リーマン幾何学手法による操作量飽和のある双線形熱交換システムの制御

抄録

In the temperature control of lumped parameter heat exchangers, it is well known that the system behaves as a bilinear system when the flow rates are manipulated. This paper presents a design method of the controller for the bilinear plant by an approach using Riemainnian geometry. When the suitable curvilinear axes are selected as the state space axes instead of the orthogonal straight ones, the integral manifold of the bilinear system may also be regarded as that of an imaginary linear system. Through the construction of a linear optimal regulator for this linear system, a controller for the bilinear plants can be designed. A partial differential equation which determines the homeomorphism between two integral manifolds of the bilinear system and the linear system is derived. And a convenient calculation method of this partial defferential equation is presented.
This paper also finds a solution for the saturation problem in the manipulated variables by imbedding the saturation characteristics in the connection coefficients of the Riemannian geometric model.
Finally, it is confirmed that the proposed design method is realizable and effective by experiments of a 2-step lumped parameter heat exchanger system.