Computer Aided Interactive Multiobjective Satisfaction and its Application to Control System Design

Abstract Recently, in the various kinds of design fields, such as mechanical design, computer aided design systems have been or are being developed actively. One of the main purposes is directed to the drawing techniques with graphic displays after the size of each element has already been determined. On the other hand, in most designs, the size of each element is determined by trial and error. It is considered that in the future, it will become more important to correct the size of each element or parameter systematically and efficiently and to set the adequate values using the man-machine interaction. Based on such ideas, we will consider the case that the mechanical design is formulated as a multiobjective optimal design problem, and various optimization methods can be applied in o-rder to determine the optimal design condition systematically and efficiently. In order to develop the useful method which decreases the load of the designer, "Satisfaction" may be considered instead of "Optimization". In the former, a solution satisfying the permitted limit is searched for. In the actual design problem, the formulation of satisfaction is rather more spontaneous than that of optimization. Besides, in even the opposite case, because the preference and the ability of the decision-making of the designer usually include uncertinety, determining a satisfactory solution from within the bound set of solutions is rather more practical than determining a unique preference solution using optimization. Accordingly, a new satisfaction method is proposed for solving multiobjective satisfactory design problems. It is composed mainly of two ideas; the techniques for judging the existence of the solution satisfying the permitted limit, and the systematical setting and correcting of the value of the permitted limit based on interactive information with a designer. Compared with the other interactive methods in multiobjective optimization, in the proposed method the total amount of calculation and the iteration number of interaction can be decreased. Moreover, the load of a decision maker at each interaction may be decreased. These roles are usually borne by the non-professional designer in the mathematical programming area. This method is applied to a computer aided design of control system. In the model follow control method as one of the control system design techniques, the transfer functions of a control system can be coincided with transfer functions which are given in advance as desired ones using a certain procedure. Computer aided control system design using the model following control method is composed each of the decision process of the desired transfer functions and the decision process of the control system. The latter is composed of the desired transfer functions and the transfer functions of the actual plant are input and, as a result, a .controller is output. However, the decision process of the former has not been so clear until now, and it was necessary to determine the form of the desired transfer functions to satisfy the design specification with correcting its parameter by trial and error. If this process is aided by the proposed satisfaction method, the desired transfer functions can be determined systematically and efficiently. The decision process problem of the desired transfer functions is formulated by the following factors. As for the performance of the control system, the relative stability, the speed of response and the accuracy should be sythesized and assessed. The overshoot and setting time in the step response characteristic are taken as the factors for the relative stability; the rise time, delay time and band width in the frequency response characteristic for the speed of response; and the velocity constant for the accuracy, where the band width includes the meaning to decrease the influence of the noise. The proposed interactive method is applied to the actual systems in order to confirm its efficiency. The first example is a 60 000 ton tanker 219 m in the length, 32.2 m in width, and 6 m in the mean draught. The problem is formulated, the desired transfer functions are determined and the control system is constructed. The next example is the control system design for the refrigerating machine. This is a three input-three output system with interactions between variables, but for convenience sake this overall system is considered as three independent one input-one output subsystems. For the actual testing plant of a refrigerating machine, the problem is formulated and the desired transfer functions are decided using the proposed method.