*PID-like Fuzzy Controller Design for Anti-Slip System in Quarter-Car Robot DOI: http://dx.doi.org/10.5772/intechopen.110497*


#### **Table 3.** *FAM of ki.*

**Figure 9.** *Linguistic variables for the output (a) kp, (b) kd, and (c) ki.*

*ki* does not present any alteration in how it computes its value. The range of existence is 3½ � *:*5,14*:*5 . The integral action eliminates the steady error; for this particular case, if *ki* is big enough, it compensates the error. If the error is small, the integral of the error will also reduce its magnitude considerably.

The singleton is used as a membership function in the defuzzification phase to reduce the computational cost when searching for the profit values. It is important to respect this consideration since there is only one defuzzification phase in the conventional fuzzy controller. In contrast, the proposal for this controller consists of three fuzzy steps, one for each control gain. It is necessary to mention that this process is the same for computing *kd* and *ki*. The centroid method, presented in Eq. 18, is used in the defuzzification stage of each gain.

$$K\_{p,d,i}[n] = \frac{\sum\_{i=1}^{n} \mu\_c(z\_i) \cdot z\_i}{\sum\_{i=1}^{n} \mu\_c(z\_i)}\tag{18}$$

where *μc*ð Þ *zi* represents degree of membership function, and *zi* the position of the singleton.
