Typical temperature control methods of a cooler for machine tools are hot-gas bypass and compressor variable speed control. The hot-gas bypass system has been widely used to control the cooler temperature in many general industrial fields. On the contrary, the compressor variable speed control is focused on special fields such as aerospace and high precision machine tools which need high precision control. The variable speed control system usually has two control variables such as target

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... ture and superheat. In other words, the variable speed control system is basically multi-input multi-output(MIMO) system. In spite of MIMO system, the proportional integral derivative(PID) feedback control methodology that based on single-input single-output (SISO) system is generally used for designing the variable speed control system. Therefore, it is inevitable to describe transfer functions for dynamic behaviors of every controlled variables and decide the PID gains with tremendous iteration process. Moreover, the designed PID gains do not provide optimum system performances. To solve these problems, high performance controller design method based on a state space model is suggested in this paper. An optimum controller is designed to minimize both control errors and energy inputs. This method was more simple to describe dynamic behaviors and easier to design the cooler controller which is MIMO system.