Invention | Free Full Text | Fractional-Order Active Disturbance Immunity Control for Conical Active Magnetic Bearing Supported Pumps with Shielded Motors

1. Introduction

Active Magnetic Bearings (AMBs) have grown in popularity in recent decades.They are essential for suspending shafts that rotate at high speeds without mechanical contact or lubrication [1,2,3]. AMBs are currently used worldwide in a variety of industrial, space and laboratory applications such as turbo compressors, vacuum pumps and flywheel energy storage systems [4,5]. The widespread adoption of this technology is mainly due to its numerous advantages over traditional bearing technology [6]. Pumps are often manufactured in industries where the pump and motor are kept separate and the fluids they handle may leak from the pump casing and cause electrical isolation problems. To alleviate some of the problems of conventional pumps, canned motor pumps use an integrated pump and motor structure while sealing the liquid inside.The pump utilizes AMB to eliminate the need for mechanical bearings and shaft seals, which in some processes have low life expectancy [7]The elimination of seals, bearings and lubrication is especially desirable for pumps pumping harsh chemicals in extreme environments or where pumped fluids need to maintain high purity. Allaire at [8]. A number of similar projects with greater power were reported in subsequent years [9,10].
Current trends in active bearings focus on the development of various geometric bearing designs to save axial space for mounting additional mechanical components such as gearboxes. One potential development path is to use conical active magnetic bearings (CAMB). The structure of the CAMB allows the simultaneous application of force in both axial and radial directions, saving a pair of electromagnets and thus reducing size.However, CAMB designs are more complex than standard cylindrical solutions, especially in the control design phase [11,12]. Furthermore, the geometry of the CAMB allows higher rotational speeds in cylindrical solutions limited by the strain growth in the axial bearing disc.Nonetheless, CAMB emphasizes two coupling properties: galvanic coupling and geometric coupling effects [13], making the dynamic modeling and control of these frameworks particularly cumbersome. Furthermore, the nonlinear nature of the dynamics, the small natural damping in the process, the stringent positioning specifications often required by the application, and the unstable open-loop system dynamics make the controller design of CAMB systems a challenging task. In most cases, a proportional-integral-derivative (PID) controller is chosen because of its simplicity and intuitiveness in tuning the controller parameters. However, sometimes conventional PID controllers fail to meet industry performance standards for CAMB systems. Several control methods of CAMB have been proposed by many previous researchers.Lee and Zheng [12] Using optimal control based on a linearized dynamic model that includes the link between input voltage and output current in conical magnetic coils, but omits geometric coupling effects.Conical magnetic bearings described by Mohamed and Emad [11] Simulate the controlled system in terms of state variables and use the Q parametric design controller.exist [14], Huang developed TS fuzzy modeling and control for a general-purpose six-DOF conical magnetic bearing. Then a stable fuzzy control is synthesized for high-speed, high-accuracy CAMB control using parallel distributed compensation.Based on the estimation of external disturbances, offset-free model predictive control (OF-MPC) is used [15] Effectively handles coil current saturation. Because OF-MPC handles the coupling of rotational and axial control actions and the effects of low axial forces, it is well suited for CAMB systems. Although these control methods have good control performance, they still haven’t fully considered the nonlinear characteristics.
In this paper, a coupled dynamics model of a canned rotor pump combining hydrodynamics, rotordynamics, and electromagnetic bearing dynamics is developed (see Figure 1). A new control strategy based on fractional-order active disturbance rejection control (ADRC) is proposed to stabilize the model. The principle of ADRC is to treat the compensation of unpredictable disturbances and model uncertainties as lumped disturbances and actively reject [16,17]Although ADRC does not require an accurate model of the plant, it has strong robustness and dynamic characteristics, and is an effective and practical algorithm. However, the application of ADRC in the industrial field has been limited due to the complexity of its structure and the difficulty of parameter tuning, until the linear ADRC (LADRC) was proposed. [18]. In recent years there has been increasing interest in improving the results of LADRC regulators by applying concepts from fractional calculus [19,20], has been generalized to fractional active disturbance rejection control.Integer order controllers are used in different applications such as roll-to-roll [21,22]car [23,24]motor [25,26]robot [27,28], etc. Since fractional calculus was created, it has been widely used in different fields of science.Fractional-order controllers have the potential to provide higher, more robust control performance than integer-order controllers, researchers find [29], which makes them particularly important and fascinating in the field of control engineering.Many fractional-order controllers have been proposed, including fractional-order sliding mode controllers [30,31]Fractional order PID controller [32,33]Fractional order intelligent PID controller [34], etc. The FOADRC controller was first proposed for linear fractional order systems (FOS) with linear response [35], which combines a fractional-order proportional-derivative (FOPD) controller and a fractional-order extended state observer to improve control performance. However, according to the strict conditions of the proposed FOADRC, the order of FOPD and FOESO must correspond to the order of FOS.exist [36], the author used the ESO-based FOPD controller to control the single-flexible-link manipulator, but did not give the parameter tuning rules.A strategy combining FOESO and a simple proportional controller is proposed [37] Using tuning methods based on frequency-domain specifications, this is difficult for industrial applications with accurate mathematical descriptions that are often not available.This structure applies to [38,39] For systems that respond relatively slowly and are not suitable for models that require fast response, such as AMB.
To solve these problems, this paper proposes a FOESO-based FOADRC combined with PD controller for integer-order systems to enhance the transient response of the closed-loop system [40] And a simple parameter tuning method is recommended, which is crucial for industrial applications. The main contributions of this paper are as follows: (1) The integration of tapered active magnetic bearings into shielded motor pumps is proposed, and some dynamic vibration structures that are usually neglected in other related works are analyzed; (2) All coupled and The nonlinear time-varying dynamics are estimated as the total disturbance, and the PD controller achieves optimal tracking performance. The simulation results demonstrate the control performance advantage of the designed FOADRC compared to traditional ADRC and PID controllers.
The remainder of this paper is organized as follows. Section 2 presents the mathematical model of the tapered active magnetic bearing pump with shielded motor system; the structure, system stability analysis and parameter adjustment of FOADRC are introduced in Section 3; the simulation verification is in Section 4; Section 5 Some concluding observations are given.

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