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1. Field of the Invention The present invention relates generally to a scanning system driving device used in an image forming apparatus, having a scanning system for illuminating and scanning a document, such as a copying machine or an image scanner, and more particularly, to an improvement in transmission control of a driving force of the scanning system driving device. As a scanning system provided for a copying machine or the like, there are two types of scanning systems: a scanning system in which an optical system is moved relative to a still document, and a scanning system in which a document platen is moved relative to a still optical system. In this specification, the term "scanning system" is used as a general term for the above described two types of scanning systems. Consequently, a scanning system driving device includes both a device for moving and controlling an optical system and a device for moving and controlling a document platen. 2. Description of the Prior Art An image forming apparatus such as a copying machine includes a scanning system for optically scanning a document by driving an optical system or a document platen. For example, in a copying machine comprising a scanning system in which an optical system is driven, a moving body holding a light source and a reflecting mirror is displaced at uniform speed relative to a document. Consequently, the surface of the document is illuminated and scanned. In the process, a photoreceptor is exposed by light reflected from the document, and an electrostatic latent image is formed on the surface of the photoreceptor. This electrostatic latent image is developed into a toner image, and the toner image is transferred and fixed to copy paper, to achieve copying. In such an image forming apparatus such as a copying machine, there are strong demands toward improvements in the image quality, along with miniaturization and higher speed. Therefore, improvements have been made for shortening the rise time elapsed before the scanning speed of the document by the scanning system reaches a predetermined speed, as well as preventing the nonuniformity of speed from occurring during the scanning of the document. The electrostatic latent image formed on the surface of the photoreceptor is formed by the light reflected from the document illuminated and scanned. In order to increase the copying speed, therefore, it is essential that the scanning system be moved at high speed. Furthermore, in order to accurately reproduce a document image, it is necessary to keep the scanning speed constant. On the other hand, if the copying machine is miniaturized, the moving distance of the scanning system from the home position to the position where illumination and scanning are started is short. Therefore, it is necessary to rapidly increase the moving speed of the scanning system. If the moving speed of the scanning system is thus rapidly increased so-called overshoot is produced. That is, the speed of the scanning system once exceeds the rated speed immediately before the speed of