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UBC Theses and Dissertations

Discrete-time closed-loop control of a hinged wavemaker Hodge, Steven Eric


The waves produced by a flap-type wavemaker, hinged in the middle, are modelled using first-order linear wavemaker theory. A simplified closed-loop, discrete-time system is proposed. This includes a proportional plus integral plus derivative (PID) controller, and the wavemaker in order to compare the actual wave spectral density with the desired wave spectral density at a single frequency. Conventional discrete-time control theory is used with the major difference being the use of a relatively long timestep duration between changes in waveboard motion. The system response is calculated for many controller gain combinations by the computer simulation program CBGANES. System stability is analyzed for the gain combinations by using two different methods. One method is an extension of the Routh criterion to discrete-time and the other is a state-space eigenvalue approach. The computer simulation and the stability analysis provide a means for selecting possible controller gains for use at a specific frequency in an actual wave tank experiment. The computer simulation performance response and the two stability analyses predict the same results for varying controller gains. It is evident that integral control is essential in order to achieve a desired response for this long duration timestep application. The variation in discrete timestep duration and in desired spectral density (an indirect indication of frequency variation) provide variation in the constraints on controller gain selection. The controller gain combinations yielding the fastest stable response at a single frequency are for large proportional gain and small integral and derivative gains.

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