Design and Control of Multicoil Active Magnetic Bearing System for High-Speed Application

Abstract

In the rotating machinery sector, active magnetic bearing (AMB) has drawn great attention due to its benefits over the conventional bearing system. The high-speed technology is enhanced by AMBs, which also reduce maintenance costs and eliminate friction loss. This paper presents a unique, simpler, efficient design and hardware implementation for high-speed applications using two-coil I-type active magnetic bearings. To maintain the 10 mm air gap between the actuator and the rotor, two categories of controllers have been designed for the proposed system to control the position and another for detecting the coil current through the power amplifier. The AMB system is incorporated into a 3D finite element model for determining magnetic properties. The magnetic analysis is then carried out under various situations, and the attractive force characteristics have been evaluated for this suggested system to check the performance of the multicoil AMB system along with the stability analysis. The system is designed and simulated in MATLAB Simulink and implemented in hardware to validate the different outputs viz. position response and current response. Finally, an AC magnet is designed to rotate the rotor after the levitation, and a higher speed of 19,643 rpm is achieved in comparison to conventional bearings, which can be utilized in different industrial applications.

1. Introduction

The demand for high-speed rotating machinery in the future is mainly reflected in high-speed, high-precision, and other aspects. In this regard, AMB recommends air suspension as an innovative solution that can meet this need. The sensor and power amplifier make this sort of technology cost-effective. The count of the pole or axis determines the power amplifier and sensor number. A single power amplifier is required for a single coil, whereas additional coils require multiple amplifiers. Because the presented system uses a double coil, the average cost is slightly higher than a single coil but lower than three and four coils.

AMBs have developed and attained resolution for high-speed applications thanks to recent improvements in power electronics and control technologies. The AMBs use electromagnetic force to lift the rotor, eliminating touch and friction. As a result, friction-free component wear is decreased, and maintenance is reduced. Cost reductions, decreased noise, and reduced vibration are some frequent benefits. Recent research has concentrated on the control features of a high-speed AMB application [1,2,3,4] and the building approach for a specific type of bearing [5,6,7]. Because of the strong influence of rotor dynamics, the bearing arrangement has a substantial impact on the AMB structure [8,9].

More than thirty years of research and application have led to active magnetic bearings (AMB). More research is going on for better control of the AMB system. S. L. Chen et al. worked on a three-pole AMB system’s imbalance adjustment. On the basis of immersion and invariance control (I&I) theory, an adaptive compensation strategy is suggested. In a lower-order target system, a higher-order system is to be submerged [10]. S. Wang et al. explained that an active disturbance rejection control approach based on the BP neural network was used to decouple the three-degree-of-freedom six-pole active magnetic bearing (3-DOF 6-pole AMB) with strong couplings, nonlinear, and unstable disturbance (ADRC-BP) [11]. Y. Xu et al. developed and proposed a dynamic modeling approach for the AMB system that takes into account both rotational and translational base motions. According to the derivation, the rotating base motion corresponds to the external torque applied to the rotor, while the translational base motion corresponds to the external force applied to the rotor [12]. A. Heya et al. suggest a triaxial, asymmetric active control magnetic bearing (AMB). This study uses a prototype to show how the suggested AMB was developed. Results from analysis and measurements are used to compare the properties of the radial and thrust suspension forces [13]. In a study by Z. Li et al., an air-floating multi-DOF motor (AMM) is shown, which uses compressed gas to support the rotor. First, an electromagnetic analysis of the AMM using the FEM is used to determine the distribution of the motor’s magnetic field. The flow field is then numerically evaluated in accordance with the gas lubrication theory [14]. Z. Jin et al. proposed a reliable multiobjective optimization approach to achieve good performance for a three-pole AMB. The Kendall correlation coefficient is used to help determine the sensitivity in order to improve the efficiency of the optimization process. Three layers of the parameters are created, and a three-level multiobjective framework is created [15]. The performance variation of the AMB system for various actuator shapes is still in its very early stages. Numerous factors, including the actuator’s shape and material composition, influence this fluctuation. U, E, and I are three of the many varieties of actuators that are available. I-type actuators are better than U-type and E-type in comparison. Three lines of force are included in this E-type actuator; if the proper design is not used, the outcome will be an uneven magnetic field. The attractive force is greater in I-type actuators because the leakage flux is smaller in those than in E-type and U-type actuators. From a control point of view, the researcher implemented classical and advanced controllers to control the levitated position. BP neural network-based control strategy is used to control the six-pole machine [16], flux density feedback control is used for the flywheel energy storage application [17], and metaheuristic optimization techniques are used to control the AMB for high-speed applications [18]. In comparison to these, control strategies proposed two loop-control that is simple and efficient in controlling the desired stable position and is cost-effective.

