# Accelerated Iterative Learning Control of Speed Ripple Suppression for a Seeker Servo Motor
## 1 Introduction  
The permanent magnet synchronous motor has the advantages of high efficiency, high power density, and a high torque inertia ratio [1] and has been widely applied to the fields of aerospace, robotics, and transportation [2; 3; 4; 5]. In recent years, as the requirements for system performance and accuracy have increased, how to suppress the speed ripple of the permanent magnet synchronous motor has become an active research area. In particular, in the direct drive system, because there is no transmission link involving gears, the rotation speed of the motor is relatively low, and the problems of low-frequency noise and vibration caused by the speed ripple are more severe. The torque ripple is the main source of the speed ripple. Based on extensive study, researchers worldwide have proposed multiple methods to suppress the torque ripple of the permanent magnet synchronous motor, which are mainly divided into two classes: Improving the main body design of the motor and optimizing the design of the software control algorithm. The methods to improve the main body of the motor involve the stator slot [6], fractional slot [7], and toothless stator structure [8]. These methods can attenuate the speed ripple to some extent, but the design challenges are numerous, and the design cost is high. Regarding the aspect of software control, a previous study [9] adopted an adaptive filter to filter the feedback current and improve the performance of the current loop. Based on a PI controller, [PERSON] et al. [10] superimposed an oscillating controller and used the torque current, generated by this controller, to counteract the load torque ripple. [PERSON] et al. [11] adopted a speed-loop control strategy using a PI regulator and a repetitive controller in parallel. Without affecting the dynamic performance, this configuration improved the steady-statecharacteristics of the system and suppressed the periodic speed ripple, but no strict mathematical proof was given to ensure convergence. Another study [12] proposed a method based on the optimization of the voltage vector that improved the model predictive control and adopted duty cycle control, thus reducing the torque ripple, but the parameter selection of the cost function was found to be relatively challenging. Iterative learning control [13; 14; 15] is a type of model-less control with a simple structure that does not need specific model parameters. Over a limited interval, only through a sufficient number of repeated iterations can the behavior of the execution object satisfy the expected requirements. Iterative learning control has important significance for situations with nonlinearity, strong coupling, challenging modeling, and the requirement of high-accuracy trajectory control [16]. The existing studies on the theory of iterative learning control concentrate mainly on proofs of convergence for the learning algorithm, the learning velocity, studies of the structural form for the learning law, the robustness of, and analysis method, for the iterative learning process, the initial values, and assorted engineering applications [17; 18; 19; 20; 21; 22; 23]. There have been few studies on iterative learning control of the servo system for the permanent magnet synchronous motor. [PERSON] et al. [24] proposed to adopt the method of cascade iterative learning control to revise the reference input signal and improve the system accuracy by iteratively correcting the reference input. Another study [25] combined sliding mode control and iterative learning and proposed a robust iterative learning control strategy using a performance weighting function to improve the system robustness. In this paper, to address the speed ripple of a permanent magnet synchronous motor, we propose an accelerated iterative learning control. The characteristics of the proposed method are as follows: For the learning interval of this control, as the number of iterations increases, the actual interval that needs correction constantly shortens, which accelerates the convergence speed.