This study proposes a novel variable-gain mechanism with a minimal number of tuning parameters to enhance the performance of conventional backstepping controllers for nonlinear systems while avoiding singularity and peaking phenomena. The proposed approach is simple, computationally efficient, and well suited for real-time implementation without imposing a significant computational burden. Its effectiveness is validated through real-time experiments conducted using a dSPACE DS1104 controller board and a 7.5-kW induction motor (IM). Simulation results demonstrate that the proposed controller outperforms the conventional backstepping controller. Robustness analyses under variations in stator resistance, load inertia, and viscous friction coefficient reveal substantial reductions in the integral squared error (ISE), from 42.78 to 0.73, 67.4 to 1.38, and 3.65 to 0.53, respectively. Experimental results further confirm that the proposed method achieves superior tracking performance and enhanced robustness against disturbances compared with existing methods reported in the literature.

In this study, a method for modifying the settings of fractional order PI-PD (FOPI-PD) controllers to handle time-delayed stable, unstable, and integrating processes is presented. The goal is to reduce the computational complexity associated with fractional controller design using analytical techniques. The approach involves updating the analytical weighted geometrical center (AWGC) method for tuning FOPI-PD controllers. The fractional integral and derivative orders are computed by minimizing the Integral of Squared Time Error (ISTE) using straightforward formulas. Additionally, there are analytical formulas provided for robustness characteristics such as maximum sensitivity (Ms), phase margin (PM), and gain margin (GM). The effectiveness of the technique is illustrated through unit-step responses under nominal, disturbed, and measurement situations. The method was evaluated using various metrics and an inverted pendulum mechanical system to demonstrate its industrial applicability. The results showed satisfactory outcomes in both performance and robustness.

This study introduces a proportional-integral-derivative plus second-order derivative (PIDD2) controller, featuring an innovative multiplier to address time delays, utilizing the direct synthesis method (DSM) for load frequency control (LFC) in time-delayed microgrid (MG) systems. The parameters of the proposed PIDD2 controller are tuned using the direct synthesis method, an analytical tuning approach. In the proposed design method, the best values of PIDD2 controller parameters were found by using the integral of time-weighted absolute error (ITAE). The proposed design approach has been developed for four different scenarios of time-delayed MG systems and compared with existing studies in literature. Real system data were utilized to illustrate the relevance of the proposed design methodology in real-time systems characterized by unmodeled dynamics, measurement noise, parameter fluctuations, and stochastic load variations. Based on Monte Carlo simulations conducted under parameter uncertainties, the proposed PIDD2 controller demonstrated improvements of up to 55.22 % in the ITAE index, 20.19 % in settling time, and 33.73 % in overshoot. Moreover, it significantly enhanced system stability across different random load pattern segments, with Integral of Time weighted Absolute Error (ITAE) improvements reaching as high as 99.99 %. The findings of this study provide significant insights into enhancing the stability of MG systems and improving efficiency in energy management.

This study proposes a state feedback-based controller design for Load Frequency Control (LFC) in isolated power systems employing a non-reheated turbine. The controller architecture integrates a proportional-integral (PI) control structure, with its tuning parameters analytically derived using standard forms, particularly based on the ISTE and IST ${ }^{\mathbf{2}} \mathbf{E}$ performance indices. The method allows direct computation of the PI controller gains without requiring iterative optimization procedures, thereby simplifying the design process. Comprehensive simulations reveal the effect of standard form parameters on the system’s dynamic performance and demonstrate that the proposed method enhances both transient and steady-state responses under varying operating conditions. Compared to conventional PI-PD and PID controllers, the proposed ISTE and IST2 E methods achieve up to $38 \%$ improvement in settling time and a $72 \%$ reduction in peak value over PI-PD, and $52 \%$ improvement in settling time and $92 \%$ reduction in peak value over PID, respectively. These results highlight the practical advantages of the standard form approach, particularly in achieving robust and efficient LFC.

Combining feedforward controllers with feedback controllers improves control performance and lowers tracking error. The paper proposes and practically analyzes an intelligent feedforward regulator known as iterative learning control for improving the performance of already built in flight controllers. As the proposed method doesn’t use the mathematical model of the system to design the controller, it independent from the effects of system parameters variations. Real-time results using a quadrotor system show that the proposed controller significantly reduces the tracking error relative to LQR controller. Additionally, it has been shown how straightforward it is to add the proposed feedforward term to an already built-in commercial flight controller.