The actuator, rotor, and controller are designed in this article, and the actuator’s properties are examined [19]. Simulation software is used to simulate the complete model, and the results are obtained. Eventually, a hardware model is built up, and its results are evaluated to compare to those generated by the simulation. Traditional and magnetic-bearing methods are used to determine the rotor’s speed [20,21]. The schematic arrangement of the two-axis AMB system is presented in Figure 1 and demonstrates that it is a two-actuator-based structure. The electromagnetic field is provided by the actuators, which are the coils; the position sensor detects the rotor position and sends feedback to the rotor position controller. The current controller is used to control the input of the coils with the help of an amplifier. The input current for the AMB coil must be precisely regulated to fulfill the demand for attractive power. A single-switched power amplifier controls the coil current to keep the rotor in a stable position. After levitation, the rotor disk is positioned in the middle of a C-type ac magnet. By increasing the ac magnet voltage, the rotor will rotate.

In this manuscript, an I-type electromagnet is employed for an advanced magnetic bearing. Because compared to other structures, the I-type is more advantageous. For example, U-type and E-type actuator leakage flux are more, so the attractive force is less. Here, we are aiming to achieve a highly attractive force even with less voltage.

The rotor levitated position can be maintained by the single and double coil. However, a double-coil AMB has more advantages than a single-coil. The attractive force is more in a single coil, but by using a double coil, more stable levitated conditions can be achieved. In the case of a single coil, if any disturbance happens in the coil, the system will be stopped; in the case of a double coil, if one coil is disconnected, another can maintain a stable position. The double-coil active magnetic bearing system is more stable and reliable.

The objective is to design and fabricate a multi-axis-based AMB system typically used in high-speed applications. While a single-axis AMB system may be useful for some industrial applications, most require multi-axis control, which may necessitate the usage of a multiple-magnet-based AMB system. This section of the paper describes how to control an AMB system that uses two attraction-type magnets mounted on opposing sides of the platform to evenly distribute the system’s weight. Two electromagnets are normally arranged on opposite sides for symmetrical operation and easy balancing. The air gap on each side of the platform will be controlled by each electromagnet.

In this manuscript, a unique two-coil I-type structure has been designed for the proposed AMB system. A sufficient attractive force is achieved to levitate the rotor and also maintain the stable levitated position. A single-switch power amplifier is designed for the system to reduce the cost, and the rotation speed of 19,643 rpm has been achieved at a low input voltage (100 V). This type of proposed system (AMB) is preferred for machine tool applications, such as high-speed blowers, vacuum cleaners, etc.

2. Design and Analysis of Active Magnetic Bearing

2.1. Design of AMB

Figure 2 displays the graphical representation of the AMB system. The actuator and rotor are placed axially in this system with an AC magnet. The rotor is rotated using the ac magnet once it has been levitated. In the following sections, we have described the design of all the components of the AMB system [22,23,24,25,26].

2.1.1. I-Type Electromagnet (Actuator)

This I-type core is made from a highly permeable material with a thin lamination of stainless steel and silicon. In order to reduce the magnetic losses in the magnetic route, thin laminations are integrated. These laminations are often placed one after another to form a synchronized connection; with additional lamination sets, the desired core thickness is achieved [27,28,29,30,31,32,33,34]. Specification of both actuators is identical and is given in

Table 1. Specification of actuators.

