Control structure selection for open-loop unstable plant with pure integrators using multi-projected systems

Selection of inputs and outputs for stabilizing an open-loop unstable process is discussed in this paper. The procedure includes decomposition of the process into multiple projections in order to isolate its unstable poles. Several projected subsystems are produced in state-space form indicating pure integrators, slow and fast modes as their only poles. By examining the numerical values of these state-space matrices, one can identify the outputs and inputs, which have strong connections with unstable pole(s). Tennessee-Eastman test-bed problem [4] has been chosen for the case study due to its umpteen I/O combinations. The process, linearized around its base case operating point, shows six unstable poles (including two pure integrators), which are separated as three antistable projections of the overall process. Analysis shows that by closing three loops, it is possible to stabilize the entire plant. PI controllers are designed for the TE plant and simulation results confirm the closed-loop stability of the plant.