Application of symmetry groups to control a packed bed reactor

A non-isothermal packed bed reactor, defined by a set of coupled partial differential equations, is used to illustrate the method of symmetry groups to control a general nonlinear distributed parameter system. The control objective is to maintain a desired temperature on the catalyst in the reactor by manipulating the input heat. The heat of reaction acts as a disturbance. First, the explicit form of the infinitesimal generator for the symmetry groups is derived from the given set of equations. Then, the boundary and initial conditions are used to find conditions for existence of symmetry groups. An input equation is obtained by imposing invariance conditions on the control objective. Simulations demonstrate the effectiveness of the method.