Control theory, Feedback control systems, Process control
A model (NONLINRK) was developed for a closed tank system under feedback control by an ideal proportional-integral-derivative controller. Under servo action the fluid level in the tank is altered from its equilibrium set point. Under regulatory action the feed pressure to the inlet valve and/or the outlet valve percentage opening are varied from equilibrium settings. The numerical model uses Gill’s fourth-order Runge-Kutta algorithm to solve the system equation. The equation was made separable by approximating an exponential factor by the tangent at the beginning of each time step in the numerical solution. NONLINRK simulation trials exhibited many characteristics of linear system including unequal offset under proportional control for the setpoint changes equal in magnitude but opposite in sign, harmonics in the response to a sine wave input on fluid level setpoint and bounded response in spite of increased gain settings. In addition, further simulation trials showed the system response converges to that of a linear system for sufficiently small setpoint of load variations. A second model using the modeling language TUTSIM provided corroboration of the results produced by NONLINRK. Proportional and proportional-integral control simulations differed by less than .1% and the models showed the same rates of convergence as the time step was decreased. Under PID control TUTSIM simulations developed severe instabilities, but NONLINRK exhibited the expected trends in the increased ability to react to a ramp function disturbance and the decrease in phase lag in response to a sinusoidal setpoint function.
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Master of Science (M.S.)
College of Engineering
Length of Campus-only Access
Masters Thesis (Open Access)
Bishop, Charles W., "Model for a Nonlinear Tank System Under Proportional-Integral-Derivative Control" (1985). Retrospective Theses and Dissertations. 4796.