Application of feedback control principles for solving differential- algebraic systems of equations in process control education

Simulation of control systems often involves the solution of systems of ordinary differential and implicit algebraic equations (DAE's). The software packages which are most widely used in process control education (MATLAB, POLYMATH, MATHEMATICA, for example) cannot solve DAE's directly, and often dedicated programs, must be used for this purpose. The controlled integration method presented in this paper is based on the use of feedback controllers to adjust the value of variables, so that the residual of the implicit algebraic equations arc kept very close to zero during integration. Any standard integration algorithm can be used to solve the mixed system of equations. The same principles and techniques that are used for design and tuning of process controllers are used for the design and tuning of the "controllers" associated with the controlled integration. The use of the proposed method is demonstrated in a realistic problem of simulation and control of an exothermic batch reactor.