Abstract
The purpose of this paper is to present the details of design procedure of a nonlinear regulator by Riemannian geometric approach and to apply it to the case of a double-effect evaporator. A nonlinear geometric model is proposed on a direct product space of a state vector and a control vector as well as in the previous papers by the authors. The geometric model is derived by replacing the orthogonal straight coordinate axes of a linear system with the curvilinear coordinate axes. The integral manifold of the geometric model becomes homeomorphic to that of a fictitious linear system. For the geometric model a nonlinear regulator with a performance index is designed renewedly by the procedure of optimization. The construction method of the curvilinear coordinate axes on which the nonlinear system behaves as a linear system is discussed. To apply the above regulator theory to double-effect evaporators especially to the pilot plant at the University of Alberta, a suitable nonlinear model is determined by the plant dynamics. The optimal control law is derived through the calculation of the homeomorphism. As a result it is confirmed that the regulator is effective and superior to that of the conventional control.
