| Chemical processes present special control problems and offer special opportunities due to their inherent nonlinearity. The use of a linear controller often limits the range of operation to restricted feed-stocks (e.g. fluid catalytic cracking) and limits the speed of recovery from process disturbances. Nonlinear controllers that invert the process model require the computation of Lie derivatives, defined as the inner product of a real valued function and a vector field. These derivatives can be computed analytically and symbolically only for relatively simple nonlinear systems. This work simplifies the design and software maintenance of nonlinear controllers for complex highly nonlinear systems. The ADIFOR2.0 code (Automatic Differentiation in Fortran) appends derivative code to computer codes for function evaluations, handles branches, loops, subroutines, and computes numerical values of derivatives within machine precision. Our experience show that for complex nonlinear system, ADIFOR2.0 can produce efficient and portable computer code for the Lie derivatives and Jacobians required to calculate the control law and evaluate the local stability of the closed-loop control system. Furthermore an efficient and user friendly MATLAB5.3-ADIFOR2.0-FORTRANcompaq6.0 CONTROL (MAFC) software package was developed to calculate the relative order, compute, and simulate the control law and analyze the local stability of the closed-loop system for invertible complex highly nonlinear processes using Symbolic and Automatic Differentiation. |
