오일쿨러의 상태공간모델에 기반한 Robust LQG 제어

Abstract

Recently, high speed and high precision are required in machine tools to promote efficiency of them. However, the high speed causes unintended deterioration of accuracy due to harmful thermal displacement. Therefore, the machine tools need a variable speed oil cooler system to eliminate noxious thermal load immediately and to save energy. The variable speed oil cooler system is basically multi-variable control system that controls oil outlet temperature and superheat simultaneously. Many control manners for the variable speed oil cooler system have been suggested during a recent decade. Actually, artificial intelligence techniques such as a fuzzy logic control are desirable methods for nonlinear system like the oil cooler system to obtain favorable control performance and robustness. However, they don't give any useful systematic information to analyze dynamics of the controlled system. A PID controller is the most preferred type among suggested controllers for variable speed refrigeration system because of simple design and fairly good control performance. However, It requires an exact transfer function model between input variables and output variables. Besides, obtaining an accurate transfer function model is very difficult because it is mainly built by the perturbation method in a thermal equilibrium state of the refrigeration system. Moreover, the PID logic does not assure optimum control performance because of strong inherent nonlinearity of the system and noises even though we got the transfer function model. Furthermore, the PID controller can hardly solve the interference problem between controlled variables, oil outlet temperature and superheat. Hence, the PID technique is not the best policy for the oil cooler control system which has some process and measurement noises. Thus, the robust linear quadratic Gaussian (LQG) controller design is desirable for the oil cooler system to establish high-efficiency control performance and strong robustness. In this paper, the LQG controller design method based on a state space model is presented to improve control performance of a refrigeration cycle under process noise and measurement noise. First, a state-space model of the oil cooler is derived as a 4th system equation by several governed equations and some assumptions based on a moving boundary model. Next, the LQG controller is designed by the linear quadratic regulator (LQR) gain and the Kalman gain to minimize an evaluation function and influence of noises individually. Two gains can be independently determined by each the Riccati equation using the separation theorem. If weighting matrices of the evaluation function are set to satisfy desired control performance and input energy condition, the LQR gain are determined conclusively by a designer. Finally, The validity of the proposed design method is proven by some computer simulations and real experiments. Some experimental results of the proposed design method and PI controller were compared to reveal feasibility of the proposed method.