A common type of nonlinear system in the field of process industry is asymmetrical heating and cooling processes. These systems have two operating modes, heating and cooling, each with a particular dynamic feature. This study deals with identifying and controlling such processes. The relay feedback identification method based on the state-space approach, which results in exact estimates, is used in the identification procedure to achieve two first-order plus dead time (FOPDT) process models. Following process identification, two sets of PI-PD controller parameters are acquired in line with the user-defined gain and phase margin specifications, and the system is controlled using a gain-scheduled PI-PD control method. Some simulation examples are provided to demonstrate the use and profitability of the suggested identification and control approaches. Comparisons with a similar study are provided for both identification and control approaches to clearly demonstrate the benefits of the suggested procedures.

Disturbance rejection has always been a major phenomenon in control theory. Disturbances that arise in control of unstable or integrating unstable processes with time delay present considerable difficulties for classical PID controllers. This paper supplies analytical tuning rules, derived from optimum disturbance rejection responses to minimise the error signal according to several integral performance criteria to identify the tuning parameters of the I-PD controller. The provided analytical rules offer the advantage of calculating controller parameters without the necessity of employing an optimisation algorithm. This simplifies the tuning process and allows for a straightforward determination of the controller's parameters, making it more convenient and efficient for practical implementation in control systems. Comprehensive simulations were performed to validate the effectiveness of the proposed I-PD controller in terms of disturbance rejection responses, control signals, perturbation in process parameters, measurement noises, TV values, Ms values, and integral performance indicators. Overall, the outcomes demonstrate that the introduced method for the tuning of I-PD controllers offers notable advantages when compared to other tuning methods found in the literature.

PI-PD controllers have superior performance compared to traditional PID controllers, especially for controlling unstable and integrating industrial processes with time delays. However, computing the four tuning parameters of this type of controller is not an easy task. Recently, there has been significant interest in determining the tuning rules for PI-PD controllers that utilize the stability region. Currently, most tuning rules for the PI-PD controller are presented graphically, which can be time-consuming and act as a barrier to their industrial application. There is a lack of analytical tuning guidelines in the literature to address this shortfall. However, the existing analytical tuning guidelines do not consider a rigorous design approach. This work proposes new robust analytical tuning criteria based on predefined gain and phase margin bounds, as well as the centroid of the stability region. The proposed method has been tested using various simulation studies related to a DC–DC buck converter, a DC motor, and a heat exchanger. The results indicate that the proposed tuning rules exhibit strong performance against parameter uncertainty with minimal overshoots. Furthermore, the suggested technique for simultaneous control of yaw and pitch angles has been tested in a real-time application using the twin rotor multi-input multi-output system (TRMS). Real-time results indicate that, compared to other methods under investigation, the suggested approach provides nearly minimal overshoots.

This paper suggests a new dynamic sliding mode controller incorporating a disturbance observer for controlling integrating processes with time delay. Here, a new reaching law has been introduced to expedite the system response without evoking chattering. The convergence of this law is also studied. Additionally, the whole system stability is proved using the Lyapunov stability theory. This paper also proposes a new disturbance observer to improve the disturbance rejection and to help suppress chattering further. The suggested observer has only one parameter to be designed. Therefore, this observer can easily be implemented. Several simulation examples and a real-time application are considered to prove the superiority of the suggested controller over the reported controllers in the literature.

The increasing load demand in power system (PS) networks necessitates the improvement of system stability and the preservation of the reliability of electrical power systems (EPS). This case is critical for ensuring energy supply security and maintaining sustainable system performance. Specifically, sudden load changes cause deviations in frequency and tie-line power values from their nominal levels in interconnected power systems (IPS), making load frequency control (LFC) an essential requirement. This research presents a Proportional-Integral-Derivative plus Second Order Derivative (PIDD2) controller design for LFC in IPS, tuned using the Direct Synthesis Method (DSM). The design is developed for single, and two-area PS, encompassing both reheated and non-reheated thermal turbine models. In the proposed design method, controllers are designed for disturbance rejection. The controller parameters were obtained using a novel objective function that includes the settling time and Integral of Absolute Error (IAE). The results demonstrate that the proposed design surpasses the compared methods in terms of frequency and tie-line power deviations, and the robustness of the system is validated through testing under ±25% parameter variations.

