Background on the controller selection and tuning procedure
The control selection and tuning procedure works as follows. First, some essential canal properties (delay time, surface area, critical resonance frequency, if any, and corresponding resonance peak gain) are derived from the nonlinear hydrodynamic model of the canal. With these canal properties, as well as some additional data on the control hardware that needs to be used (such as the sample time), and preferences on the control structure, an 'initial' feedback control system is selected, consisting of Proportional Integral (PI) controllers with or without decouplers (see below). 
Then for each PI controller its limit settings (= the settings of the control constants at which control is close to instability) are computed and the control constants are optimised using a multiple model optimisation technique [1], [2]. 
Then the control system is tested if it will satisfy the performance requirements. If not, a control system with better performance is selected (see below) and tuned again using multiple model optimisation. 

Details on the control structure [2]
An hierarchical master-slave control structure is always applied. The master controller controls the water level by adjusting the flow through the check-structure (such as a gate). The slave controller controls the flow through the check-structure by adjusting the check-structure inputs, such as gate openings. The advantages of applying this hierarchical master-slave control structure are multiple:

  • nonlinearities of the check-structure do not affect the water level control loop which improves performance;
  • complicated requirements on the operation of the check-structure are easily taken into account (for instance, operating requirements to avoid damage to the canal walls);
  • interactions between two adjacent reaches are avoided which improves performance (decoupling).

Master controller
Depending on the preferred choice, completely decentralized feedback control system (distributed control) can be applied as master controller, or a centralized one. For a completely decentralized feedback control system, local PI controllers are selected. For a completely centralized feedback control system, PI controllers are selected first that add their control input signal to an adjacent PI controller (PI control with decoupler).

Slave controller
The slave (flow) control algorithm that is usually applied is a bisection algorithm that numerically 'inverts' the gate-discharge relation. The algorithms have guaranteed convergence and solve the problem fast enough to allow real-time operation. Gate-discharge relations do not need to be known exactly for this, (nor do they have to be calibrated). 

In some cases, a filter is connected in series with the PI controller to improve performance. The tuning procedure automatically detects if such a filter is useful. 
If the resulting performance of the controlled canal is inadequate, the control problem is hard and a feedforward controller has to be added. The feedforward controller is provided either with a schedule of disturbances and/or real-time measured disturbances (depending on your preferences) and computes anticipating control actions based on that knowledge. The feedforward controller is simple to program and very reliable, because it makes use of a very simple algorithm. The control signal of the feedforward controller is added to that of the feedback controller.
If the resulting performance is still inadequate, more advanced feedback controllers, such as LQG, and/or more advanced feedforward controllers or Model Predictive Control. 

References¹
[1] P.J. van Overloop. 'Model Predictive Control on Open Water Systems', ISBN 1-58603-638-6, 2006, The Netherlands.

[2] J.Schuurmans. 'Control of Water Levels in Open-Channels', ISBN 90-9010995-1, 1997, The Netherlands.

[3] J. Schuurmans, A. Hof, S. Dijkstra, O.H. Bosgra, R. Brouwer, 'Simple Water Level Controller for Irrigation and Drainage Canals', J. of Irr. and Drainage, 125(4), p. 189-195

More information on our method of modelling irrigation canals can be found in:
[4] J. Schuurmans, A. Hof, S. Dijkstra, O.H. Bosgra, R. Brouwer, 'Simple Water Level Controller for Irrigation and Drainage Canals', J. of Irr. and Drainage, 1999, ASCE, 125(4), p. 189-195.
[5] Overloop, P.J. van, Schuurmans, J., Brouwer, R., Burt, C.M., 'Multiple Model Optimization of PI-Controllers on Canals', Journal of Irrigation and Drainage Engineering, 2005.
[6] Overloop, P.J. van, Schuurmans, W., Brouwer, R., 'Model Predictive Control of water systems in the Netherlands', USCID-Proceedings International Conference, Phoenix, 2003.

¹Any of this references can be obtained by contacting info@canalcontrol.com