This paper proposes a new approach for robust nonlinear proportional derivative (PD) controller. In this approach a nonlinear function (sigmoid) is added to the conventional proportional integral derivative (PID) controller with filtering for the derivative, in order to improve system response and to reduce the effects of the nonlinearity and uncertainty due to variations of hydrodynamic coefficients of ship with the speed. The gains of nonlinear PD controller are tuned by applying particle swarm optimization (PSO) technique. The simulated results by MATLAB program give satisfactory performance with regard to maximum overshoot, settling time and zero steady state error for step, ramp and proposed trajectory as input to the system. The robustness of the autopilot was checked by changing the plant parameters and adding disturbance to the plant input. The used autopilot is nonlinear PD controller because the gain of integral term by PSO is approximately zero which simplifies the controller construction. The results show that the proposed controller has superior transient response and robustness on the conventional PID designed by using symmetrical optimum criterion with pole assignment technique.
The dissolved oxygen concentration in the wastewater treatment process (WWTP) must remain in a specific range while the factory operates. The augmented positive identification (PID) controller with a nonlinear element (sigmoid function) is proposed to assure stability and reduce uncertainties in the wastewater direct reuse/recycling model. The nonlinear controller gains (PID controller with sigmoid function) for uncertain wastewater treatment processes are tuned using the particle swarm optimization (PSO) technique. The proposed robust method for controlling wastewater treatment processes has good robustness during model mismatching, reduces treatment time compared to traditional positive identification (PID) controllers tuned by PSO, is easy to apply, and has good performance, according to simulation results.
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