Adaptive head control of a hydraulic open channel model. (English) Zbl 0669.93048
We are concerned with the head control of a reach of an open channel. We consider a control configuration where the head sensor and actuator (gate position) are located nearby. This configuration does not seem to have been explored in the literature since the control task is made considerably difficult by the aftereffect of the water reflecting wave.
To design the controller, the open channel reach is modeled by a linear retarded differential equation, where the retarded part takes into account the delays. Using the theory developed in R. Johansson [Automatica 22, 555-560 (1986; Zbl 0599.93037)] we design an adaptive controller that compensates for the latter. Simulation results of the proposed controller applied to a partial differential equation model of the channel are given in C. T. Constantinides, T. Kia- Koojoori and R. G. Jacquot [Int. J. Syst. Sci. 7, 989-1003 (1976; Zbl 0332.93056)] and V. Chow [Open channel hydraulics (Maidenhead/U.K. 1973)].
To design the controller, the open channel reach is modeled by a linear retarded differential equation, where the retarded part takes into account the delays. Using the theory developed in R. Johansson [Automatica 22, 555-560 (1986; Zbl 0599.93037)] we design an adaptive controller that compensates for the latter. Simulation results of the proposed controller applied to a partial differential equation model of the channel are given in C. T. Constantinides, T. Kia- Koojoori and R. G. Jacquot [Int. J. Syst. Sci. 7, 989-1003 (1976; Zbl 0332.93056)] and V. Chow [Open channel hydraulics (Maidenhead/U.K. 1973)].
MSC:
| 93C40 | Adaptive control/observation systems |
| 93C20 | Control/observation systems governed by partial differential equations |
| 34K35 | Control problems for functional-differential equations |
| 93C95 | Application models in control theory |
References:
| [1] | Åström, K., Adaptive feedback control, (Proc. IEEE, 75(2) (1987)) · Zbl 0941.93543 |
| [2] | Begovich, O., Control Adaptable de Sistemas con Retardo, (M.S. Thesis (1987), CINVESTAV IPN: CINVESTAV IPN Mexico) |
| [3] | Chow, V., Open-channel Hydraulics, ((1973), McGraw-Hill: McGraw-Hill Maidenhead, U.K) |
| [4] | Clarke, D.; Mohtadi, C.; Tuffs, P., Generalized predictive control, Part 1: the basic algorithm, Automatica, 23, 137-148 (1987) · Zbl 0621.93032 |
| [5] | Constantinides, C. T.; Kia-Koojoori, T.; Jacquot, R. G., Stability of a feedback controlled distributed system by model representation, Int. J. Syst. Sci., 7 (1976) · Zbl 0332.93056 |
| [6] | Cunge, J. and D. Woolhiser, Irrigation systems. In K. Mahmood and V. Yerjevich (Eds), Unsteady Flow in Open Channels; Cunge, J. and D. Woolhiser, Irrigation systems. In K. Mahmood and V. Yerjevich (Eds), Unsteady Flow in Open Channels |
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| [8] | Ioannou, P.; Kokotovic, P., Instability analysis and improvement of robustness of adaptive control, Automatica, 20, 583-594 (1984) · Zbl 0548.93050 |
| [9] | Johansson, R., Estimation and direct adaptive control of delay-differential systems, Automatica, 22, 555-560 (1986) · Zbl 0599.93037 |
| [10] | Johansson, R., Estimation of continuous-time dynamic systems, (Proc. of the 25th IEEE Conf. on Decision and Control. Proc. of the 25th IEEE Conf. on Decision and Control, Athens, Greece, December 1986 (1986)) |
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