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The deviation in this case is known as offset, and it increases with proportional band. With a 200 percent band, which was necessary for >i-amplitude damping in the previous example, a 10 percent change in load would produce a 20 percent offset-an int,olerable amount. The characteristics of a dead-time process under proportional control may be observed in a simple algebraic simulat.ion. Let the present output of the controller equal the measurement one dead time later:

Ellipsoid centered at the origin Again, imagine that we have a perfect sphere centered at the origin in Cartesian xyz space Let s lengthen one of the axial radii while leaving the other two unchanged This stretching process produces an ellipsoid It s elongated, like a football with blunted ends Figure 17-7 shows an example Imagine that we take the sphere from Fig 17-3 and then stretch it in the z direction The general equation for an ellipsoid centered at the origin is

The sooner we see that we are o course, the less it costs to get back on track The rst two items should be identi ed in the weekly status meetings Others we identify by comparing what is actually happening to the project plan Once we see a problem, we should work with our team to respond immediately and e ectively..

x2/a2 + y2/b2 + z2/c2 = 1 where a is the x-axial radius, b is the y-axial radius, c is the z-axial radius, and exactly one of the following relationships is true: a>b=c b>a=c c>a=b

You ask, Do the commutative, associative, distributive, and other rules of arithmetic and algebra work with functions in the same ways as they do with numbers and variables The answer is a qualified yes All the rules of addition, subtraction, multiplication, and division of functions are identical to the rules for arithmetic or algebra involving numbers or variables, as long as we heed the cautions outlined earlier in this section

Here s a challenge!

We can set up a very simple, clear system for escalating issues. This solves several common management misunderstandings: Executives do not like to be blindsided, that is, hit with a problem when they thought nothing was wrong. Executives often misread manager s status reports, either jumping in when they are not wanted, or not addressing issues where their help is needed. Executives like to hear problems and solutions.

Define the real-number domains of all the sum, difference, product, and ratio functions we ve found in this section

This represents a process whose gain is unity and whose When the controller is introduced to close the loop,

We found the real-number domains (which we can call the real domains for short) of the functions f1, f2, and f3 earlier in this chapter Here they are again, for reference: The real domain of f1 (x), which subtracts 1 from x, is the set of all reals The real domain of f2 (x), which squares x, is the set of all reals The real domain of f3 (x), which takes the nonnegative square root of x, is the set of all nonnegative reals The real domains of the sum, difference, and product functions are the intersections of these Let s list them: The real domains of ( f1 + f2), ( f1 f2), and ( f1 f2) are the set of all real numbers The real domains of ( f2 + f1), ( f2 f1), and ( f2 f1) are the set of all real numbers The real domains of ( f1 + f3), ( f1 f3), and ( f1 f3) are the set of all nonnegative real numbers The real domains of ( f3 + f1), ( f3 f1), and ( f3 f1) are the set of all nonnegative real numbers The real domains of ( f2 + f3), ( f2 f3), and ( f2 f3) are the set of all nonnegative real numbers The real domains of ( f3 + f2), ( f3 f2), and ( f3 f2) are the set of all nonnegative real numbers

Our solution is built on the model of tra c lights: Green means everything is okay, the project should come in with quality, on time, and on budget Yellow means: alert, caution, there may be trouble ahead We are giving the project sponsor a heads-up, so he will not be blindsided later With yellow alert, we are also telling the sponsor that we do not need any help right now Red alert means we need help: a meeting, ideas, approvals, money, or a change of schedule, right now If it appears that a problem may be impossible to resolve with existing resources, we escalate it early, going to yellow alert.