Systematic Design of Split Range Controllers

Multiple-Input Single-Output Control for Extending the Steady-State Operating Range—Use of Controllers with Different Setpoints

“…For each input, the SR-block can be represented as the linear function u i = α i v + u 0 i ∀i ∈ {1, 2, 3}. The slopes (α i ) in Table A4 are found with the procedure described in Reference [7] using the tuning parameters in Table A3. Here we consider v = 0 and all inputs closed at the nominal operating point.…”

“…Figure 1 shows the block diagram of a split range controller (SRC) with two inputs (u 1 and u 2 ) for one output (y). Here, there is a common controller (C) that produces an internal signal in deviation variables (v) that is the input to the split range (SR) block, which calculates the values for u i (in physical variables) [7].…”

“…The split point (v * ) or, equivalently, the corresponding slopes (α i ) in Figure 2, can be used as degrees of freedom to counteract the differences in the effects of the various inputs (u i ). The approach introduced in Reference [7] considers not only the static effect but also the dynamics. Nevertheless, there are limitations in terms of tuning, as only the controller gains can be adjusted using the slopes; for example, the integral time needs to be the same for all inputs.…”

“…We implement a classical split range controller as shown in Figure 9. We use the procedure proposed by Reference [7] to find the tuning parameters for the common controller and the slopes in the split range block (see Appendix C). The common PI-controller has a proportional gain K C = 0.1277 kW/ • C and integral time constant τ I = 1200 s. For all inputs, the setpoint is always fixed at y sp = T sp = 21 • C, which would correspond to having a huge penalty for setpoint deviation (p T → ∞, in Equation 10 Figure A1.…”

Systematic Design of Active Constraint Switching Using Classical Advanced Control Structures

“…Finally, we bring m tot sp back to its initial value at t = 70 s. All the tunings were found using the SIMC tuning rules. 43 The split range control structure was designed using the systematic procedure proposed by Reyes-Luá et al 35 When we do not follow the input saturation pairing rule and do not implement any advanced control structure (Case B), y 2 = ṁt ot is highest, but it comes at the expense of not keeping y 1 = x MeOH at its set point and, thus, violating its maximum constraint (see Table 1).…”