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Chapter 29: Control Theory 271siso plant:G(s) =s − 2(s + 2)(s − 1)+----+-------------------->| W1 |---> v1z | +----+----|-------------+| || +---+ v y +----+u *--->| G |--->O--*-->| W2 |---> v2| +---+ | +----+| || +---+ |-----| K || W1 |----> z1w | | +----+2 ------------------------+| | || v +----+ v +----++--*-->o-->| G |-->o--*-->| W2 |---> z2| +----+ | +----+| |^vu y (to K)(from controller K)⎡ ⎤ ⎡ ⎤⎣z 1z 2y⎦ = P ⎣Discrete system:This is not a true discrete design. The design is carried out in continuoustime while the effect of sampling is described by a bilinear transformationof the sampled system. This method works quite well if the samplingperiod is “small” compared to the plant time constants.w 1w 2u⎦