| Time-optimal control of chemical processes is difficult to implement using conventional techniques because, to find the correct switching times, an accurate dynamic model of the system is required. However, one algorithm has been presented (Beard, 1971) which allows time-optimal control of linear single-input single-output second-order systems when only the steady-state model of the system is known, provided the system is initially at steady-state. Using model dead time as a tuning parameter, the algorithm was also shown to give good suboptimal control of nonlinear systems and systems of higher than second-order. In this dissertation, it is demonstrated theoretically why time-optimal control can be implemented without knowing a dynamic system model. In addition, new algorithms are presented to time-optimally control multi-input multi-output systems without knowing a dynamic system model. These algorithms are demonstrated on linear first-, second-, and fifth-order systems with dead time, a nonlinear distillation column, and a linear double-effect evaporator. All of the systems used are computer simulations. Finally, additional results concerning the application of the model-independent time-optimal algorithms are developed. Among these is the demonstration that the algorithms provide good control even if the steady-state model is not accurately known. On the other hand, controlling a system not initially at steady-state is shown sometimes to be risky. Time-optimal control of underdamped systems was also studied. Although an underdamped second-order system can require any number of control switches for time-optimal control if the system is not initially at steady-state, it is shown that only one switch is needed if the system is at steady-state. The last topic investigates time-optimal control applied with the limits of the manipulated variables used by a PID controller which is controlling the same system. The results demonstrate that very large changes in the manipulated variables are not required in order to obtain fast responses. |
