PIDNN control for Vernier-gimballing magnetically suspended flywheel under nonlinear change of stiffness and disturbance

Abstract

Vernier-gimballing magnetically suspended flywheel is often used for attitude control and interference suppression of spacecrafts. Due to the special structure of the conical magnetic bearing, the radial component generated by the axial magnetic force and the change of the magnetic air gap will cause the nonlinearity of stiffness and disturbance. That will lead to not only poor stability of the suspension control system but also unsatisfactory tracking accuracy of the rotor position. To solve the nonlinear problem of the system, this article proposes a proportional–integral–derivative neural network control scheme. First, the rotor model considering the nonlinear variation of disturbance and stiffness parameters is established. Then, the weight of neural network is adjusted by the gradient descent method online to ensure the accurate output of magnetic force. Finally, the convergence analysis is carried out based on the Lyapunov stability theory. Compared with the general proportional–integral–derivative control and the radial basis function neural network control, the simulation results demonstrate that the proposed method has the highest tracking accuracy and excellent performance in improving stability. The experimental results prove the correctness of the theoretical analysis and the validity of the proposed method.

Magnetic Bearing: Structure, Model and Control strategy

“…[146] used a RBF neural network controller to solve the nonlinear problem of displacement stiffness caused by the change of clearance of conical rotor with large angle deflection. Subsequent studies used BP neural network control for vernier gimbal maglev flywheels [147], and analyzed the disturbance force characteristics in rotor translation control, as well as the nonlinear changes in current stiffness and displacement stiffness (Fig. 30).…”

Control Strategies for Highly Gyroscopic Outer Rotors with Diametral Enlargement in Active Magnetic Bearings

“…The decay rate of the critical precession motion at maximum rotational speed remains the same. In contrast to the standard DFC, the setup of the control law of the presented new DVFC involves a calculation of the air gap s (see Equation (27)) in order to fulfill the desired identity between k s design and k s (Ω) as well as k i design and k i (Ω). The accuracy of this identity depends on the uncertainties of the initial air gap s 0 , the coefficients a Ω and b Ω from the FE simulation and the measured rotational speed Ω.…”

“…Thus, by inserting Equation (27) into Equation ( 25), the closed-loop stiffness and damping of one magnetic bearing again become speed-dependent, resulting in a speeddependent drift of the eigenfrequencies and decay rates of the rigid-body modes. Figure 10 shows the resulting closed-loop behavior in presence of uncertainties.…”

“…Most literature covering a varying air gap considers the change in the air gap as uncertainty for the controller design [12,26]. In [27], a change in the magnetic air gap occurs due to a special design of the system. Decentralized feedback in combination with a neuronal network is used to control the system.…”