Ab block

Resolution. Interpretation Use the block generators to determine how the runs are assigned to the blocks. If the number of replicates is not a multiple of the number of blocks, then the design uses a block generator. For example, to construct a ½ fraction, 4-factor design with 1 replicate and 2 blocks, Minitab uses AB as the block generator. Minitab does the following: Construct the ½ fraction, 4-factor design in standard order where –1 and +1 represent the low and high factor levels, respectively. A B C D –1 –1 –1 –1 +1 –1 –1 +1 –1 +1 –1 +1 +1 +1 –1 –1 –1 –1 +1 +1 +1 –1 +1 –1 –1 +1 +1 –1 +1 +1 +1 +1 Generate the runs for the blocks by multiplying the settings for factors A and B together. Rows with the same value of the block generator are assigned to the same block. For example, the value of AB for the first run is −1 × −1 = 1. The value for the second run is 1 × −1 = −1. These runs are assigned to different blocks. A B C D AB Blocks –1 –1 –1 –1 +1 1 +1 –1 –1 +1 –1 2 –1 +1 –1 +1 –1 2 +1 +1 –1 –1 +1 1 –1 –1 +1 +1 +1 1 +1 –1 +1 –1 –1 2 –1 +1 +1 –1 –1 2 +1 +1 +1 +1 +1 1 Group the runs by block. Then, randomize the order of the blocks and the order of the runs within the blocks. A B C D AB Blocks +1 –1 +1 –1 –1 2 –1 +1 +1 –1 –1 2 –1 +1 –1 +1 –1 2 +1 –1 –1 +1 –1 2 +1 +1 +1 +1 +1 1 +1 +1 –1 –1 +1 1 –1 –1 +1 +1 +1 1 –1 –1 –1 –1 +1 1Alias structure The alias structure describes the confounding pattern that occurs in a design. Terms that are confounded are also said to be aliased. Aliasing, also known as confounding, occurs in fractional factorial designs because the design does not include all of the combinations of factor levels. For example, if factor A is confounded with the 3-way interaction BCD, then the estimated effect for A is the sum of the effect of A and the effect of BCD. You cannot determine whether a significant effect is

Equations (4) and (5), a transfer function with xema as the output and TL and Fema as inputs can be obtained as follows: x ema = η ema k ema T L R − F ema s ( s m ema + B fr ) (6) The model is not specific to the roller-screw type, but is instead general. Equations (5) and (6) are written in the case of an opposite load, and for simplification the case of an aiding load is not considered, although the EMA works in both cases.The open-loop system model block diagram of the planetary-roller screw pair is shown in Figure 3. 3.3. Force SensorSince the force sensor has very small inertia and operates within the range of elastic deformation, the force analysis equation of the force sensor can be obtained as follows: F ema = K s ( x ema − x fs ) (7) Thus, the open-loop system model block diagram of the force sensor is shown in Figure 4. 3.4. Load Connection PointIn order to make the model more perfect, the inertial load is selected in the mathematical model; the mass of the inertial load is 0.001 kg, which is equivalent to no load.Considering the connection stiffness between the LEMA and the load connection point, the force analysis equation at the load connection point can be obtained as follows: F ema = m el x ¨ ema + S t ( x ema − x a ) (8) Thus, the open-loop system model block diagram at the load connection point is shown in Figure 5. 4. Anti-Disturbance Control Strategy for the Force Servo System 4.1. Establishment of an Open-Loop Model of the Force Servo SystemBased on the model block diagrams of each core component, an open-loop model block diagram of the force servo system with the input command u and the external position disturbance xa as inputs and Fema as the output can be obtained, as depicted in Figure 6. Its open-loop transfer function is expressed as follows: F ema = R k ema η ema K i K v C T u − s F ab ( F ema K s + F ema + S t x a s 2 m el + S t ) s L m + R m + K i K f (9) where Fab can be obtained as follows: F ab = { R k

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