Unit 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)... 

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... 

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) ... 

Z(w) = 1/wC, and in the s-domain Z(s) = 1/sC. The Laplace transforms of some very important excitation waveforms are very simple for example, for a unit impulse it is 1, a unit step function 1/s, a ramp 1/s, etc. That is why the excitation with, for example, a unit impulse is of special interest examining the response of a system. In the extended immittance definition, calculations with some nonsinusoidal waveforms become very simple. Even so, Laplace transforms are beyond the scope of this book. 

For integrating objects, the course of the output function corresponds to the accumulation process and to the operation of integration. The object responds to a generated unit pulse with an output signal, which is equivalent to the unit step function the response of the object to the unit step function is a linearly rising function production of the ramp forcing function stimulates the response of the object according to the relation... 

Load coming on-line without grid connection. The requested power from the load coming on-line is a step function, while the inertia-less micro source always takes a finite amount of time to ramp up to the newly requested value. Since the unit cannot change its output power instantaneously, the power is balanced by voltage reduction. As the power injected from the micro source increases to supply the needed load the voltage is restored. 

The catalytic activity of the prepared catalysts for methane combustion was tested in a flow reactor unit. Bottled methane (99.995 % purity from AGA, Sweden) and air were fed to the system using mass flow controllers, giving a methane concentration of 2 vol%. The space velocity in all experiments was 50,000 h". The catalysts were placed in a vertical tubular Inconel reactor situated in a tubular furnace. The exiting gases were analyzed by gas chromatography using a Packard model 427 GC, equiped with a Poraplot Q fused silica capillary column and a thermal conductivity detector. The temperature in the furnace was controlled to give a linear temperature ramp of 2 °C/min in all experiments. Hence, the conversion of methane to carbon dioxide and water was determined as a function of the gas inlet temperature. 

The three important inputs discussed above—step, ramp, rectangular pulse—are depicted in Fig. 5.2. Note that many types of inputs can be represented as combinations of step and ramp inputs. For example, a unit height (isosceles) triangular pulse of width tyy can be constructed from three ramp inputs, as shown in Fig. 5.3. In this case, we write a single expression for the triangular pulse function... 

Thermal characterization of an emulsion polymer essentially means the measurement of the glass transition temperature Tg, that is the temperature above which the hard, glass-like polymer film becomes viscous or rubber-like. Polymers whose Tg lies well above room temperature are designated as hard , those with a Tg much lower than room temperature as soft . Normally Tg is measured by differential scanning calorimetry (DSC [25]). In this technique, the difference between the heat absorbed per unit time by the polymer film to that absorbed by a thermally inert reference material is recorded during a linear temperature ramp. The sample and the reference are placed on a sensor plate of defined thermal resistance R, and the temperature difference AT between the sample and the reference is then recorded over the temperature ramp. Usually, the heat flow difference, which is the negative quotient of AT and R, is plotted as a function of temperature (Fig. 3-11). 

---