# Multivariable Feedback Control: Analysis and Design by Sigurd Skogestad, Ian Postlethwaite

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For disturbances entering directly at the plant input (which is a common situation in practice { often referred to as a load disturbance), we have Gd = G and we get jKminj = 1, so a simple proportional controller with unit gain yields a good trade-o between output performance and input usage. Notice that a reference change may be viewed as a disturbance directly a ecting the output. 17), from which we get that a maximum reference change r = R may be viewed as a disturbance d = 1 with Gd (s) = ;R where R is usually a constant.

272 is for an input in the direction v = 0 794 . 3. 42) both inputs a ect both outputs, we say that the system is interactive. This follows from the relatively large o -diagonal elements in G1 . Furthermore, the system is ill-conditioned, that is, some combinations of the inputs have a strong e ect on the outputs, whereas other combinations have a weak e ect on the outputs. 42) is 7:343=0:272 = 27:0. 5 Shopping cart. Consider a shopping cart (supermarket trolley) with xed wheels which we may want to move in three directions forwards, sideways and upwards.

75) ! )), to measure the size of the matrix N at each frequency. 78) that j 1 j 0:707 and j 2 j 0:707. That is, p there is a possible \error" in each speci cation equal to at most a factor 2 3pdB. In general, with n stacked requirements the resulting error is at most n. This inaccuracy in the speci cations is something we are probably willing to sacri ce in the interests of mathematical convenience. In any case, the speci cations are in general rather rough, and are e ectively knobs for the engineer to select and adjust until a satisfactory design is reached.