The pure integrating process model with dead-time is inherently an unstable open-loop system. This paper presents a 2-DOF (2-degree of freedom) PID controller, based on the direct synthesis (DS) method, to improve the set-point tracking and load disturbance rejection performance for the pure integrating processes with time delays (PIPTD) models. The 2-DOF PID controller consists of a linear PID controller for rejecting the load disturbance in regulatory response and a set-point filter for relieving the overshoot in servo response. The DS method is based on comparing the desired closed-loop characteristic equation with the closed-loop characteristic equation, consisting of plant and PID controller. The adjustment parameter is only one desired time constant, with the roots of the desired characteristic equation placed at the same location, and the desired time constant was expressed as a function of the maximum magnitude of the sensitivity function (MS), for providing convenience in the selection of the desired time constant. The proposed controller is simulated by applying it to three other processes and comparing it with conventional methods, to demonstrate its effectiveness and applicability.

This study proposes a direct synthesis-based two-degree-of-freedom (2-DOF) controller for various types of integrating processes with time delays. This 2-DOF controller includes a proportional-integral-derivative (PID) controller to enhance load disturbance rejection performance and a set-point filter to improve servo response performance. The main PID controller parameters are expressed as process model parameters and a single adjustment variable, while the set-point filter is composed of PID controller parameters with weighted factors. The adjustment variable is tuned to achieve an optimal balance between response performance and robustness, based on the maximum magnitude of the sensitivity function (Ms). Controller parameters for various Ms values and guidelines for setting these parameters are provided in a consistent formulaic form using a curve-fitting method. These parameter-setting formulas facilitate the accurate implementation of PID controllers with specified Ms values and allow the controller design to be extended to processes with larger dimensionless time delays for a given Ms value. Although a 2-DOF controller was proposed, the adjustment variable for setting the parameters of the main PID controller and the set-point filter was solely the desired time constant. The proposed method was applied to various integrating processes with time delays, and its performance was compared with existing methods reported in the literature, based on performance indices such as settling time, overshoot, integral of absolute error, total variation in input usage, and global performance index. Simulations were conducted using six examples of various integrating processes with time delays to verify the effectiveness and applicability of the proposed controller.

In most chemical industries, continuous stirred-tank reactors (CSTRs) are essential for the production of chemicals. The CSTR process is highly nonlinear and has both stable and unstable equilibrium points. Control system engineers face a difficult issue when designing a single controller for temperature control in both stable and unstable areas. Due to these problems, implementing the conventional proportional-integral-derivative (PID) controller may lead to instability in controlled variables. Therefore, in this paper, the entire operating region is divided into three regions. The fractional-order PID controller as a local controller is designed in each operating region to control the temperature, and its parameters are tuned with a genetic algorithm by minimizing the integral of absolute error and control input change with a weighting factor. Then, a fuzzy gain scheduling scheme based on the Tagaki-Sugno fuzzy model is used to properly interpolate the outputs of the local controllers. A set of simulations are carried out to demonstrate the effectiveness of the proposed controller, and its performance is compared with that of an adaptive nonlinear controller and fuzzy gain scheduling of the PID controller.

This study proposes a two-degree-of-freedom PID controller design and tuning method based on a simple pole placement approach to enhance servo and regulatory performance while ensuring the stability of diesel engines. In the modeling of the control target, the actuator is analytically modeled. In contrast, the type of model for the diesel engine is derived analytically, and its parameter estimation uses operational data from naval ships. The proposed controller consists of a PID controller to improve regulatory performance and a set-point filter to enhance servo response. PID controller parameters consist of the parameters of the controlled plant model and a single tuning variable. At the same time, the set-point filter comprises the controller parameters and a single weighting factor. To ensure the robust stability of the controller, the controller parameters are tuned based on the maximum sensitivity. To verify the effectiveness of this study, simulations for the speed control of a diesel engine with inherent nonlinearity were conducted under three scenarios. Performance was quantitatively analyzed using the integral of time-weighted absolute error, 2% settling time, 2% recovery time, specified maximum sensitivity, and maximum peak response value, and was compared with Skogestad’s IMC and Lee’s IMC. Based on evaluation indices, the proposed controller demonstrated superior performance in both servo and regulatory responses compared to the two existing control techniques while ensuring stability.

Gas turbine engines at sea, characterized by nonlinear behavior and parameter variations due to dynamic marine environments, pose challenges for precise speed control. The focus of this study was a COGAG system with four LM-2500 gas turbines. A third-order model with time delay was derived at three operating points using commissioning data to capture the engines’ inherent characteristics. The cascade controller design employs a real-coded genetic algorithm–PID (R-PID) controller, optimizing PID parameters for each model. Simulations revealed that the R-PID controllers, optimized for robustness, show Nyquist path stability, maintaining the furthest distance from the critical point (−1, j0). The smallest sensitivity function $Ms$ (maximum sensitivity) values and minimal changes in $Ms$ for uncertain plants confirm robustness against uncertainties. Comparing transient responses, the R-PID controller outperforms traditional methods like IMC and Sadeghi in total variation in control input, settling time, overshoot, and ITAE, despite a slightly slower rise time. However, controllers designed for specific operating points show decreased performance when applied beyond those points, with increased rise time, settling time, and overshoot, highlighting the need for operating-point-specific designs to ensure optimal performance. This research underscores the importance of tailored controller design for effective gas turbine engine management in marine applications.

Temperature control in a continuous stirred tank reactor (CSTR) poses significant challenges due to the process’s inherent nonlinearities and uncertain parameters. This study proposes an innovative solution by developing an adaptive nonlinear proportional–integral–derivative (NPID) controller. The nonlinear gain that dynamically scales the error fed to the integrator is enhanced for optimized performance. The network’s ability to approximate nonlinear functions and its online learning capabilities are leveraged by effectively integrating an NPID control scheme with a radial basis function neural network (RBFNN). This synergistic approach provides a more robust and reliable control strategy for CSTRs. To assess the proposed method’s feasibility, a set of simulations was conducted for tracking, disturbance rejection, and parameter variations. These results were compared with those of an adaptive RBFNN-based PID (APID) controller under identical conditions. The simulations indicated that the proposed method achieved reductions in maximum overshoot of 33.7% and settling time of 54.2% for upward and downward setpoint changes and 27.2% and 5.3% for downward and upward setpoint changes compared to the APID controller. For disturbance changes, the proposed method reduced the peak magnitude (M_peak) by 4.9%, recovery time (t_rcy) by 23.6%, and integral absolute error by 16.2%. Similarly, for parameter changes, the reductions were 3.0% (M_peak), 26.4% (t_rcy), and 24.4% (IAE).