Design in the s-plane

This type of controller design has been around for many years. The pole-placcmcnt methods that are used in aerospace systems use the same basic idea the controller is designed so as to position the poles of the closedloop transfer function at the desired location in the s plane. This is exactly what we do when we specify the closedloop time constant in Eq. (11.63). 

The tools used in this chapter are those developed in Chapters 7 and 8. We use transfer functions to design feedforward controllers or to develop the characteristic equation of the system and to find the location of its roots in the S plane. 

Sampled-data controllers can be designed in the same way continuous controllers are designed. Root locus plots in the z plane or frequency-response plots are made with various types of >(z) s (different orders of M and N and different values of the a, and 6, coefficients). This is the same as using different combinations of lead-lag elements in continuous systems. 

Figure 21 Part of the crystal structure of (14)2 (DMSO) projected in the ah plane, showing the O-H 0=S and C-F FI-CH2-SO interactions (dashed lines) present between the two components. Atom designators O heavy stippling, S black, and F vertical hatching.

Fig. 2 a. Focusing geometry of a SAXS-camera [11, 32]. b. Schematic design of a focussing SAXS-camera with a pinhole geometry. S, and S2 are the aperture and guard slits. The optical element could be a mirror or a monochromator, m corresponds to the — idealized — extension of the diffuse scattering in the detector plane. as is the size of the source point and and a that of the focus. Note that the calculations of SAXS-resolution assume that F2 L, + L2... 

The first two sampled-data controller design methods use conventional root locus and frequency response methods, which are completely analogous to the techniques in continuous systems. Instead of looking at the s plane, however, we look at the z plane. The third sampled-data controller design method is similar to the direct synthesis method discussed in Chapter 9. 

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