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542   Chapter Fifteen


                               Ideal function
            y=
            Braking
            torque                      Actual
                                        relationship



                               M=Foot
                               force

                              (a)


                                    Ideal function
           y=
           Braking
           torque
                                    Actual
                                    relationship


                               M=Foot              Figure 15.6 Actual relationships
                               force               between foot force and braking
                                                   torque. (a) Not robust, (b) robust.
                              (b)


           1. To make sure that the main transformation (in the car brake case,
              it is an energy transformation process) process of the high-level
              function (stopping or slowing down the car) can perform robustly at
              different magnitudes of transformation.
           2. To make sure that the brake system has excellent controllability for
              this transformation process; this is illustrated by pursuing the per-
              fect linear relationship between the signal (M   foot force) and the
              magnitudes of transformation (measured by brake torque) with a
              high degree of robustness.
           In summary, the “robustness at different magnitudes of transforma-
           tion” and the “robustness at controllability” are the real focuses of
           Example 15.1.
             Let’s examine a few more examples of ideal functions.

             Example 15.2 Example of Ideal Functions
             1. Semiconductor oxidation process
                a. Main function. To oxidize a thin layer of material
                b. Main transformation. Material transformation (changing material
                   with a chemical reaction)
                c. Ideal function
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