Magnetically suspended control moment gyro (MSCMG) has been considered as an indispensable inertial actuator for the attitude control of agile maneuver satellites due to its high-precision, long life and large output torque generation [1
]. Single gimbal MSCMG gimbaled in one axis only, consists of a high-speed rotor system and a gimbal servo system, as shown in Figure 1
. The rotor system, which is suspended by magnetic bearing, generally operates at a high constant speed to supply the demanded angular momentum
. The gyro torque is the output to adjust the spacecraft attitude when the direction of the angular momentum is changed by the rotation of the gimbal servo system. The output torque can be expressed as
is the angular speed of the gimbal servo motor. It is obvious that high-precision angular speed-tracking performance of the gimbal servo system must be achieved to ensure the accuracy of the MSCMG output torque.
A permanent magnet synchronous motor (PMSM) is applied in the gimbal servo system for a MSCMG due to its distinct advantages of high power density and efficiency, compactness and ease of control. Generally, in order to achieve high performance, the gimbal servo system is directly driven by a PMSM without gear drive [5
]. The gimbal servo system is an ultra-low-speed mechanical servo system, and the speed range of the research object in this paper is −2 rad/s to 2 rad/s.
The main factors affecting the gimbal servo system performance include friction torque, inherent torque ripples in the PMSM and other external torque disturbances. Various algorithms have been proposed for friction torque compensation [6
]. A model-free control method with an elasto-plastic friction observer is proposed in [7
] and an adaptive friction compensation scheme is proposed in [8
]. However, general friction compensation cannot fully inhibit the friction torque in an MSCMG gimbal system due to the gyroscopic effect [9
]. Methods based on time delay control and internal model control [9
] and methods based on a cascade extended state observer [10
] are presented for the friction compensation of gimbal servo systems in double gimbal control moment gyro (DGCMG). However, the influence of inherent torque ripples and other external torque pulsations, especially the torque ripple caused by high-speed rotor systems, are not investigated.
Regardless of the PMSM, torque pulsations come from various sources, and they can be attributed to cogging torque, flux harmonics and errors in current measurements [11
]. Among these, the former two factors are often the main causes of the poor control precision of PMSMs. Broadly speaking, the techniques for torque ripple suppression can be divided into two categories. The first approach focuses on the optimal design of PMSM [11
] and inhibits torque ripples by means of skewing the stator slots or rotor poles. Nevertheless, there are many occasions in which these methods are not sufficient to eliminate torque ripples. The second group of techniques, which is our interest, emphasizes various control algorithms of stator currents [13
]. These approaches include model predictive control (MPC) [13
], artificial control [15
], iterative control [16
], repetitive control [17
], and so on. A cascade -MPC method [13
], and an MPC and extended state observer based approach [14
] are presented to suppress torque ripple and optimize the control performance of the PMSM servo system. Reference [15
] proposes a self-learning solution based on artificial neural networks to reduce the torque ripple in a permanent-magnet nonsinusoidal synchronous motor. The abovementioned approaches improve the performance of the PMSM from different aspects. However, they all suffer from the disadvantage of complex computation.
Both the torque pulsations that come from cogging torque, flux harmonics and the torque ripple inherited from high-speed rotor systems vary periodically, which make periodic control techniques naturally suited to this situation. Compared with iterative controllers [16
] and repetitive compensations [17
], resonant controllers (RCs) have become one of the most popular periodic disturbance rejection methods due to their advantages of simplicity, relatively simple turning process and easy frequency adaptation [18
]. RCs are widely used in power systems to suppress harmonic disturbances [18
]. In [18
], RCs are used for current control in grid-connected converters. In [21
], the torque ripple is inhibited by multiple RCs in a doubly-fed induction generator-direct current (DFIG-dc) system and positive results have been obtained. However, RCs used in power systems are usually tuned to a single frequency and achieve excellent performance only in a narrow frequency range. This narrow frequency range is unsuitable for a gimbal servo system in MSCMG, whose torque ripple frequencies vary with their operation speed. RCs are also introduced for torque ripple suppression in PMSM control [22
]. In [22
], RC is implemented in the stationary frame, which makes it quite resource consuming, as online trigonometric computation is needed. Reference [23
] optimizes the implementation of RCs by designing the controller in a synchronous reference frame, and this improvement permits the reduction of the number of RCs and the computation burden. In [24
], a technique for the torque ripple minimization of PMSMs using a proportional RC is proposed. However, they all report preliminary simulations and experimental results and do not include any discussion of the tuning process of the controller. Reference [25
] develops a cascade proportional integral RC structure for a low-speed, high-torque PMSM with a current and speed control as the inner and outer loops. This method can only work in a specific steady-state as its resonant frequencies are designed according to the speed reference. Moreover, the parameter tuning of the RCs is complicated in [25
To overcome the drawbacks of the aforementioned RC schemes, a multiple phase-shift resonant controller (MPRC) is proposed to suppress the periodic torque ripples of the gimbal servo system at variable speed. Compared with the previous schemes, the novelty of this paper mainly contains the following three aspects:
Torque ripples caused by high-speed rotor dynamic imbalance in a gimbal servo system for MSCMG are first discussed and modeled.
The absolute closed-loop stability and robustness of the overall system is ensured by the proposed MPRC approach and the phase angle is adjusted for wide and multiple resonant frequency-varying conditions.
The design and tuning processes of the MPRC are discussed and simplified. These are important and practical, especially for a gimbal servo system with multiple frequency RCs both in current and speed control loops.
This paper is organized as follows. In Section 2
, the dynamic modeling and disturbance analysis of a gimbal system are presented. In Section 3
, the MPRC is designed for current and speed controllers to suppress multiple frequency components of torque disturbance simultaneously. Section 4
provides the simulation and experimental results to validate the effectiveness of the proposed scheme. Section 5
provides the conclusion.