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In controller design, linear PID controllers have something of a dilemma relationship: a fast response requires large gains, which in turn, give rise to a large overshoot. For this reason, a variety of feedback control forms and related tuning methods have been implemented to guarantee satisfactory performance. Recently, multiple studies which introduce nonlinearities into the structure of the standard PID controller have been performed to solve this conflicting relationship. This study proposes an EA-based nonlinear PID controller with a first-order filter added to the derivative action to achieve the desirable quick response with low overshoot. This is realized by introducing a new type of nonlinearities in the controller gains that are time-varying functions in terms of the error and/or error rate. In addition, the nonlinear controller is designed by considering a saturation element. Then, the parameters of the nonlinear PID controller are optimally tuned by an evolutionary algorithm. In tuning the nonlinear PID controller gains, the integral of time-weighted absolute error is used as the performance evaluation of the overall control system. A set of simulation works performed on two processes with actuator saturation shows the feasibility of the proposed method.

The integrating process with time delay (IPTD) is a fundamentally unstable open-loop system due to poles at the origin of the transfer function, and designing controllers with satisfactory control performance is very difficult because of the associated time delay, which is a nonlinear element. Therefore, this study focuses on the design of an intelligent proportional-integral-derivative (PID) controller to improve the regulatory response performance to disturbance in an IPTD, and addresses problems related to optimally tuning each parameter of the controller with a real coded genetic algorithm (RCGA). Each gain of the nonlinear PID (NPID) controller consists of a product of the gains of the linear PID controller and a simple nonlinear function. Each of these nonlinear functions changes the gains in the controller to on line by nonlinearly scaling the error signal. A lead-lag compensator or first-order filter is also added to the controller to mitigate noise, which is a disadvantage of ideal derivative action. The parameters in the controller are optimally tuned by minimizing the integral of time-weighted absolute error (ITAE) using a RCGA. The proposed method is compared with three other methods through simulation to verify its effectiveness.

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CSTR (Continuous Stirred Tank Reactor) which plays a key role in the chemical plants exhibits highly nonlinear behavior as well as time-varying behavior during operation. The control of CSTRs in the whole operating range has been a challenging problem to control engineers. So, a variety of feedback control forms and their tuning methods have been implemented to guarantee the satisfactory performance. This paper presents a scheme of designing a nonlinear PID controller incorporating with a GA (Genetic Algorithm) for the temperature control of a CSTR. The gains of the NPID controller are composed of easily implementable nonlinear functions based on the error and/or the error rate and its parameters are tuned using a GA by minimizing the ITAE (Integral of Absolute Error). Simulation works for reference tracking and disturbance rejecting performances and robustness to parameter changes show the feasibility of the proposed method.