DISCRETE QUANTITATIVE FEEDBACK TECHNIQUE
This chapter focuses on the application of the QFT technique to MISO sampleddata control systems.14 The QFT sampled-data (S-D) system design process is tuned to the bounds of uncertainty, the performance tolerances, and the sampling time T (or sampling frequency ωs = 2π/T). The QFT technique requires, as discussed in Sec. 4-5, the determination of the minimum sampling frequency (ωs)min bandwidth (BW) that is needed for a satisfactory design. The larger the plant uncertainty and the narrower the system performance tolerances, the larger must be the value of (ωs)min. The use of the z-to the w′ domain bilinear transformation13 permits the analysis and design of sampled-data systems by the use of the digitization (DIG) technique.13 That is, the w′-plane detailed QFT design procedure essentially parallels very closely that for continuous-time systems of Chapter 3, the difference being that the design must take into account the right-half-plane (RHP) zero(s) that result in the w′ plant transfer function due to the bilinear transformation. Note, when a plant P(s) is m.p. it becomes a n.m.p. plant when transformed into the w′-domain. Thus, proper care must be exercised in satisfying the stability bounds prescribed for the QFT design
The pseudo-continuous-time (PCT) approach, which is discussed in Sec. 48, is another DIG technique that allows the QFT design of the D(z) controller to be done in the s-domain. Once the s-domain controller has been synthesized, in the manner described in Chapter 3, it is transformed into the z-domain by use of the Tustin transformation, a bilinear transformation, to obtain D(z). The advantage of this approach, when the plant is m.p., is that it eliminates dealing with a n.m.p. plant and the problem associated in satisfying the stability bounds. Thus, the transformation either into the w′- or s-domain of the S-D MISO or MIMO control
system enables the use of the MISO QFT analog design technique to be readily used, with minor exceptions, to perform the QFT design for the controller D(w') or D(s). If the w'- or s-domain simulations satisfy the desired performance specifications then by use of the bilinear transformation the z-domain controller G(z) is obtained. With this z-domain controller a discrete-time domain simulation is obtained to verify the goodness of the design.