*4.3.1 Point-to-point motion*

The positioning responses with the increased mass are shown in **Figures 18** and **19**. As the mass is increased, the FF PI-PD controller shows overshoot occurrence at both positive and negative directions. Thus, the FF PI-PD controller fails to demonstrate its robust performance. On the other hand, the FF PI-PD + *K*<sup>z</sup> controller demonstrates high robustness via demonstrating zero overshoot at all the step responses regardless of the variation of mass. Hence, the experimental positioning results proved that the disturbance compensation control scheme is comprised in the FF PI-PD + *K*<sup>z</sup> controller and it has led to the less sensitive to parameter variation characteristic of the controller. Although the FSF controller performs its good robustness through showing *Enhanced Nonlinear PID Controller for Positioning Control of Maglev System DOI: http://dx.doi.org/10.5772/intechopen.96769*

**Figure 18.**

*Experimental step responses of the three control systems at positive side direction. (a) Responses to a 0.5 mm step input (increased mass). (b) Responses to a 1.0 mm step input (increased mass).*

#### **Figure 19.**

*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).*

*4.3.1 Point-to-point motion*

**Figure 17.**

**Table 4.**

**104**

The positioning responses with the increased mass are shown in **Figures 18** and **19**. As the mass is increased, the FF PI-PD controller shows overshoot occurrence at both positive and negative directions. Thus, the FF PI-PD controller fails to demonstrate its robust performance. On the other hand, the FF PI-PD + *K*<sup>z</sup> controller demonstrates high robustness via demonstrating zero overshoot at all the step responses regardless of the variation of mass. Hence, the experimental positioning results proved that the disturbance compensation control scheme is comprised in the FF PI-PD + *K*<sup>z</sup> controller and it has led to the less sensitive to parameter variation characteristic of the controller. Although the FSF controller performs its good robustness through showing

*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).*

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

**Reference input Controller** *E***max** *E***rms**

Trapezoidal, 0.5 mm FSF 2.28 <sup>10</sup><sup>1</sup> 5.72 <sup>10</sup><sup>2</sup>

Trapezoidal, 1.0 mm FSF 2.95 <sup>10</sup><sup>1</sup> 1.04 <sup>10</sup><sup>1</sup>

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

**Average, mm Average, mm**

FF PI-PD 1.21 <sup>10</sup><sup>1</sup> 3.04 <sup>10</sup><sup>2</sup> FF PI-PD + *<sup>K</sup>*<sup>z</sup> 1.18 <sup>10</sup><sup>1</sup> 3.05 <sup>10</sup><sup>2</sup>

FF PI-PD 1.51 <sup>10</sup><sup>1</sup> 4.24 <sup>10</sup><sup>2</sup> FF PI-PD + *<sup>K</sup>*<sup>z</sup> 1.56 <sup>10</sup><sup>1</sup> 4.27 <sup>10</sup><sup>2</sup> zero overshoot at all the step responses, it takes longer positioning time than the FF PI-PD + *K*<sup>z</sup> controller to reach the steady-state (**Table 5**).

**Table 6** shows the quantitative comparison of twenty (20) repeatability tests for the point-to-point motion in the presence of mass variation. As can be seen from **Table 6**, when the mass of table is increased, the FF PI-PD controller fails to demonstrate its robustness by producing a large overshoot. The change of mass has caused the overshoot of the FF PI-PD controller is increased by 20% of the default mass condition and the settling time of the FF PI-PD controller is 47.9% longer than the FF PI-PD + *K*<sup>z</sup> controller. In contrast, the FF PI-PD + *K*<sup>z</sup> controller has successfully remained its high robust performance via demonstrating zero overshoot at all the step responses. It is evident that the FF PI-PD + *K*<sup>z</sup> controller enhances the robustness of the FF PI-PD controller via introducing the disturbance compensation


control scheme. On the other hand, the FF PI-PD + *K*<sup>z</sup> achieves approximately three (3) times shorter settling time than the FSF controller when the mass increased. In short, the FF PI-PD + *K*<sup>z</sup> controller demonstrates the best positioning performance

As referred to the **Figure 20**, the FF PI-PD + *K*<sup>z</sup> controller performs smaller sensitivity function magnitude than the FF PI-PD controller. Hence, it is less sensitive to parameter variation. In short, despite the variation of mass and amplitude, the FF PI-PD + *K*<sup>z</sup> controller demonstrates a superior tracking performance than the FF PI-PD and FSF controllers, where it tracks the trapezoidal command accurately

In this chapter, the architecture of the FF PI-PD + *K*<sup>z</sup> control system for enhanc-

ing the positioning, tracking and robust performances of the maglev system is presented. Initially, a two-degree-of-freedom (2 DOF) PID control – PI-PD, is used to improve the transient response of the conventional PID controller by minimizing the resonance peak. However, the PI-PD control has not sufficiently performed promising positioning responses. A as solution, a model-based feedforward (FF) control is integrated to the PI-PD control for further improving the following characteristic and overshoot reduction capabilities of the mechanism. Lastly, a disturbance compensator (*K*z) is served to enhance the system robustness via lowering the sensitivity function magnitude. Although the framework of proposed controller - FF PI-PD + *K*<sup>z</sup> control system is slightly complex than the conventional PID controller, but the design procedure of FF PI-PD + *K*<sup>z</sup> control system remains simple, straightforward, and ease to understand. This advantageous highlight the applicability of the FF PI-PD + *K*<sup>z</sup> control system in the industrial applications. The effectiveness of the proposed controller is evaluated experimentally in point-to-point and tracking motions in comparison to the FF PI-PD and Full State Feedback (FSF) controllers. The robust performance of the controllers is examined in the presence of the mass variations. As an overview, the FF PI-PD + *K*<sup>z</sup> control system performs well in the positioning and robustness performances as compared to the FF PI-PD and FSF controllers. The comparative experimental results are sufficient to prove the contribution of the FF PI-PD + *K*<sup>z</sup> control system in overshoot reduction and robustness enhancement. As for future work, the robustness performance, and the positioning

among the compared controllers regardless of the mass variation.

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

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

*Sensitivity response of the FF PI-PD +* K*<sup>z</sup> and the FSP controllers.*

and precisely via illustrating the lowest *Emax* and *Erms* values.

accuracy of the FF PI-PD + *K*<sup>z</sup> control system will be improved.

**5. Conclusions**

**107**

**Figure 20.**

OS*: overshoot, ts: settling time.*
