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165 170 175 Figure 4: VRB Discharging Simulation using Convex Combination Feedback Gains For comparison, we also present the alternative (more computationally complex) controller im- plementation, whereby the controller feedback gains are computed by solving the algebraic Riccati equation at each time step (27), with results shown in Figure 5. Comparing the online LQR (27) results of Figure 5 with the proposed convex combination (36) results of Figure 3, we observe that there is no significant improvement, despite the increased computational burden. The tracking performance of the proposed method is almost identical, with a very minimal increase in control magnitude (and hence pump power consumption) in response to aggressive changes in charging current (see t ≈ 1980s, t ≈ 3160s) relative to the online LQR controller method. We also conducted simulation studies with fixed feedback gain control approaches using a fixed linearised model (about a target conversion per pass and SOC), including both traditional state feedback and PI-based de- signs and found those approaches completely ineffective in controlling the electrolyte conversion per pass, through an effective range of SOC and under variable supply or load (not illustrated here), due to the nonlinearity of the battery dynamics. For this reasoning, the experimental implementa- tion is completed using the parameter varying feedback gains computed via a convex combination of vertices. 19 0.8 0.6 0.4 0.2 1.6 1.4 1.2 0.1 0 0.025 0.02 0.015 20 15 10 -10 -20 0 500 1000 1500 2000 2500 3000 3500 4000PDF Image | Electrolyte Flow Rate Control Vanadium Redox Flow Batteries
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