By Tongwen Chen PhD, Bruce Allen Francis PhD (auth.)
ISBN-10: 1447130375
ISBN-13: 9781447130376
ISBN-10: 1447130391
ISBN-13: 9781447130390
Among the numerous ideas for designing linear multivariable analogue controllers, the 2 hottest optimum ones are H2 and H ¿ optimization. the truth that such a lot new commercial controllers are electronic presents powerful motivation for adapting or extending those concepts to electronic regulate structures. This publication, now on hand as a corrected reprint, makes an attempt to take action. half I provides oblique tools of sampled-data controller layout: those methods comprise approximations to a true challenge, which comprises an analogue plant, continuous-time functionality necessities, and a sampled-data controller. half II proposes an instantaneous assault within the continuous-time area, the place sampled-data structures are time-varying. The findings are awarded in kinds which can with ease be programmed in, e.g., MATLAB.
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Additional info for Optimal Sampled-Data Control Systems
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5/7r)s + l' The weight W is then taken to have bandwidth one-fifth the Nyquist frequency: 32 CHAPTER 2. 2 AND 'H. 10: Bode magnitude plots: 1/(1 + pkj) (solid), tV (dash), j (dot). 01. 10 shows the results of the design using hinfsyn. The solid curve is the Bode magnitude plot of the sensitivity function, that is, the transfer function from WI to e, namely, 1/(1 + pkj). Also shown are the magnitude plots for W (dash) and F (dot). Evidently, the design has achieved some tracking error attenuation over the bandwidth of W.
We begin with an example. 1 Again, the setup is ~ .. Y!.... S H __ ,~------~v v ------~ Gd Let w, denote the sampling frequency (rad/s), that is, w, 211" :=-,;. Take G to be an oscillator with '( ) gs = S 2W,s +w,2· Now consider applying the unit step at v. Then u is the unit step in continuous time. Hence y(t) inverse Laplace transform of sinw,t, t ~ s 2 w, 2 +w, 0 and so t/J(k) = 0, for all k ~ o. == O. So here is a nonzero system G whose discretization is zero. But the discretization of G = 0 is also Gd = O.
Which is better? Indeed, how can we judge how good a discretization is? This section provides a way to answer this. We'll do the SISO case for simplicity. 5. DISCRETIZATION ERROR 55 Suppose 9a(8) is a transfer function of an analog system and kd(A) is a discretization, for example, kd = 9ad or 9abt. Let Ga and Kd denote the corresponding linear systems. We cannot talk about the error between G a and Kd just as we cannot compare apples and oranges. Suppose, however, that G a is an analog controller that has been designed, and Kd is its discretization.
Optimal Sampled-Data Control Systems by Tongwen Chen PhD, Bruce Allen Francis PhD (auth.)
by Kevin
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