## 1 Introduction  
Biaxial gantry systems are often found in industrial settings because of their high-speed and high-precision planar motions. Applications include CNC machines, automotive assembly lines, material handling, surface chip mounters, and positioning stages. To provide accurate Cartesian movement information to a multiple-axis configuration, the control stage must be managed in a synchronous manner, especially when carrying heavy loads. Conventional control methods use independent axis control, regardless of the other axes. Synchronous errors cannot be reduced effectively through independent axis control, and this leads to decreased precision in use. Design of a servo control system with synchronous motion techniques [1; 2; 3; 4] is critical for high-precision gantry systems, especially where heavy loads could lead to process safety issues or damage to equipment. Parallel synchronous control schemes are often driven by two linear motors. Without any mechanical transmission, such as lead screws or gears, the payload can be directly driven. The design in this paper uses a permanent magnet linear synchronous motor (PMLSM) [5] for its compact structure, rapid response, and high force density. Several other approaches to the multi-axis de-synchronization problem have been proposed, such as a master-slave motion control arrangement and cross-coupled controls. In [6], the authors applied a nonlinear feedback control scheme to control the PMLSM position, and overcome inherent nonlinear functions and parametric uncertainties. In [7], a synchronous control was developed on a platform with only one axis, which is actuated by servo motors and dual parallel ball screws. In addition, an identification method was proposed to build a coupled system model. The cross-coupled synchronous control method [8; 9] reduced the contouring error in the gantry system. An optimized cross-coupled synchronizing control [8] was proposed to improve synchronization accuracy in dual-feed drives. The performance index includes the synchronous error, which is to be minimized. A cross-coupled synchronous control system was also combined with a complementary sliding mode control [9], to simultaneously converge position tracking and synchronous errors for the gantry position stages with uncertainties. In this study, the authors designed a PID control scheme for an X-Y-type gantry. Since a conventional PID control cannot overcome problems associated with speed changes, load disturbances, and steady-state errors, a fractional-order fuzzy PID (FOFPID) is incorporated for more flexible parameter tuning than that of integer order. In recent years, fractional order differentiation and integration have become more commonly used in control design [10; 11; 12; 13]. Since the calculus orders are not necessarily to be integers, the dynamic models can be described more adequately. Also, a controller with fractional orders is often more suitable than one using integer orders. A parameter tuning approach for fractional order PD controllers was proposed [14] for a class of second-order systems. This method can increase the robustness by fulfilling the given gain phase margin and crossover frequency. A temperature control with a digital fractional order controller has been demonstrated [15]. Furthermore, the practical application and improvement of PID controllers using fractional order have also been shown [16; 17; 18]. Another fractional-order fuzzy PID controller design [19] considered tuning the orders in the fuzzy controller, and then used a genetic algorithm to optimize the controller by minimizing error indices. Although fractional order differ-integrations make the controller adapt to the plant more adequately, tuning the parameters becomes difficult.