## 1 Introduction  
The concept of more electric aircraft was proposed for the replacement of centralized hydraulic power systems with distributed power-by-wire systems because of the promising benefits of higher reliability, increased dynamic performance, convenient maintainability, weight reduction and easier manufacture. The core component of the distributed power-by-wire system using electric power directly has yielded three types of approach, including the electrohydraulic actuator (EHA), the electromechanical actuator (EMA) and the integrated actuation package (IAP) [1,2]. We propose the idea of a linear-driven electrical hydraulic actuator (LEHA) which is required to be of high frequency and large output force. The linear pump is driven by a linear oscillating motor (LOM), as shown in Figure 1, so it is of great importance to have detailed research on the LOM, especially on the dynamic performance of the LOM with external force loads. The linear motor, providing reciprocating motion without any other ancillary components, was proposed in America more than a century ago. At the beginning of the exploration of the linear motor, [PERSON] in Germany proposed a kind of magnetically levitated vehicle propelled by linear motor. After that, LOMs related to the maglev became hot spots until the end of 1990s when the low loss short-stroke LOM became increasingly popular. Actually, linear motors have vital and typical applications on machine tool slid tables, recorders and free piston engines. Since 1999, LOMs especially LOMs have been vitally and extensively applied to air compressors, pumps, electromagnetic valves, active shock absorbers, vibrators and earphones [3; 4; 5; 6; 7]. The application of LOMs to the LEHA, a kind of hydraulic pump controlled actuator, leads to consequence of good reliability, high power density and convenient maintenance, which requires excellent dynamic displacement output with external load force and large force output. So it is promising to study LOM dynamic performance as well as efficiency in order to apply the LOM better to the LEHA. Until now, most research has concentrated on force output, motor design and optimization, and control strategy of LOMs. [PERSON] explored the permanent magnetic array, the thrust force capability, the optimal design parameters, etc. to improve the static output force and reduce the cogging force [8; 9; 10; 11; 12]. As for the force control, some internal forces of the LOM such as cogging force, detent force, ripple force and force of friction have been taken consideration into the trajectory track of LOMs. [PERSON] took the cogging force into compensation control to improve the industrial gantry position control accuracy, but no external load is considered except for the friction force [13]. A detent force compensation control was conducted by [PERSON] without any external force involved [14]. [PERSON] had a proposal of a field-programmable gate array (FPGA)-based computed force system to improve the position control performance of the linear ultrasonic motor for various reference trajectories with no load force acting on the LOM [15]. [PERSON] applied the Jacobian linearization observer to the ripple force compensation control to improve the position trajectory accuracy [16]. All these research works above focused on the LOM itself, not taking multiple external force loads such as spring force, rectangular force and damping force into consideration to study the dynamic performance of the LOM. Therefore, it is meaningful and offers promising prospects to have research on the effects of multiple external force loads on the trajectory track of the LOM and it is necessary to develop a linear oscillating load system (LOLS) for the LOM. As for force loads forms, there are four types including magnetic powder brake, compressed air, weight and voice coil motor (VCM). The magnetic powder brake, a kind of traditional and mature instrument for a rotary motor, is unsuitable for the LOM load simulation because of its ability to impose rotary damping force on the shaft.