The application of multivariable optimal control to non-linear chemical processes
Thesis DisciplineChemical Engineering
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
Higher production rates, more extreme processing conditions, tighter product specifications and more highly integrated processing plant are envisaged as some of the reasons for encouraging the chemical industries to look more closely at the potential advantages of Modern Control Techniques. The advent of the process control computer has failed to bring about any significant shift away from the established conventional control techniques, perhaps because of the innate conservatism of the control engineers but more likely due to the apparent complexity of the mathematical techniques control, and a lack of confidence involved in so-called "Optimal" in the ability of optimal controllers to perform significantly better than the already highly-developed single-loop controllers. The aims of this study are two-fold: (1) To demonstrate straightforward techniques for the solution of the optimisation problems which are the basis of optimal control theory, and (2) To demonstrate, by implementation of the control laws so obtained, some. of the advantages which can accrue from multivariable optimal control. Some of the standard multivariable control techniques are introduced and Dynamic Programming is selected for further development because of its versatility as an optimisation technique. The recurrence relationship is established for staged processes and the judicious use of some simplifying assumptions results in an iterative technique which converges rapidly to the solution of the steady-state control law. The Dynamic Programming approach is equally applicable to the optimisation of continuous processes and results in the Hamilton-Jacobi equation. Once again the use of simplifying assumptions leads to a straightforward method of solution and a steady-state multivariable control law. The control laws are tested on a range of linear and nonlinear systems and their performance compared with that of single- and multi-loop controllers under conditions of bounded controls, random disturbances and process and control variable "dead-time". The particular advantages of multivariable controllers are found to be (1) More effective control, as measured by the process control criterion, (2) An ability to stabilise the process under more severe disturbances, (3) Greater process stability in the face of process or control variable "dead-time", (4) The use of significantly less control effort in controlling the process, and (5) The ability to control naturally unstable processes with tighter limits on the control variables. Multivariable feedforward controllers are also developed and are shown to have significant advantages even on single-stage processes, although the quality of the process model is shown to be important. A non-linear feedforward compensator is seen to possess quite dramatic load rejection potential. The multivariable optimal controllers are thus seen to be reasonably simple to implement, robust in operation and very effective. Possibly the greatest single advantage of multivariable over multi-loop control strategies is the elimination, at a stroke, of the configuration problem.