Efficiency analysis of the second-order identifier application in closed loop time-optimal control systems for distributed parameter objects with incomplete information about the plant characteristics

This paper devoted to one of the most complicated current problem of the modern control theory which is the problem of searching such an optimal control that operates under conditions of incomplete information about the plant characteristics. The statement of a time-optimal control problem is given. The solution of synthesis of optimal control closed-loop system of the induction heating process of cylindrical billets before forging was found. It was found under representative conditions of interval uncertainty of the initial temperature and heat losses values that were considered as the uncertain parameters of the process. An obtained time-optimal control algorithm with feedback was completed initially with a first-order identifier. It is given as a linear function where the uncertain parameters and the feedback coefficients are depends upon the values of measured temperatures at selected points on the billet. The necessity of a second-order identifier were proposed and analyzed. As one of the results of analysis procedure a non-linear correlation between the feedback coefficients and the convection surface heat transfer coefficient was found. The structure of the time-optimal control system for the obtained control algorithm with feedback and the second order identifier was proposed. After the procedure of modeling the obtained closed-loop control systems with first-order identifier and second-order identifier the results have been compared and it was shown that the control system with the identifier of second order provides a much more accurate temperature distribution at the end of time-optimal process that is closer to a deterministic one with complete information about the process parameters.