Transfer function representations of various plants still have significant positions in design and analysis of control systems, because new frequency-domain control techniques, such as H∞ control theory, are now easily available. This paper describes applications of transfer function representations of resources processing plants. The authors at first have showed examples of processes when the idea proposed in a paper of Åström et al. (1992) is applied to resources processing plants.
The authors have, subsequently, calculated 4 transfer functions of one-dimensional reactive-diffusive models, which are typically found in resources processing plants, under 4 types of boundary conditions. Then, behaviors under Bo → ∞, 0 have been established based on the transfer functions calculated above. The transfer function representation of a free-flow flotation process proposed by Niemi (1966) seems to be lack of generality, because of the boundary conditions adopted. The authors have showed a new transfer function representation of the flotation process, under appropriate boundary conditions. The new transfer function model has been investigated to validate the idea of Åström et al. (1992), which attempts to apply Ziegler Nichols's PID tuning method through analyzing dimensionless numbers. The main results are summarized as follows :
· Achievable performance of the PID control system is not affected by normalized reaction constant K, but by Bodenstein number Bo.
· Relation between normalized process gain κ and normalized deadtime θ can empirically be described by an equation κ = 1 + 0.46 / θ 1.67. Relation κ = 2 (11 θ + 13) / (37 θ - 4) for finite-dimensional systems also gives rather a good approximation.
· Within recommended region 0.1< θ < 0.6 of Ziegler-Nichols's ultimate gain method, crude approximations κ λ ≈ 1.4 and τ ≈ 1 hold.
The latter half of the second term and the whole of the third term mentioned above show the validity of the idea of Åström et al. (1992), while the reactive-diffusive models are infinite-dimensional. This suggests usefulness of dimensionless numbers.
Relations between other tuning methods and dimensionless numbers, applications to back-mixing models which are also familiar models in resources processing plants are the remaining themes to be studied.