Unstable processes plus time delays are very frequent in the industry. PI-PD controllers are used for controlling unstable industrial operations as they give more robust performance relative to PID controllers. However, designing the parameters of PI-PD controllers is quite difficult. Recently, the centroid of the stability region based on the Weighted Geometrical Center (WGC) approach has been proposed for overcoming the tuning difficulty of the controller. Nevertheless, the current version of WGC available in the literature is time-consuming. Thus, this paper proposes new simple tuning rules to implement WGC when it is used for computing the parameters of the PI-PD controller for controlling unstable processes with time delays. An isothermal continuous stirred tank reactor is used for evaluating the performance of the proposed method.

The regulation of tie-line electricity flow and frequency of electrical power systems (EPS) is crucial for ensuring their robustness to parameter changes and efficient management of disturbances. To this end, a novel cascade control design approach utilizing a serial Proportional-Integral-Derivative controller with a filter (PIDF) is proposed in this paper. The parameters of the controllers are derived analytically, and it is employed in both loops of the cascade control system to regulate the Load Frequency Control (LFC) of EPS. The implementation of PIDF controllers in both loops is utilized in the cascade control scheme for various power systems featuring different turbine topologies. This approach has been applied to single, and two-area power systems and has exhibited enhanced performance compared to other commonly referenced studies in the literature. To assess the effectiveness of the cascade control approach proposed performance metrics such as settling time, peak value (overshoot), and integral absolute error (IAE) value of frequency and tie-line power variations are utilized to gauge the system's response to a load perturbation. Additionally, the suggested cascade control technique and design process have undergone robustness testing with ±50% changes in system parameters to validate their reliability.

Integrating processes, whose one or more poles are located at the origin, are common in the process industry. This paper focuses on maximum sensitivity (Ms)-based control of these types of processes. Integral–proportional derivative (I-PD) controllers are designed by exploiting the direct synthesis method for different forms of integrating processes. The suggested design approach is based on comparing the characteristic equation of the closed-loop system, which comprises the integrating system and I-PD controller with a lead/lag filter, with the desired characteristic equation. Simple and analytical adjusting rules are followed to determine the parameters of the I-PD controller and the lead/lag filter according to desired robustness specified by maximum sensitivity (Ms). The formulas provided contain process transfer function parameters and a tuning parameter that is used for setting the desired Ms. The benefits of the proposed technique are demonstrated by simulation examples and a real-time application of cart position control on an experimental set-up. Comparisons with some reported proportional–integral–derivative (PID) and I-PD design techniques are presented to demonstrate the advantages of the proposed design method more evidently.

The proportional–integral and proportional–derivative controller is characterized by its capability to effectively control integrating processes compared with proportional–integral/proportional–integral–derivative controllers. Recently, several graphical methods have been proposed for tuning the PI-PD controller parameters by computing the centroid point of the stability boundary locus. However, these approaches are time-consuming because they entail plotting the stability boundary locus for finding the centroid point. Another disadvantage of those design methods is that the design procedure has to be redone as the transfer function changes. In this article, a generalized stability boundary locus is constructed in terms of the controller and assumed plant transfer function model parameters to enable the designer to avoid replotting the stability boundary locus as the process transfer function changes. More importantly, two analytical approaches, which simplify the design of the proportional–integral and proportional–derivative controller very much, are proposed to compute the centroid point of the generalized stability boundary locus. Analytical expressions for computing the performance measures of the designed closed-loop system have also been provided so that one can predict the performance of the designed closed-loop system. It has been shown by simulation examples that the analytical centroid of convex stability region method provides quicker responses with faster disturbance rejections compared to other reported design methods. Also, the simulation results have displayed that analytical weighted geometrical center gives more robust closed-loop responses in terms of gain margin, phase margins, and maximum sensitivity than analytical centroid of convex stability region. Finally, the feasibility of the proposed methods is tested using a real-time application based on an aerodynamical system. Real-time results have demonstrated that the analytical centroid of convex stability region and analytical weighted geometrical center methods give quicker responses with small overshoots compared to other reported methods.

This paper introduces the design of integral–proportional derivative (I-PD) controllers for unstable first-order plus time-delay and integrating-unstable first-order plus time-delay processes. Minimization of the error based on integral performance criteria is performed to derive analytical rules using curve fitting techniques. Obtained analytical formulas may be used to determine the necessary tuning parameters of the I-PD controller from the known plant transfer function parameters. Advantages of the introduced tuning of I-PD controllers are shown by comparisons with other existing ones in terms of unit step responses, measurement noise, control signals, perturbations in plant transfer function parameters, and integral performance indices. Results have shown that some significant advantages have been achieved with the introduced tuning of I-PD controllers when compared to others in the literature.

