Unit ramp

Fig. 3.15 Unit ramp response of a first-order system.

Find the pulse transfer function and hence calculate the response to a unit step and unit ramp. T = 0.5 seconds. Compare the results with the continuous system response Xo t). The system is of the type shown in Figure 7.9(b) and therefore... 

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)... 

In testing process systems, standard input disturbances such as the unit-step change, unit pulse, unit impulse, unit ramp, sinusoidal, and various randomised changes can be employed. 

A MB3MB pcogras tso ctAaln a unit-ramp pcmaented Ijaunr togetliar uitii this taiit-ra ... 

Another auxiliaiy unloading system that has proven to be very effective and efficient involves the use of moveable, hydraulically operated truck dumps located at the disposal site. Operationally, the trailer is backed up onto one of the tipping ramps, with or without its tractor. The back of the trailer is opened, and the unit is then tilted upward until the wastes fall out by gravity. The time required for the entire unloading operation typically is about 5 min per trip. 

Because we need to know how long the refined section of the bar is, it is important to describe the ramping up of the compositions in a quantitative way. We can do this by writing a differential equation which describes what happens as the zone moves from some general position x to a new position x + 8x (Fig. 4.4g). For a bar of unit cross-section we can write the mass conservation equation... 

The dual-slope instrument incorporates an integrator operated in conjunction with a time difference unit, and this is one of a range of units employing a combination of the above techniques designed to take advantage of the favorable characteristics of each. It is subject to the same limitations as the linear ramp instrument described above but it does have the advantage of inherent noise rejection. 

RAMP TEMP TO OVER ... 

Temperature-programmed reduction (TPR) profiles of fresh catalyst samples were obtained using a Zeton Altamira AMI-200 unit. Calcined fresh samples were first heated and purged in flowing argon to remove traces of water. TPR was performed using 30 cc/min 10% H2/Ar mixture referenced to argon. The ramp was 5°C/min from 50 to 1,100°C, and the sample was held at 1,100°C for 30 min. 

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) ... 

If a logarithmic ramp is performed, then the data should not be fit with linear models (unit m.i). These data should be plotted as viscosity versus shear rate on logarithmic axes and the Carreau-Yasuda or Cross models (or subsets) should be used instead. It is unlikely that the zero-shear plateau will be seen in these types of tests. For a complete flow curve, the equilibrium tests described in Basic Protocol 2 should be used. 

Figure 7. Thermal desorplion polytherms for r-butylamine from sand as received (solid line) and after one ramp (dots). DU indicates detector units.

---