Sl. No	Components	Details
1	Material used for actuator core	Cold rolled grain oriented silicon steel
2	Actuator type	I
3	Copper wire gauge size	21 SWG
4	Number of turns	685 Turns
5	Resistance	2.21 Ω
6	Inductance	36.7 mH

.

The core manufactured with CRGOS reduces eddy current by increasing its resistivity. In addition, it increases the flux flow by providing high permeability as cold-rolled stainless steel is used.

2.1.2. Rotor

In this design, a disc shape rotor is placed between the actuators, where the disc material is aluminum, and in the center of the disk, a cylindrical shape iron piece is placed. The role of the iron is to provide levitation due to attraction force, and the rotation is built up by using an aluminum disc.

The description of the rotor design is presented in

Table 2. Specification of rotor.

Sl. No	Components	Details
1	Iron cylinder diameter	2.3 cm
2	Aluminum disc diameter	5.6 cm
3	Rotor weight	59.4 gm

.

2.1.3. AC Magnet

C-type magnet rotates the rotor during levitation. Figure 2 shows the construction of the C-type magnet. The copper winding turns are 700. In one coil, a few additional windings of copper are employed to increase the angle between current and voltage; if one coil is more inductive, it helps to rotate the rotor.

As the name suggests, this magnet is supplied with ac supply to induce an eddy current in the aluminum disk. The magnetic field force and the eddy current in the disk interact with each other, which establishes a driving torque in the rotor disk, and the disk starts to rotate.

Figure 3 illustrates the overall AMB block representation for both coils. Since both coils are identical, data for one coil was identified. The proposed system uses two control loops; the position is controlled by the outer loop, while the current is maintained by the inner loop. Current control is handled by a PI controller, while rotor position is handled by a lead controller. The amplifier modifies the electromagnetic actuator current in accordance with the current controller to keep the rotor in a steady position. The following sections provide a detailed overview of developing controllers and power amplifiers.

Two different controllers are used for the two actuators. Position data is feedback to these position controllers. Here, two attractive forces will be generated from two actuators. Both controllers are designed to keep the rotor in its place. The position sensor is placed in such a way when the rotor position is in the middle of the actuators, it will send the signal to the controller. According to the signal actuator and coil, the current will be maintained.

2.1.4. Current Controller

The current controller receives the signal after comparing the position controller’s and the current sensor’s outputs, and it drives feedback signals according to the parameters of the controller’s tuned values. This controller’s output determines the current in the electromagnet, and the magnetic force is produced based on the intensity of the current value.

The PI controller is employed as the current controller. Control system engineers have historically favored PI controllers because of their simplicity and durability. The inner loops in Figure 3 highlight the primary arrangement of recent feedback control systems and demonstrate how the PI controller is implemented as a block diagram. By analyzing the discrepancy between the measured value and the target set point, the operating theory develops a corrective signal, feeds it back to the input side, and then modifies the process as necessary. The following can be used to express the Gc(s).

$${\mathrm{G}}_{\mathrm{c}}(\mathrm{s})={\mathrm{K}}_{\mathrm{p}}+{\mathrm{K}}_{\mathrm{i}}(\frac{1}{\mathrm{s}})$$

(1)

and

$${\mathrm{G}}_{\mathrm{c}}(\mathrm{s})={\mathrm{K}}_{\mathrm{p}}\left[1+\frac{1}{{\mathrm{T}}_{\mathrm{i}}\mathrm{s}}\right]$$

(2)

In this case,

• ${\mathrm{K}}_{\mathrm{p}} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l} \mathrm{g}\mathrm{a}\mathrm{i}\mathrm{n}$;
• ${\mathrm{K}}_{\mathrm{i}} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{a}\mathrm{l} \mathrm{g}\mathrm{a}\mathrm{i}\mathrm{n}$;
• ${\mathrm{T}}_{\mathrm{i}} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{s} \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}$.

