## 1 Introduction  
Pedestals play a substantial role in satellite tracking, as they are important modules in satellite tracking stations. The antenna in the pedestal is, ideally, in constant, uninterrupted orientation with the signal source. Because either the target, the platform, or both are in constant motion, the pedestal may be adjusted by the associated motors so as to ensure that the payload has continuous and uninterrupted tracking of the source [1]. The best quality of data reception is obtained when the telemetry signal is stronger, i.e., where the satellite is closest to the ground station [2]. The most common and well-known type of pedestal is the Elevation over Azimuth (EI/Az). The main disadvantage of the EI/Az pedestals is their inability to track the target near their zenith position. When the satellite is directly overhead, the EI/Az system will stop tracking at zenith, because at this point the azimuth angle after zenith is 180 degrees different from the azimuth angle immediately prior to zenith. To continue tracking, the azimuth motor must turn the payload nearly 180 degrees within a brief period of time while the satellite crosses the zenith position. However, even the fastest motors are unable to turn the payload 180 degrees in non-zero time [1,2]. In the late of 1990s, another type of pedestal known as the X-Y pedestal (which has been referred to by a variety of terms, including: X over Y; cross elevation over elevation; traverse over elevation; cross level over elevation; dual elevation; two-axis zenith search) was designed and manufactured so as to receive satellite data in fixed and mobile earth stations. An X-Ypedestal system has the ability to rotate about the X and Y axes, which are substantially orthogonal to each other but not necessarily coplanar [1]. In comparison to common El/Az structures, the design and implementation of X-Y pedestals is more complex due to their different mechanical and control features. However, X-Y pedestals are considered to be a very suitable option for the design and construction of small and medium sized pedestals [3; 4], due to the possibility of applying cheaper equipment, obtaining greater reliability, requiring less maintenance, and the feasibility of achieving high accuracy. In this line, X-Y Pedestals are considered as a suitable solution for Low Earth Orbit (LEO) satellite tracking, especially in the tracking of the target near their zenith position where the well-known El/Az pedestals cannot track the target. Despite all of the benefits of X-Y pedestals, control of them remains a challenging task. Some of the advantages and applications of X-Y mounts have been described in [5; 6; 7]. The PID controllers [8; 9; 10; 11] were the first choice for X-Y pedestal control in satellite tracking, as was the case for many industrial applications. The nonlinear and multivariable nature of the X-Y pedestal and the variations of the operating point (caused by the changes in the pedestal center of gravity) result in weak performance of these controllers. Hence, the application of more complex controllers became necessary [12; 13; 14]. Model predictive controllers [15; 16; 17] are particularly appropriate for LEO satellite tracking due to the specified orbit of the LEO satellites, which can be realized by solving the satellite motion equations or through satellite motion simulation software. Predictive Functional Control (PFC) [18] is one of the model predictive controllers, and is characterized by two distinctive features: the control signal is structured as a linear combination of predetermined basis functions and the concept of coincidence points helps to evaluate the cost function on the prediction horizon. PFC is convenient for fast processes and nonlinear systems [15; 18]. Many applications of PFC have been reported in recent years in industrial processes [19; 20; 21; 22].