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. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The goal of this research is to develop an equation describing the two, dimensional motion of an inviscid incompressible fluid in the rectangular wavemaker of constant depth. The boundary value problem of the rectangle is transformed to the upper half plane with the use of Jacobian elliptical functions. The boundary value problem is then transformed to the unit disc. The solution to the mixed value problem of the disc is found using a general solution satisfying the Laplace equation in polar coordinates. In order to solve the coefficients of the general solution, a system of equations is developed using a method similar to the one applied for the coefficients of a Fourier series. The system is converted to matrix form and the coefficients are calculated using Mathematica. Four approximate solutions are calculated for depths of 3.96 m and 4.42 m with N equal to 2 and 10. / Graduation date: 1993