The circuit diagram of the PI controller is represented in Figure 4, and the controller design parameters are calculated below:

Z = 10 mm, L = 36.7 mH, R = 2.21 Ω, ω = 314. ${\mathrm{K}}_{\mathrm{p}}$ and ${\mathrm{K}}_{\mathrm{i}}$ are described as, ${\mathrm{K}}_{\mathrm{p}}=0.7242$, ${\mathrm{K}}_{\mathrm{i}}=$ $194.834$, Let ${\mathrm{R}}_{\mathrm{p}}=1\hspace{0.17em}\mathrm{k}\Omega$.

We may write based on Figure 4.

$${\mathrm{K}}_{\mathrm{p}}=\frac{{\mathrm{R}}_{\mathrm{p}}}{{\mathrm{R}}_{\mathrm{i}\mathrm{n}}}$$

(3)

and

$${\mathrm{K}}_{\mathrm{i}}=\frac{1}{\mathrm{R}\mathrm{C}}$$

(4)

From Equation (3)

$${\mathrm{R}}_{\mathrm{i}\mathrm{n}}=\frac{1\times {10}^3}{0.7242}=1379\hspace{0.17em}\mathrm{k}\Omega$$

(5)

Applying the values of R and C to the expression (4), we obtained

$${\mathrm{R}}_{\mathrm{i}}=\frac{1}{1\times {10}^{-6}\times 194.834}=51.326\hspace{0.17em}\mathrm{k}\Omega$$

(6)

2.1.5. Position Controller

The position controller receives the signal after comparing the position sensor and the reference position signal, and it drives the feedback signal according to the parameters of the controller’s tuned values. The block representation of the controller is illustrated in Figure 3.

A pole (Pc) should be positioned farther down the negative real axis to lessen the effects of high-frequency noise.

The expression for the transfer function is [24,25,26,27],

$$\mathrm{G}(\mathrm{s})=\mathrm{K}\left[\frac{\mathrm{s}+{\mathrm{Z}}_{\mathrm{c}}}{\mathrm{s}+{\mathrm{P}}_{\mathrm{c}}}\right]$$

(7)

Here, Pc is named as the pole, and Zc is named zero, where K is the compensator gain.

Figure 5 shows how to make a lead controller with resistors and capacitors using an operational amplifier. The rating of the design’s passive elements is determined.

For an AMB system, in order to regulate position, a lead controller is designed. The current control loop is observed with the 10 mm air gap set to unity.

We can write it from the position controller loop as

$${\mathrm{Z}}_{\mathrm{c}}=\frac{1}{{\mathrm{R}}_1\mathrm{C}}$$

(8)

$${\mathrm{P}}_{\mathrm{c}}=\left[\frac{{\mathrm{R}}_1+{\mathrm{R}}_2}{{\mathrm{R}}_1{\mathrm{R}}_2\mathrm{C}}\right]$$

(9)

$${\mathrm{Z}}_{\mathrm{c}}=45, {\mathrm{P}}_{\mathrm{c}}=450, \mathrm{C}=1\hspace{0.17em}\mathsf{\mu }\mathrm{F}\hspace{0.17em}\mathrm{a}\mathrm{n}\mathrm{d}\hspace{0.17em}\mathrm{R}=1\hspace{0.17em}\mathrm{k}\Omega$$

The parameters required to design the position controller are calculated below:

Considering the values of ${\mathrm{Z}}_{\mathrm{c}},\mathrm{C},{\mathrm{P}}_{\mathrm{c}}$ in Equations (8) and (9)

$${\mathrm{R}}_1=23.646 \mathrm{k}\Omega$$

(10)

$${\mathrm{R}}_2=2.433 \mathrm{k}\Omega$$

(11)

The plant block is contained in the position controller loop. It is possible to derive the plant transfer function as the coil in Figure 6 produces the following magnetic force:

$$\mathrm{F}(\mathrm{i},\mathrm{z})=-\frac{\mathrm{d}}{\mathrm{d}\mathrm{x}}\left[\frac{1}{2}\mathrm{L}(\mathrm{z})\mathrm{i}{(\mathrm{t})}^2\right]$$

(12)

where $\mathrm{L}(\mathrm{z})$ is the inductance of the coil for a certain air gap z, and the coil current is $\mathrm{i}(\mathrm{t})$.

