Optimization of controller parameters based on nondimensional performance indicators for canal systems

Abstract: Automatic canal control plays an increasingly important role in water delivery systems, for it is effective in distributing the water resource rationally and reducing the discharge of wastewater. For the control of an open-canal system, the first issue is how to define the control performance indicator, and then the controller could be designed by pursuing the optimized value of performance indicators. The characteristics of canal systems result in the diversity and complexity of performance indicators, marked by big lag, strong nonlinearity, high coupling and multi-input multi-output (MIMO) topology. Therefore, the objective of this study was to improve the existing performance indicators and propose a general indicator reasonably and overall. We tried to demonstrate the feasibility of them by applying in 2 actual canal systems. In this paper, traditional performance indicators of canal control systems were concluded and analyzed, and some additional indicators were replenished and some of them are nondimensionalized by using the design discharge or constant depth of the control point or other inherent parameters. A set of indicators which can evaluate different canal systems were proposed by weakening the influence of canals' dimension parameters. This set was applied to 2 canal systems with different scales: The large-size canal system is 24 km long × 15 m wide × 6 m deep and the small-size canal system is 18 km long × 5-7 m wide × 2.5 m deep, and the larger is around 20 times the size of the smaller. A simulation model of canal systems' control based on MATLAB was constructed, which consisted of 7 modules: physical model establish of canal systems, steady flow state profile calculation, feedforward control module, feedback control module, gate discharge calculation, gate opening transformation and unsteady flow calculation. Among the models, energy equations and de Saint-Venant system of equations were used to compute the constant flow and unsteady flow, and the canal control system was designed which regarded flow rate as the feedforward and the water level as the feedback. Relying on the imulation model of canal systems' control, we optimized the controller parameter aimed at different nondimensional performance indicators, and conducted the comparison between each other. The simulation proved that the optimal values of indicators had high consistency in the order of magnitude with little concern to the canal scale. For example, the optimal NIAQ (nondimensional integrated absolute discharge change) of both canal systems was 10-5. So this series of indicators could be used to compare the performance of different canal systems. However, due to the different optimization effect of single indicator, pursuing the extreme of any single indicator might result in an unbalanced system. Through the analysis of genetic relationship and representativeness among the series of dimensionless performance indicators, a general indicator (GI) was given based on the water level deviation, flow rate changes and transition time with weight. And as far as we're concerned, the control performance was fit for our requirement when the value of GI was no more than 10-3 in magnitude. The simulation results showed that this aimed GI could stabilize the system and balance all dynamic performances of canal systems well compared with a signal indicator. What was more, we studied the flow and water level procedure lines the canal systems showed under different controller parameters by controlling variable. And we discussed the relationship between proportional-integral-derivative (PID) controller parameters and performance indicators. There existed an insensitive range in which the proportional gain could control the flow rate smoothly in pure proportional (P) controller (proportional gain was smaller than 4 in No.1 canal system, and smaller than 15 in No.2 canal system), and the integral time had a similar effect on water level in proportional-integral (PI) controller. Thus the optimizing method of finding a robust controller was proposed preliminarily: searching the intersection of controller parameters which worked well under different conditions. The series of non-dimensional indicators and GI proposed by this paper can be used to evaluate different canal control systems and different controllers, which can be used as benchmark while designing a new canal control system. This work suggests quite promising solution for the operation of a large number of water delivery systems and irrigation district canal networks in China.