**5. Conclusions**

zero overshoot at all the step responses, it takes longer positioning time than the FF

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

**Step height Performance index FF PI-PD +** *K***<sup>z</sup> FF PI-PD FSF** 0.5 mm *OS*, % Average 0.00 0.00 0.00

1.0 mm *OS*, % Average 0.00 1.40 <sup>10</sup><sup>1</sup> 0.00

0.5 mm *OS*, % Average 0.00 2.80 101 0.00

1.0 mm *OS*, % Average 0.00 1.75 <sup>10</sup><sup>1</sup> 0.00

*Experimental positioning performances of twenty (20) experiments for three controllers (increased mass).*

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

Trapezoidal, 0.5 mm FSF 1.92 <sup>10</sup><sup>1</sup> 5.33 <sup>10</sup><sup>2</sup>

Trapezoidal, 1.0 mm FSF 2.99 <sup>10</sup><sup>1</sup> 9.87 <sup>10</sup><sup>2</sup>

*Average of twenty (20) experiments trapezoidal tracking motion for three controllers (increased mass).*

OS*: overshoot, ts: settling time.*

**Table 5.**

**Table 6.**

**106**

Standard deviation 0.00 0.00 0.00 *<sup>t</sup>*s, s Average 1.13 <sup>10</sup><sup>1</sup> 1.77 <sup>10</sup><sup>1</sup> 3.92 <sup>10</sup><sup>1</sup>

Standard deviation 1.60 <sup>10</sup><sup>2</sup> 1.05 <sup>10</sup><sup>1</sup> 1.28 <sup>10</sup><sup>1</sup>

Standard deviation 0.00 2.52 <sup>10</sup><sup>2</sup> 0.00 *<sup>t</sup>*s, s Average 1.50 <sup>10</sup><sup>1</sup> 2.95 <sup>10</sup><sup>1</sup> 5.08 <sup>10</sup><sup>1</sup>

Standard deviation 1.47 <sup>10</sup><sup>2</sup> 9.75 <sup>10</sup><sup>2</sup> 8.60 <sup>10</sup><sup>2</sup>

Standard deviation 0.00 2.85 <sup>10</sup><sup>2</sup> 0.00 *<sup>t</sup>*s, s Average 1.15 <sup>10</sup><sup>1</sup> 2.77 <sup>10</sup><sup>1</sup> 3.59 <sup>10</sup><sup>1</sup>

Standard deviation 5.40 <sup>10</sup><sup>2</sup> 1.93 <sup>10</sup><sup>1</sup> 8.42 <sup>10</sup><sup>2</sup>

Standard deviation 0.00 3.66 <sup>10</sup><sup>2</sup> 0.00 *<sup>t</sup>*s, s Average 2.27 <sup>10</sup><sup>1</sup> 4.32 <sup>10</sup><sup>1</sup> 4.57 <sup>10</sup><sup>1</sup>

Standard deviation 1.17 <sup>10</sup><sup>2</sup> 4.67 <sup>10</sup><sup>2</sup> 6.87 <sup>10</sup><sup>2</sup>

FF PI-PD 1.53 <sup>10</sup><sup>1</sup> 3.50 <sup>10</sup><sup>2</sup> FF PI-PD + *<sup>K</sup>*<sup>z</sup> 1.26 <sup>10</sup><sup>1</sup> 3.05 <sup>10</sup><sup>2</sup>

FF PI-PD 1.72 <sup>10</sup><sup>1</sup> 4.04 <sup>10</sup><sup>2</sup> FF PI-PD + *<sup>K</sup>*<sup>z</sup> 1.57 <sup>10</sup><sup>1</sup> 3.84 <sup>10</sup><sup>2</sup>

**Average, mm Average, mm**

**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

PI-PD + *K*<sup>z</sup> controller to reach the steady-state (**Table 5**).

In this chapter, the architecture of the FF PI-PD + *K*<sup>z</sup> control system for enhancing 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 accuracy of the FF PI-PD + *K*<sup>z</sup> control system will be improved.

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