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The only serious failing of the feedforward technique is its dependency on accuracy. To provide perfect control, a system must model the plant exactly; otherwise whatever error may exist in positioning the manipulated variable causes offset. Errors may arise from several sources: 1. Inaccuracy in the measurement of load and manipulated variables 2. Errors in the computing components 3. Failure of the computing system to adequately represent the characteristics of the plant 4. Exclusion of significant load components from the feedforward system The first and second items alone limit the accuracy of practical systems to the vicinity of 1 to 2 percent.

Do you use checklists Do you keep a shopping list, and add to it whenever you think of something you need How could you make better use of checklists Do you ever have to interrupt yourself in the middle of a job to go get something you need What could you change in the way you work so that this would not happen any more How could you improve the way you plan for meetings How could you improve the way you follow through after meetings Can you think of a time where a meeting became confused, or even turned into a con ict Can you imagine doing that meeting again in a di erent way by putting everything in front of the team at the meeting, and working on it together Explain something you are doing in terms of inclusions and exclusions.

You ask, How we can write down relations and functions intended for polar coordinates as opposed to those meant for Cartesian coordinates It s simple When we want to denote a relation or function (call it f ) in polar coordinates where the independent variable is q and the dependent variable is r, we write r = f (q) We can read this out loud as r equals f of q When we want to denote a relation or function (call it g) in Cartesian coordinates where the independent variable is x and the dependent variable is y, we can write y = g (x) We can read this out loud as y equals g of x

Here s a challenge!

Provide an example of a graphical object that represents a function in polar coordinates when q is the independent variable, but not in Cartesian xy coordinates when x is the independent variable

What are you doing What are you not doing And why Think of a time when having a picture as well as a written plan helped, or could help, you and a team focus on a job Have you ever been stuck with a problem in testing, and no time to make a good x and retest What happened The next time you have a problem, think of it as a gap Where are you now Where do you want to be How will you close the gap Would you say you work in a mostly no-blame environment, or in an environment with a lot of blame How do you participate in that Do you want to change the way you are doing that.

Consider a polar function that maps all inputs into the same output, such as f (q) = 3 Because f (q) is another way of denoting r, this function tells us that r = 3 The graph is a circle with a radius of 3 units In Cartesian coordinates, the equation of the circle with radius of 3 units is x2 + y2 = 9 (Note that 9 = 32, the square of the radius) If we let y be the dependent variable and x be the independent variable, we can rearrange this equation to get y = (9 x 2)1/2 We can t claim that y = g (x) where g is a function of x in this case There are values of x (the independent variable) that produce two values of y (the dependent variable) For example, if x = 0, then y = 3 If we want to say that g is a relation, that s okay; but g is not a function