The attracting force tends to weaken with increasing distance.

The inductance is at its highest when the item is close to the coil and decreases to a constant value when it is moved to $\mathrm{x}=\infty$ [14].

The analysis is challenging due to the nonlinear dynamic equations of the system. In order to specify the linear model, the equations are linearized around a plausible operating point. If the position of the rotor is moved away from the stable point by a certain extent $\Delta \mathrm{i}(\mathrm{t})$$\Delta \mathrm{F}(\mathrm{t})$, the corresponding current and force will modify.

The transfer function is expressed as

$$\frac{\Delta \mathrm{Z}(\mathrm{s})}{\Delta \mathrm{I}(\mathrm{s})}=\frac{\frac{{\mathrm{K}}_{\mathrm{a}}}{\mathrm{m}}}{{\mathrm{s}}^2-\frac{{\mathrm{K}}_{\mathrm{x}}}{\mathrm{m}}}$$

(13)

where ${\mathrm{K}}_{\mathrm{a}}=2\mathrm{C}\left[\frac{{\mathrm{i}}_0}{{\mathrm{z}}_0^2}\right]\hspace{0.17em}\hspace{0.17em}\mathrm{a}\mathrm{n}\mathrm{d}\hspace{0.17em}\hspace{0.17em}{\mathrm{K}}_{\mathrm{x}}=2\mathrm{C}\left[\frac{{\mathrm{i}}_0^2}{{\mathrm{z}}_0^3}\right]\hspace{0.17em}$ are force constants.

$${\mathrm{L}}_0={\mathrm{L}}_{\mathrm{t}}-{\mathrm{L}}_{\mathrm{c}}=0.0358-0.0328=0.003\hspace{0.17em}\mathrm{H},$$

$$\mathrm{C}=1.0255\hspace{0.17em}\times \hspace{0.17em}{10}^5,{\mathrm{K}}_{\mathrm{a}}=0.5\frac{\mathrm{N}}{\mathrm{A}},{\mathrm{K}}_{\mathrm{z}}=122.108\hspace{0.17em}\mathrm{N}/\mathrm{m}$$

So,

$${\mathrm{G}}_{\mathrm{p}}(\mathrm{s})=\frac{7.581}{{\mathrm{s}}^2-1798}$$

(14)

where ${\mathrm{L}}_0$ is the incremental inductance, ${\mathrm{L}}_{\mathrm{t}}$ is the total inductance, and ${\mathrm{L}}_{\mathrm{c}}$ is the coil inductance.

2.1.6. Power Amplifier

Single-switch power amplifier circuit diagram is presented in Figure 7. The chopping procedure is performed with a MOSFET switch (IRF460) and the quick recovery power diode MUR460. A DC capacitor (10 F, 400 V) and a variable resistor (130Ω) are used in the energy dump circuit [35].

The total voltage throughout the coil increases once the input is turned on, along with the current. In every switching operation, the coil’s current is directly proportional to the ON period of the signal pulse. Due to the previous operation, the energy dump capacitor (10 F, 400 V) is partially drained by the rheostat during ON time. During the switch OFF period, the quick recovery power diode provides a route for the coil current to combine the resistor and capacitor. With a negative polarity, the capacitor voltage rises successfully across the coil. When the coil voltage is reversed, the coil current typically decreases with a slope specified by the coil inductance and capacitor voltage.

The transfer function is expressed as

$${\mathrm{G}}_{\mathrm{c}\mathrm{h}}(\mathrm{s})=\left[\frac{{\mathrm{K}}_{\mathrm{c}\mathrm{h}}}{1+{\mathrm{T}}_{\mathrm{c}}}\right]$$

Here, ${\mathrm{T}}_{\mathrm{c}}$ is the amplifier time, and ${\mathrm{K}}_{\mathrm{c}\mathrm{h}}$ represents the chopper gain.

