**1. Introduction**

Magnetic levitation (maglev) system produces an electromagnetic force as the electric current flow through the coils to support a levitated object. This indicates that the maglev system eliminates the mechanical contact and friction between the moving and stationary parts. Due to the advantages, the maglev system has been successfully and widely implemented for many high-speed motion applications such as the high-speed maglev passenger trains, magnetic bearing system, flywheel energy storage system and vibration isolation system [1]. However, the maglev system is open loop instability and inherent nonlinearities. In addition, it is a nondamping system which has fast response, yet sensitive to vibration. Therefore, it remains a challenging task to design a feedback controller for attaining a good positioning performance in the maglev system.

Although a lot of advanced control strategy has been proposed for controlling maglev system, the classical controllers such as proportional integral derivative

(PID) and lead–lag compensators still are regularly employed in the industrial applications due to their simple structure, straightforward design procedure and easy to implement. In the past, a lead compensator [2] and cascaded lead compensation scheme [3] were designed to stabilize the maglev system. However, the classical controllers can only perform well in limited operating range and failed to demonstrate a satisfactory robustness performance. Thus, many advanced controllers such as feedback linearization [4], sliding mode control [5], *H*<sup>∞</sup> control technique [6], disturbance observer control approach [7], adaptive robust backstepping method [8] and model predictive control [9–11] as well as intelligent controllers which include fuzzy logic control [12] and neural network [13] have been dedicated to procure the high positioning and robustness performances in the maglev system. Despite the good positioning and robustness performances of the advanced controllers, sufficient knowledge of control theory is strictly needed in the design procedure. Furthermore, the intelligent controllers consist of complex architecture require a high computational effort. Often, the intelligent controllers do not have any systematic design procedure. These drawbacks depict barrier to their practical use.

The remainder of this chapter is outlined as follow. In Section 2, the experimental setup and mathematical modeling of the maglev system are represented. Section 3 explains the control structure, design procedure and stability analysis of the FF PI-PD + *K*<sup>z</sup> controller. In Section 4, the experimental results are discussed. Lastly,

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

This section presents the experimental setup and dynamic modeling of the

The single-axis maglev mechanism (Googoltech GML 2001), as shown in **Figure 1** is used as a testbed to clarify the usefulness of the proposed controller. The maglev system is only able to control object to move up and down. The control purpose is to keep the magnetic levitation ball stable in a given position or to make

The maglev mechanism consists of an electromagnet (number of windings, *Nw* = 1000 turns) to exert a tractive force across the air gap to levitate a steel ball (mass, *M* = 94 g). Besides, it is a voltage-controlled (control signal, *u* = 0–10 V) maglev mechanism, which is comprised of a power amplifier to actuate the electromagnet. The maximum electrical power consumption is around 16 W. The maximum levitation height of the maglev system is 15 mm. In the experiments, the initial position is set at 10.5 mm and the operating range is within 2.5 mm. A laser position sensor (Panasonic laser distance sensor HG-C1050) with resolution of 1.83 μm is used to measure the levitation displacement. As experimentally examined, the resolution of the laser sensor output in open loop is recorded at 15 μm. To measure the controlled current of the mechanism, a hall effect current sensor

the conclusion is drawn in Section 5.

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

maglev system.

**Figure 1.** *Maglev system.*

**89**

**2.1 Experimental setup**

the ball track a desired trajectory.

**2. Experimental setup and dynamic modeling**

Due to the above-mentioned reason, researchers kept devoting their effort in enhancing control performance of classic control in maglev system. The problem associated with 1-DOF PID control was overcome with the proposed of modified PID control and/or 2-DOF PID control. In 2007, Leva and Bascetta in [14] have realized a model-based feedforward control to the PID controller to improve the tracking performance of a maglev system. Unfortunately, it still demonstrated huge spike occurrence when the ball started moving at the initial position. After few years, Ghosh et al. has proposed a 2-DOF PID controller to improve the system transient response with zero percentage of overshoot. However, the proposed controller suffered from long settling time which was around 2 s. Besides, its positioning accuracy was recorded poor due to the derivative action on the reference signal [15]. In order to solve the positioning accuracy, Allan et al. has introduced the 2- DOF Lead-plus-PI controller [16]. The experimental evidence reported the improvement in the positioning accuracy, yet to point-to-point motion performance was deteriorated as the levitation height was increased.

Thus, in this research, a proportional integral-proportional derivative control with feedforward and disturbance compensations (FF PI-PD + *K*z) control approach is proposed to stabilize the maglev system and enhance the positioning performance as well as its robustness. The proposed controller consists of a PI-PD controller, a model-based feedforward control and a disturbance compensator. The PI-PD controller is designed by using the pole-placement method; the model-based feedforward control is constructed based on the system driving characteristic in open loop; the disturbance compensator is developed via the system current dynamics in closed loop. The derivative action of the PI-PD control amplified the measurement noise that affected the positioning accuracy. Hence, a low pass filter is featured with the PI-PD control to suppress the bad influence of the derivative action. Besides, a model-based feedforward control is incorporated with the PI-PD controller to further improve the following characteristic of the mechanism in attaining a better overshoot reduction characteristic. At the same time, the positioning time is greatly reduced. Lastly, a disturbance compensator is integrated as an additional feedback element for robustness enhancement via lowering the sensitivity function magnitude. The effectiveness of the FF PI-PD + *K*<sup>z</sup> controller is validated experimentally through two types of motion control that are point-topoint and tracking motions. In this present paper, the robustness of the FF PI-PD + *K*<sup>z</sup> controller is examined via applying an impulse disturbance and varying the mass. The positioning and robustness performances of the FF PI-PD + *K*<sup>z</sup> controller are compared with the FF PI-PD and the full state feedback (FSF) controllers.

*Enhanced Nonlinear PID Controller for Positioning Control of Maglev System DOI: http://dx.doi.org/10.5772/intechopen.96769*

The remainder of this chapter is outlined as follow. In Section 2, the experimental setup and mathematical modeling of the maglev system are represented. Section 3 explains the control structure, design procedure and stability analysis of the FF PI-PD + *K*<sup>z</sup> controller. In Section 4, the experimental results are discussed. Lastly, the conclusion is drawn in Section 5.
