Response times

All CD s are stored in a CD-jukebox (100 CD s per jukebox), and are accessible to all HP9000 workstations under HP-UX 9.05 via the fXOS software (Ixos-Jukeman VI.3b). The Ixos-Jukeinan software has a slow time response for filenames searches on the jukeboxes. This problem has been encompassed. Laborelec has developed a dedicated static database software. This database is loaded once for all after burning and verifying CD s. All CD s are read from the jukebox and all the filenames are saved in this database. One jukebox can contain more than 65.000 records. This dedicated software retrieves files from jukebox almost instantaneously. 

Butadiene is primarily shipped in pressurized containers via railroads or tankers. U.S. shipments of butadiene, which is classified as a flammable compressed gas, are regulated by the Department of Transportation (254). Most other countries have adopted their own regulations (30). Other information on the handling of butadiene is also available (255). As a result of the extensive emphasis on proper and timely responses to chemical spills, a comprehensive handbook from the National Fire Protection Association is available (256). 

Unlike linear optical effects such as absorption, reflection, and scattering, second order non-linear optical effects are inherently specific for surfaces and interfaces. These effects, namely second harmonic generation (SHG) and sum frequency generation (SFG), are dipole-forbidden in the bulk of centrosymmetric media. In the investigation of isotropic phases such as liquids, gases, and amorphous solids, in particular, signals arise exclusively from the surface or interface region, where the symmetry is disrupted. Non-linear optics are applicable in-situ without the need for a vacuum, and the time response is rapid. 

The manner in whieh a dynamie system responds to an input, expressed as a funetion of time, is ealled the time response. The theoretieal evaluation of this response is said to be undertaken in the time domain, and is referred to as time domain analysis. It is possible to eompute the time response of a system if the following is known ... 

Fig. 3.1 Transient and steady-state periods of time response.

The total response of the system is always the sum of the transient and steady-state eomponents. Figure 3.1 shows the transient and steady-state periods of time response. Differenees between the input funetion X[ t) (in this ease a ramp funetion) and system response Xo t) are ealled transient errors during the transient period, and steady-state errors during the steady-state period. One of the major objeetives of eontrol system design is to minimize these errors. 

In order to eompute the time response of a dynamie system, it is neeessary to solve the differential equations (system mathematieal model) for given inputs. There are a number of analytieal and numerieal teehniques available to do this, but the one favoured by eontrol engineers is the use of the Laplaee transform. 

Equation (3.79) shows that the third-order transient response eontains both first-order and seeond-order elements whose time eonstants and equivalent time eonstants are 2 seeonds, i.e. a transient period of about 8 seeonds. The seeond-order element has a predominate negative sine term, and a damped natural frequeney of 4.97 rad/s. The time response is shown in Figure 3.23. 

If a step input funetion of 10 units is applied to the system, find an expression for the time response. Assume zero initial eonditions. 

The time response depieted by equation (4.89) is shown in Figure 4.28. 

From equations (5.1)-(5.4), it ean be seen that the stability of a dynamie system depends upon the sign of the exponential index in the time response funetion, whieh is in faet a real root of the eharaeteristie equation as explained in seetion 5.1.1. 

Fig. 5.2 Graphical representation of stable and unstable time responses.

The iocus of the roots, or ciosed-ioop poies are piotted in the. v-piane. This is a compiex piane, since. v = cr jw. It is important to remember that the reai part a is the index in the exponentiai term of the time response, and if positive wiii make the system unstabie. Hence, any iocus in the right-hand side of the piane represents an unstabie system. The imaginary part uj is the frequency of transient osciiiation. 

The root locus method provides a very powerful tool for control system design. The objective is to shape the loci so that closed-loop poles can be placed in the. v-plane at positions that produce a transient response that meets a given performance specification. It should be noted that a root locus diagram does not provide information relating to steady-state response, so that steady-state errors may go undetected, unless checked by other means, i.e. time response. 

It ean be seen in Figure 5.17 that the pole at the origin and the zero at. v = —1 dominate the response. With the eomplex loei, ( = 0.7 gives K a value of 15. ITowever, this value of K oeeurs at —0.74 on the dominant real loeus. The time response shown in Figure 5.20 shows the dominant first-order response with the oseillatory seeond-order response superimposed. The settling time is 3.9 seeonds, whieh is outside of the speeifieation. 

The root locus diagram is shown in Figure 5.19. In this case the real locus occurs between. v = —5 and —3 and the complex dominant loci breakaway at rrh = —1-15. Since these loci are further to the right than the previous option, the transient response will be slower. The compensator gain that corresponds to ( = 0.7 is K = 5.3. The resulting time response is shown in Figure 5.20, where the overshoot is 5.3% and the settling time is 3.1 seconds. 

Relationship between frequency response and time response for closed-loop systems... 

The diserete time response ean be found using a number of methods. 

If the sampling time is one seeond and the system is subjeet to a unit step input funetion, determine the diserete time response. (N.B. normally, a zero-order hold would be ineluded, but, in the interest of simplieity, has been omitted.) Now... 

The time response of the state variables (i.e. position and veloeity) together with the state trajeetory is given in Figure 8.5. 

Fig. 8.5 State variable time response and state trajectory for Example 8.4. Solution...

Then the eommand veetor v (in this ease a sealar) is generated in reverse-time as shown in Figure 9.3. The forward-time response is shown in Figure 9.4. 

---