After a short time, the constant is omitted; the power amplifier’s transfer function is reduced to a simple gain.

$${\mathrm{G}}_{\mathrm{c}\mathrm{h}}(\mathrm{s})={\mathrm{K}}_{\mathrm{c}\mathrm{h}}=\frac{{\mathrm{V}}_{\mathrm{d}\mathrm{c}}}{{\mathrm{V}}_{\mathrm{c}\mathrm{m}}}$$

Here, ${\mathrm{V}}_{\mathrm{c}\mathrm{m}}$ represents the control voltage, and ${\mathrm{V}}_{\mathrm{d}\mathrm{c}}$ represents the dc-link voltage.

2.2. Magnetic Analysis of The AMB System

Figure 8 shows the geometry of a double coil I-type 3D model for simulation.

Table 3. Specification of AMB structure.

Sl. No.	Parameters	Specification
1	Actuator thickness	3.5 cm2
2	Actuator length	11 cm
3	The thickness of the coils	0.7 cm2
4	Length of the coils	9 cm
5	Diameter of the rotor	7.5 cm
6	The thickness of the rotor disc	0.7 cm2
7	No of Turns	685
8	The current of the coils	2 A
9	Boundary	12%

shows the fabricated prototype parameters, which represent the model’s size, task type, and boundary condition.

Table 4. ANSYS model material properties.

Quantities	Rotor (Iron)	Actuator (Iron)	Coil (Copper)	Units
Poisson’s ratio	0.46	0.46	0.69
Relative permeability	5500	11,100	0.85
Thermal conductivity	67	67	510	W/mK
Bulk conductivity	10,410,000	10,410,000	59,100,000	S/m
Mass density	7672	7672	8953	Kg/m3

shows the material properties employed in the three-dimensional model [16,36].

The current density must be adjusted to explore the AMB architecture in depth. The actuator and rotor are made of iron, while the winding procedure is carried out with copper.

For this analysis, a 10 mm air gap is maintained between the actuator and rotor. The designed system’s magnetic field strength in three dimensions is shown in Figure 9. Figure 10 represents the designed system’s magnetic flux density, Figure 11 illustrates the system’s current density, and Figure 12 illustrates the developed model’s attractive force. All these figures represent the analysis result for the 10 mm air gap.

From the data observed in

Table 5. Magnetic analysis results for 10 different air gaps.

Air Gap (mm)	Magnetic Field (H)A/m	Magnetic Flux Density (B)T	Current Density (J)A/m2	Surface Force (N/m2)
2	6.3125 × 104	8.5812 × 10−2	9.9986 × 106	4.9754 × 103
4	6.1245 × 104	8.3254 × 10−2	9.9094 × 106	4.6548 × 103
6	5.9852 × 104	8.0021 × 10−2	9.8394 × 106	4.3655 × 103
8	5.8265 × 104	7.7659 × 10−2	9.7624 × 106	3.9654 × 103
10	5.6905 × 104	7.5367 × 10−2	9.6946 × 106	3.6596 × 103
12	5.4321 × 104	7.2965 × 10−2	9.5656 × 106	3.2545 × 103
14	5.2654 × 104	6.9875 × 10−2	9.4152 × 106	2.9100 × 103
16	5.1023 × 104	6.6987 × 10−2	9.2912 × 106	2.5965 × 103
18	4.9905 × 104	6.3845 × 10−2	9.1654 × 106	2.3025 × 103
20	4.7865 × 104	5.9956 × 10−2	9.0136 × 106	2.0231 × 103

, the characteristics graph is drawn and presented in Figure 13.

For 10 different air gaps, this magnetic study is conducted up to 20 mm starting from 2 mm, with a spacing of 2 mm, in order to better understand the performance of the I-type AMB system.

In the diagram, vector graphs for an actuator to stator air gap of 10 mm are demonstrated.

The magnetic analysis results for 10 different air gaps are tabulated in Table 5. This analysis shows that all the properties decrease as the air gap increases.

