This paper discusses the design of a type-1 deadbeat servo system for a single-input, single-output discrete-time linear time-invariant system when the settling time is larger than the order of the controlled system. The type-1 deadbeat servo system is transformed into the deviation system. First, a theorem which relates the general deadbeat input is obtained. By using this theorem, the fixed terminal state problem is transformed into the free new terminal state problem. Then, the problem of minimizing the deviation input energy for the specified settling time is formulated, and the optimal deviation input is obtained implicitly by using the special Riccati equation. Finally, the optimal deviation input is obtained explicitly. This optimal feedback gain is independent of the initial state of the controlled system, the step command signal and the step disturbance.
Statistical methods are appropriate for the prediction around a median, but not around a quarter or three quarters. On the prediction of environmental phenomena, it is important to predict correctly at high concentrations and to reasonably explain the predictive formula. In this paper, we propose a method to predict phenomena composed of many complicated factors by modeling the process of human thinking and judgement. Input-output relations of the system are described in the form of if-then rules. Then using fuzzy reasoning, the behaviors of the system will be predicted. To improve the model, we adjust the parameters of the membership function, by the use of the non-linear optimization technique. We apply fuzzy modeling to the prediction of oxidant concentrations at Osaka area in Japan and show that it is appropriate for the prediction of phenomena with limited input-output data.
This paper gives a new method for computing a doubly coprime factorization of a transfer function matrix. From a polynomial matrix factorization, the method easily derives proper stable rational matrices which give a doubly coprime factorization. This paper also clarifies a relationship between this method and the well-known method which uses state-space representation.
Necessary and sufficient conditions are derived for real rational functions with interval coefficients to be positive real or strictly positive real. In both cases, it is shown that checking positive realness or strict positive realness of only a finite number, sixteen, of functions are required to assure the same properties for the whole family. The main tools for these results are celebrated Kharitonov's theorem and its extended version, which have been paid attention to in these couple of years in association with robust stability problems. Inspections are also made into an interrelationship between the results obtained and the (extended) Kharitonov's theorems. Though a definite answer to the relationship has not yet been established, the problem, if resolved, would shed light on implications of the Kharitonov-type theorems in concrete physical systems, i.e., electrical network systems.