While terminal sliding mode control provides faster responses and reduces steady-state errors, it has the disadvantage of having singularity and chattering issues. This study addresses these issues. To address the first issue, a novel non-singular terminal sliding surface is proposed, and to address the second, a new adaptive reaching law that may accelerate system response without resulting in chattering is developed. In addition, this article proposes a novel fractional disturbance observer for rejecting severe and time-varying disturbances. Several simulated industrial case studies and a real-time application based on a cart pendulum setup are used to show the practical benefits of the proposed controller. The suggested approach outperforms the published methods for regulatory and servo responses, according to simulation results and the integral of squared error values used to evaluate the performance of the proposed and reported methods. The proposed method successfully handles time-varying disturbances, in contrast to other reported methods, which lose stability for the mentioned types of disturbances despite the inclusion of an additional mechanism for rejecting disturbances. The superiority of the method proposed is further assured by real-time results.

This paper aims to put forward an analytical solution for tuning parameters of a fractional order PI (FOPI) controller for stable, unstable, and integrating processes with time delay. Following this purpose, the analytical weighted geometrical center (AWGC) method has been extended to the design of fractional order PI controllers. To apply AWGC, the stability equations of the closed-loop system are written in terms of process and fractional order PI controller parameters. With the proposed method, the centroid can be calculated analytically, and the controller parameters can be easily calculated without the need of repetitive drawings of the stability boundary regions. Additionally, analytical equations are derived to calculate fractional integral order, ?, using the integral of squared error (ISE) objective function. The proposed analytical equations are simple and time-saving which might attract controller engineers for applying them on the industrial level. To show the efficiency of the suggested method compared to the given methods in the literature, several simulation examples are considered. Comparisons between the reported methods are figured out in terms of unit step responses for nominal and perturbed cases. Also, rise time, settling time, maximum sensitivity (Ms), integral of squared error (ISE), and total variation (TV) values are considered to compare the performance and robustness issues. Also, a real-time application of an inverted pendulum setup is deemed to prove the feasibility of the suggested method.

Load frequency control (LFC) is an important control problem as it determines the quality of power generation by controlling the system frequency and inter-area tie-line power. To maintain a good quality power supply, LFC must be robust against unknown external disturbances and parameter variations of the power system. Therefore, this paper presents the design of PI–PD controllers, which are robust against parameter changes and have good disturbance suppression capability, for load frequency control of a single-area single- or multi-source power system. PI–PD controller parameters were obtained by applying the weighted geometric center method to the stability boundary locus of the closed-loop control system. The approach was applied to both the inner and outer loops of the PI–PD control system structure, sequentially. Performance and robustness of the proposed PI–PD control system are evaluated using some well-known integral error criteria values, settling time, and peak value (overshoot) in the analysis of the power system with both nominal values and ± 50

One of the commonly encountered type of processes in industry is integrating systems. For this type of processes, tuning formulas to calculate optimally integral–proportional derivative controller parameters to reject input load disturbance, which is an important problem in process control, are presented here. Simple tuning formulas are provided to set the integral–proportional derivative controller parameters for rejection of input load disturbance of integrating plus first order plus dead time and double integrating plus first order plus dead time processes. Time-weighted integral performance indices are exploited to derive optimal formulas for input load disturbance rejection. Achieved formulas for integral–proportional derivative tuning contain only process transfer function parameters. To show benefits and usefulness of the suggested design approach, simulation examples are imparted. Furthermore, comparisons to some available design approaches are given to reveal the superior performance of the suggested design method. In addition, proposed design method is experimentally validated by controlling a cart position.

Designing the parameters of a PI-PD controller is very challenging. Consequently, the centroid of the convex stability boundary locus approach was employed to overcome this challenge. Unfortunately, this approach requires deriving several equations for constructing the stability regions of the PI-PD controller. Also, it computes the centroid of the stability region based on visual observations without using any analytical methods. Therefore, it is time-consuming, and the accuracy of its computations is questionable. This paper suggests simple tuning rules for computing the gains of PI-PD controllers based on the centroid of the stability region to handle the limitations of the centroid of the convex stability boundary locus approach. A robustness analysis has also been conducted to gauge the performance of the proposed tuning rules. Moreover, several simulation examples and a real-time application have been considered for evaluating the effectiveness and the feasibility of the suggested approach.