In order to facilitate the cnc machining, the modeling problems encountered by the students in the learning process are generally carried out based on a given physical model, and rarely start directly from the actual controlled object. Another problem often encountered in the mathematical model modeling of ordinary machine tool control systems is linearization. Strictly speaking, actual physical systems are all linear systems, but the degree of nonlinearity is different. However, many systems can be approximated as linear systems under certain conditions. Linear systems have secondary and superimposability, which can greatly simplify the design and analysis of the system.

Ordinary machine tool refers to a cnc machining china center with a vertical spindle. Its structure is mostly a fixed column. The worktable is rectangular and has no indexing and rotation function. It is suitable for processing disk, sleeve, and plate parts. It generally has three linear motion coordinate axes. , And a rotary table rotating along the horizontal axis can be installed on the worktable to process spiral parts. Ordinary machine tools are easy to install, easy to operate, easy to observe the processing conditions, easy to debug the program, and widely used. However, due to the limitation of the height of the column and the tool changer, parts that are too high cannot be machined. When machining the cavity or concave profile, the chips are not easy to discharge. In severe cases, the tool will be damaged and the machined surface will be damaged, which will affect the smooth processing. .

The mathematical model of the ordinary cnc machine tool control system is usually not an easy task to establish an appropriate mathematical description for the actual control system. In addition to choosing a suitable modeling method, it is also necessary to deal with problems such as model simplification. In order to accurately describe the mathematical relationship between the controlled quantity and the controlled quantity, various influencing factors and situations are generally involved, which often results in the relationship becoming very complicated. The more accurate the relationship between the controlled quantity and the controlled quantity is, the more complex the mathematical model is. An overly complex model is neither convenient for research nor conducive to the realization of the control system. In order to avoid this situation, it is generally necessary to make some reasonable assumptions and simplifications in order to properly idealize the system. An idealized physical system is usually called a physical model.