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Extra resources for Linear Controller Design: Limits of Performance (Prentice Hall Information and System Sciences Series)
Sample text
Again, we follow the de nitions above: the command signals are plant inputs, not manipulable by the controller (they are presumably manipulable by some external agent issuing the commands), and so they must be exogenous inputs, and therefore included in w. 4. Diagnostic outputs are treated in a similar way. 1). 4. , functions from a real, nonnegative time variable into the appropriately dimensioned vector space: w : R+ ! Rnw u : R+ ! Rnu z : R+ ! Rnz y : R+ ! 2 ASSUMPTIONS n wsystem 29 Plant w wcommands u System n usystem udiag zsystem o z zdiag o Controller y ysystem ycommands In our framework the command signals are included in w and pass through the plant to y, so that the controller has access to them.
4 A Standard Numerical Example In this section we describe a particular plant and several controllers that will be used in examples throughout this book. 2, with 10 ; s : P0 = P0std = s12 10 +s P0std consists of a double integrator with some excess phase from the allpass term (10 ; s)=(10 + s), which approximates a 0:2 second delay at low frequencies. 11). The closed-loop systems that result from using the controllers K (a) , K (b) , K (c) , and K (d) can be compared by examining the 2 3 transfer matrices H (a) , H (b) , H (c) , and H (d) .
3]. Discussions of control architectures appear in the articles DL85] and Net86]. We noted that the 2-DOF control system is more general than the 1-DOF control system, and yet the 1-DOF control system architecture is widely chosen. In some cases, the actual sensor used is a di erential sensor, which directly senses the di erence between the reference and the system output, so that the 1-DOF plant accurately re ects signals accessible to the controller. But in many cases, the system output signal and the reference input signal are separately sensed, as in the 2-DOF controller, and a design decision is made to have the controller process only their di erence.