Ten air gaps were magnetically analyzed, and the results were compared to three different quantities. Variations in attractive force and field strength with the change in air gap are represented in Figure 14. Figure 15 shows the results of variation in attractive force and flux density with the change in the air gap, whereas Figure 16 shows the results of attractive force and current density with the change in the air gap. The changes in these three values are graphically represented as the air gap increases.

From these three figures, it is observed how these magnetic quantities change with the change in air gap from 2 mm to 20 mm.

3. System Simulation for an AMB

Comprehensive simulations of the controllers and the entire active magnetic bearing system are provided in this section. In this AMB system, two controllers are used to regulate the current and position. While the PI controller is responsible for controlling the current, a lead controller is responsible for controlling the direction of the current.

3.1. Current Controller

The overall system is a two-loop structure, and the inner loop is the current control loop. It is very common to use the PI controller as the current controller due to its fast response with minimal steady-state error. This current control loop is shown in Figure 17, and its step response is presented in Figure 18. This response has two parts: the transient response and the steady-state response. From the response plot, rise time, peak time, settling time, overshoot, and steady-state error are determined and tabulated in

Table 6. Different response parameters of current controller and position controller.

Controller	Rise time (s)	Peak Time (s)	Settling Time (s)	Overshoot	Steady State Error
Current controller	0.00206	0.00520	0.0139	10.3	0
Position controller	0.00245	0.00430	0.0120	16%	0.0010

.

Further, to confirm the system stability, frequency response is analyzed by projecting the bode plot in Figure 19, and shows a positive phase and gain margin, which signifies that system is stable.

3.2. Position Controller

The lead controller increased the stability of an active magnetic bearing by shifting the pole to the left half of the s-plane. The controller is simulated in MATLAB, and the output result is provided for the designed lead controller.

A position controller block arrangement for a 10 mm air gap is shown in Figure 20 using MATLAB SIMULINK simulation. Figure 21 displays a position controller’s output, and almost 16% overshoot is obtained. The frequency response of the lead controller is illustrated in Figure 22, which represents the positive phase and gain margin, and signifies that system is stable.

The attractive force gets weakened as the air gap increases. This results in a change in ${\mathrm{K}}_{\mathrm{a}}$ and ${\mathrm{K}}_{\mathrm{x}}$ values. Therefore, the transfer function values of AMB get changed for each value of the air gap. Hence, the lead controller parameters need to be tuned for a stable bearing operation. So, at different air gap values, 6 mm, 8 mm, 10 mm, and 12 mm, the lead controller is designed, and their frequency domain analysis has been observed. The respective bode plot with four air gap values is depicted in Figure 23, and their obtained phase margin and gain margin values are listed in

Table 7. Data of frequency domain analysis at different air gaps.

Sl. No.	Air Gap	Phase Margin (in Degree)	Gain Margin (in Absolute Value)
1	6 mm	48.5	0.0671
2	8 mm	48.6	0.0653
3	10 mm	48.7	0.0650
4	12 mm	48.8	0.0634

.

The bode plot shows that at all air gap values, the lead controller effectively maintains the stability of the closed-loop AMB system. At a 6 mm air gap, the phase margin is 48.50, and as the air gap increases, this phase margin increases.

So, as the air gap changes, the transfer function gets changed, and for the specific transfer function, the controller parameters need to adjust such that it can sustain the vibration and can minimize the error signal. From Table 7, it is observable that the lead controller is efficient in providing stable operation to the closed-loop AMB system.

3.3. Overall Control Circuit

The whole control circuit is constructed in simulation software based on the design data, and the output is presented as a result. Figure 24 shows the simulation output of all the components used in the AMB system. Green color represents the pulse simulation output, red color represents the current controller simulation output, and the triangular wave simulation output is represented by blue color. An RL load is used in this system instead of the actuator coil, and the output across the coil is shown in Figure 25.

4. Hardware Implementation

A digital oscilloscope is used to measure the output as the overall control circuit and power circuit is built in hardware in accordance with the estimated design data.

