Ramp function

From Table 7.2, it can be seen that the discrete and continuous step response is identical. Table 7.3 shows the discrete response x kT) and continuous response x t) to a unit ramp function where Xo t) is calculated from equation (3.39)... 

The advantage of using frequency converters is that the possibility exists to use a ramp function when starting and stopping the motor (soft start). By using this function, it is possible to avoid starting both fans at full speed with closed dampers it also reduces stresses on the fan transmission (belts) at the start. 

Figure 2.31. Response of the most common controller modes for step change and ramp function of the error signal.

When the reactor temperature (Tl) becomes greater than Tmax (=240 F), PERIOD = 2, and the program turns the cooling water on with flow rate Fw. This flow is controlled with a proportional controller using control constant Kc, whose set point (Pset) is varied according to the time ramp function with setting kR and whose output to the valve is Pc. This ramp is horizontal until time period Tihold has passed. Then the setpoint is decreased linearly. The temperature is sensed using a pressure transmitter with output Ptt. 

Study the effects of the parameters of the cooling water ramp function (Tihoid and kg) on the selectivity, SEL. 

We can show that with a step input, the output is a ramp function. When we have an impulse input, the output will not return to the original steady state value, but accumulates whatever we have added. (Both items are exercises in the Review Problems.)... 

In order to control those initial nonequilibrium effects, a ramp function can be added which reduces the variations from one step to the next of the external force applied in a given bin. The external force applied to the system can be chosen equal to... 

Assume a ramp function for the flow rate (F = F0 + kt) and find the values of F0 and k which give the highest value for the objective function. Remember that F must remain positive. 

Find the Fourier series expansion of the ramp function (Figure 2.11) defined over the interval [—X,X] by... 

Figure 2.11 The periodic ramp function with period 2X.

It will be left as an exercise for the reader to show that the cosine terms bn, including the mean value b0, are zero. The Fourier series expansion of the ramp function is therefore... 

In order to make the solution consistent with initial and boundary conditions, we will use for u(r,0) the ramp function defined in Chapter 2. For 0Fourier expansion of this function... 

The ramp function is one that changes continuously with time at a constant rate K. 

LAPUCE-DOUAIM DYNAMICS AND OONTKOL Therefore the Laplace transformation of a ramp function is... 

Note that we obtain a very nice ramp function through multiplying H(x) by a straight line of unit slope, and that the same result can be obtained by the self-convolution of H(x) ... 

Ramp-function space series were initially divided into two segments ramp data and nonramp data. The ramp data show the presence of a linear trend. This trend was removed, and the residual data series was retained. Virtually all the ramp data in this study are representative of inshore (i.e., coastal) data. The offshore (i.e., nonramp) data also were tested for trends. The detrended segments were tested for stationarity with the procedures just cited. 

All the data taken during the experiment, of which Figures 6-9 are representative examples, support the conclusion that most of the variance in an arbitrary cross-shelf space series can be modeled as superposition of step functions, ramp functions, binary flip-flops, and smaller-scale fluctuations. A biological and physical interpretation of these length scales is given in the discussion section. 

It is possible to vary the load or, in hard machines, the displacement, either in ramp mode or with a discontinuous increment (step mode). The ramp function needs to be smooth, as well as linear, and there is evidence (Mayo Nix, 1988) that if the ramp is digitally controlled, the data will vary for the same mean loading rate according to the size of the digitally produced load increments, unless these are very small. 

Commonly encountered forcing functions (or input variables) in process control are step inputs (positive or negative), pulse functions, impulse functions, and ramp functions (refer to Figure 44). 

Now consider a ramp function described by fit) — t[u t) The Laplace transform of this function is /s. Finally, the Laplace transform of a sine-wave disturbance, sin(cuf)> is co/(j + of). 

Figure 43 is a combination of a positive step input at t = 1, a ramp function at t = 3, a negative step input at t = 4, and a negative ramp at t = 6. Thus, the time-domain equation is... 

Stress Growth at Inception of Ramp-Function Velocity Gradient... 

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