**4.3 Robustness performance**

The robust performance of the proposed controller is evaluated in the presence of mass variation. The 25% extra load is added to the default load of the mechanism. In this experiment, the control performance is examined in two type of motions: point-to-point and tracking motions. The robust performance of the FF PI-PD + *K*<sup>z</sup> controller is then compared with the FF PI-PD and FSF controllers.

*xr* is the reference input and *x* is the levitation height. In addition, the root mean

q

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1*=N*P*<sup>N</sup>*

*Experimental step responses of the three control systems at negative side direction. (a) Responses to a* � *0.5 mm*

*Control Based on PID Framework - The Mutual Promotion of Control and Identification…*

*step input (default mass). (b) Responses to a* �*1.0 mm step input (default mass).*

*<sup>k</sup>*¼<sup>1</sup>*e*<sup>2</sup>

**Figure 17** illustrates the trapezoidal tracking performance of the FSF, FF PI-PD and FF PI-PD + *K*<sup>z</sup> control systems to 0.5 mm and 1.0 mm amplitudes. Both FF PI-PD and FF PI-PD + *K*<sup>z</sup> controllers demonstrate almost identical tracking performance. The tracking error difference between them is insignificant. On the other hand, the FSF controller demonstrates the worst tracking performance with the largest tracking error among the compared controllers. The maximum tracking

where *N* represents the number of

square error, *Erms* is calculated as

*Simulated closed-loop frequency response.*

**Figure 15.**

**Figure 16.**

**102**

data samples and *e* is the tracking error.

#### **Figure 17.**

*Comparative experimental trapezoidal tracking responses of the three controllers. (a) Responses to a trapezoidal input: 0.5 mm (default mass). (b) Responses to a trapezoidal input: 1.0 mm (default mass).*

**Figure 18.**

**Figure 19.**

**105**

*Experimental step responses of the three control systems at positive side direction. (a) Responses to a 0.5 mm step*

*Experimental step responses of the three control systems at negative side direction. (a) Responses to a 0.5 mm*

*step input (increased mass). (b) Responses to a 1.0 mm step input (increased mass).*

*input (increased mass). (b) Responses to a 1.0 mm step input (increased mass).*

*Enhanced Nonlinear PID Controller for Positioning Control of Maglev System*

*DOI: http://dx.doi.org/10.5772/intechopen.96769*


#### **Table 4.**

*Average of twenty (20) experiments trapezoidal motion for the three controllers (default mass).*
