Design of Digital Control Systems Using State-Space Methods

In Chapter 5, we discussed how to design digital controllers using transform techniques, methods now commonly designated as "classical design." The goal of this chapter is to solve the identical problem using the state-space formulation. The difference in the two approaches is entirely in the design method; the end result, a set of difference equations providing control, is identical. In fact, given the same set of specifications, the control equations should be very similar if not identical. Advantages of the state-space formulation are especially apparent when designing controllers for Multi-Input, Multi-Output (MIMO) systems, that is, those with more than one control input and/or sensed output. However, state-space methods are also an aid in the design of controllers for SingleInput, Single-Output (8180) systems because of the widespread use of CAD tools, which often rely heavily on this system representation. Chapters 2 and 3 have already demonstrated the advantages of the state-space formulation in using CAD packages for the computation of discrete equivalents. In this chapter, we will limit our state-space design efforts to SISO controllers, the same controllers found in Chapter 5 with classical methods. Techniques for MIMO design are discussed in Chapter 9. In Chapter 5, two basic methods were described: emulation and direct digital design. The same two methods apply to the state-space formulation as well. Using emulation, one would design a continuous controller using state-space methods then, transform the controller to a discrete form by using one of the discrete equivalents from Chapter 4. The discussion of the method and its accuracy in Chapter 5 applies equally well here. Furthermore,