Simple optimal downstream feedback canal controllers: Theory

A new class of downstream water-level, feedback controllers is proposed that can vary from a series of individual proportional-integral (PI) controllers (each gate adjusted based on one water level) to fully centralized controllers (each gate adjusted. based on all water levels) that include the effects of lag time. The controller design method uses discrete-time state-feedback control with a quadratic penalty function, physically based states, and no state estimation. A simple, linear model of canal pool response, the integrator-delay model, is used to define the state transitions. All controllers within this class are tuned for the entire canal using optimization techniques. This avoids the tedious task of manually tuning simple controllers. The relative performance of the various controllers within this class can be directly compared without simulation, since the same objective function is used to tune each controller. An example is provided which suggests that the fully centralized controller will perform better than a series of local controllers. However, reasonably good performance can be obtained for some intermediate PI controllers that pass information to one additional check structure upstream and downstream. This should limit some of the difficulties reported for full optimal controllers where all check structures respond to water-level. errors in all pools (e.g., saturation of inputs). The results of simulation studies of these controllers are provided in a companion paper.