Control Systems Engineering
Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 3, Problem 26P

State-space representations are, in general, not unique. One system can be represented in several possible ways. For example, consider the following systems:

  1. x ˙ = 5 x + 3 u y = 7 x
  2. x ˙ 1 x ˙ 2 = 5 0 0 1 x 1 x 2 + 3 1 u y = 7 0 x 1 x 2
  3. x ˙ 1 x ˙ 2 = 5 0 0 1 x 1 x 2 + 3 0 u y = 7 3 x 1 x 2

Show that these systems will result in the same transfer function. We will explore this phenomenon in more detail in Chapter 5.

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3. A steam power plant has an average monthly net power delivery of 740 MW over the course of a year. This power delivery is accomplished by burning coal in the boiler. The coal has a heating value of 9150 Btu/lbm. The cost of the coal is $14.20/ton. The overall thermal efficiency of the plant is, nth = Wnet Qboiler = 0.26 = 26% Determine the annual cost of the coal required to deliver the given average monthly power.

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