Figure 26 presents the test output of all the components used in the AMB system. The yellow color represents the hardware output of the current controller, the green color represents the hardware output of the triangular wave, the blue color represents the hardware output across the coil, and the pink color represents the hardware output of the pulse. After comparing the current controller response and triangular wave response pulse, output has been obtained. This pulse output is used to trigger the MOSFET of the power amplifier circuit and control the actuator coil current, which maintains the rotor levitated position.

Now for the validation of the simulation result of the current and position controller response, the hardware response is observed and presented in Figure 27. Position response with 16.2% overshoot and current response of 10.5% overshoot is achieved with almost zero steady-state error. All of the outputs are identical to those of the simulation result, and the comparison is presented in

Table 8. Comparison of simulation and hardware response of current controller and position controller.

Controller	Rise Time (s)		Peak Time (s)		Settling Time(s)		Overshoot		Steady State Error
	Simulation	Real-Time	Simulation	Real-Time	Simulation	Real-Time	Simulation	Real-Time	Simulation	Real-Time
Current controller	0.00206	0.00232	0.00520	0.00423	0.0139	0.0095	10.3%	10.5%	0	0
Position controller	0.00245	0.00253	0.00430	0.0038	0.0120	0.0099	16%	16.2%	0.0010	0.0011

.

The model of an AMB system for rotation and levitation is shown in Figure 28. In this prototype, two actuators (coil) are placed axially, and in between these two coils, one rotor is placed, to sense the position, one inductive-type position sensor is attached, and the rotor is rotated by a C-type ac magnet. While receiving the input, the rotor will hover and establish a 10 mm air gap between the actuator and the rotor. When the input voltage is around 25 V and the current is 2.1 A, the rotor is levitated. After levitation, ac power is supplied to the C-type ac magnet for rotation. The rotational speed of the rotor at 100 volts ac is 19,643 rpm.

The position and current signals seen in an oscilloscope during rotation are demonstrated in Figure 29. At rest, the signals are noise-free, although there is some noise during rotation.

Two different tests are performed for high-speed testing. The rotor is initially attached to a normal ball bearing, and the speed is then determined using a tachometer. Second, the rotor’s speed is measured when the proposed magnetic bearing is used. Data for both conditions are collected for ten different voltages and presented in

Table 9. Rotational speed of rotor (rpm).

Sl. No.	Input Voltage	Rotational Speed (rpm) (Conventional Bearing)	Rotational Speed (rpm) (Magnetic Bearing)
1	10	47	864
2	20	95	1987
3	30	143	2865
4	40	189	4113
5	50	232	5989
6	60	286	8268
7	70	335	10,421
8	80	386	13,573
9	90	441	16,875
10	100	494	19,643

. The performance graph for these two situations is presented in Figure 30.

Such experiments show that even at low voltage, magnetic bearings can rotate at high speed. By comparing the results, it was clear that the suggested magnetic bearing technology had always been appropriate for high-speed applications.

5. Conclusions

For deployment in high-speed industrial applications, a robust and long-lasting I-type AMB architecture has been recommended. From a control perspective, the suggested two-loop method is preferable to the often-described one-loop position control. The adoption of analog circuits also simplifies the controller’s implementation. Compared to a conventional bridge circuit, the power circuit is easier to understand, which has certain benefits as only one switch and one diode are in this power circuit. The system was successfully tested, displaying stable levitation and fast rotation at the necessary gap position. In this research, in comparison to the existing structure, a unique I-type actuator is used to design the AMB system; good performance has been achieved, and a high speed of 19,643 rpm has been observed for low input voltage (100 V). This system can be used for high-speed applications such as vacuum cleaners, blowers, etc.

There are several areas of research that could be explored to improve the scalability of active magnetic bearings; one challenge with active magnetic bearings is achieving high power density, which is essential for many applications. Researchers could explore new materials, designs, and control strategies to increase power density and improve the overall performance of these bearings. Another challenge is reducing the cost of active magnetic bearings, which can be expensive to produce and maintain. Future research could focus on developing more cost-effective materials and manufacturing processes, as well as exploring new applications that could benefit from the use of these bearings.