Stability error rejection

These issues of stability and error rejection become very important for stiff systems, as the time step must be chosen to accommodate the largest eigenvalue (fastest mode). We have seen above an example of a stiff system from chemical kinetics, but another important source of stiff systems is the simulation of time-dependent PDEs such as the diffusion... 

Usually the INA is a very conservative measure of stability. Compensators are found by trial and error to reshape the INA plots so that the circles are small and the system is diagonally dominant. The INA method strives for the elimination of interaction among the loops and therefore has limited usefulness in process control where load rejection is the most important question. 

Summary. In this chapter the control problem of output tracking with disturbance rejection of chemical reactors operating under forced oscillations subjected to load disturbances and parameter uncertainty is addressed. An error feedback nonlinear control law which relies on the existence of an internal model of the exosystem that generates all the possible steady state inputs for all the admissible values of the system parameters is proposed, to guarantee that the output tracking error is maintained within predefined bounds and ensures at the same time the stability of the closed-loop system. Key theoretical concepts and results are first reviewed with particular emphasis on the development of continuous and discrete control structures for the proposed robust regulator. The role of disturbances and model uncertainty is also discussed. Several numerical examples are presented to illustrate the results. 

In controlling specimen transport, the essential feature is the authority to reject specimens that arrive in the laboratory in an obviously unsatisfactory condition (such as a thawed specimen that should have remained frozen). As with other QC procedures, a small number of problems are expected, but if the error rate gets too large, there is a necessity for systems analysis of transport procedures, with resulting modifications. In tests in which stability is a major problem, the design of specific control procedures appropriate for those tests may be necessary. 

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