussed further in a following section. 

Because we want to consider the one- vs. three-photon control of IBr in three, dimensions [63], we replace the notation Z () for the initial state by Ef,Mt), s here Et is, as before, the energy of the state, J, is its angular momentum, and is the angular momentum projection along the z axis. Where no confusion arises, i ffe continue to use Et) for simplicity. 

SLiJlio), which is excited by the combined action of two laser pulses, with central uencies co0 and co to a continuum of states associated with two or more srent product channels at energy E. The frequency co0 is assumed to be in ir resonance with the transition to an intermediate bound state [ i), and is near resonance with the transition frequency between ,) and the continuum. P oj0 can ies the system from E0) to [ )), and co carries the system from ) to Lcpntinuum. To avoid confusion, note that the energy levels are labeled somewhat Terentiy from that in the previous section, q addition, as shown in Figure 11.3, the continuum is coupled to a third bound 2) by a laser of central frequency co2. Basically, the three-level two-laser ne described in Section 11.1 is being extended here to a four-level three-4 control scheme. 

Although the detailed features of the interactions involved in cortisol secretion are still unknown, some observations indicate that the irregular behavior of cortisol levels originates from the underlying dynamics of the hypothalamic-pituitary-adrenal process. Indeed, Ilias et al. [514], using time series analysis, have shown that the reconstructed phase space of cortisol concentrations of healthy individuals has an attractor of fractal dimension dj = 2.65 0.03. This value indicates that at least three state variables control cortisol secretion [515]. A nonlinear model of cortisol secretion with three state variables that takes into account the simultaneous changes of adrenocorticotropic hormone and corticotropin-releasing hormone has been proposed [516]. 

Obesity or excess adiposity was relatively rare in earlier centuries. Indeed, an ample belly was often seen as a sign of affluence and prosperity. In the last two decades, however, adult obesity has reached epidemic proportions in the United States and other developed countries. This is strikingly evident from data compiled by the Centers for Disease Control and Prevention (CDC), which estimates obesity rates by state. Data from 1990 indicate that all states had obesity rates (BMI > 30 kg/m2 or 30 lb overweight) of less than 15%. By contrast, in 2002, every state had an obesity prevalence rate of at least 15%-19% 29 states had rates of 20%-24% and the rates in three states were over 25%. Graphic representation of these data, updated annually, is available at... 

The value z is used to generate a three-state gate. The value z can be assigned to a variable in an assignment statement however for synthesis, such an assignment must occur under the control of a condition, either in an if statement, or in a case statement. Here is an example. 

If a variable is assigned a value z in an always statement in which the variable is also inferred as a flip-flop, then it becomes necessary to save the enabling logic of the three-state also in a flip-flop. Here is the same example as above except that the always statement is controlled by a clock event. 

A three-state gate is modeled by assigning the value z to a variable under the control of a condition. Here is an example. 

A portland cement plant ball mill emits particulate matter (PM) emissions that must be controlled to meet state air pollution regulations. Three PM control devices, each of which can control these emissions to the same level, are being evaluated (1) a high-energy wet scrubber (scrubber), (2) an electrostatic precipitator (ESP), and (3) a fabric filter (baghouse). Unlike the wet scrubber, the ESP and the baghouse each recover salable cement dust, and, accordingly, revenue can be attributed to those two options. Two scenarios are visualized, with after-tax hurdle rates of 6% and 18%, respectively. The economic specifications for the three devices are as follows ... 

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