An ALO-Tuned 2DOF-PID Controller for Enhanced Frequency Regulation in Hybrid PV–Thermal Power Systems

A self-tuning hierarchical controller in which a Fuzzy logic controller supervises the control actions of a conventional PID has been proposed, implemented and presented in this paper. The controller has been applied to a control study of Fluid Catalytic Cracking unit (FCCU) riser temperature, and regenerator temperature respectively. Comparison between the performance of the proposed Fuzzy-PID controller and the conventional PID was made in simulation studies of regulatory and servo performances of the two controller types. Six performance measures: Percent overshoot (OS), settling time (ST), integral absolute error (IAE), integral square error (ISE), integral time absolute error (ITAE) and integral time square error (ITSE) were employed as the tools for performance comparison between the conventional PID and the Fuzzy-PID controller. For the tracking of riser temperature with a set point at 524oC, the performance indicators under PID control gave the following results overshoot (14.5%); settling time (40 seconds) Integral absolute error (8.246), integral square error (3.3); integral time absolute error(1762);integral time square error (43.77) while for the same indicators under Fuzzy-PID control the following values: overshoot (3.3%); settling time (40 seconds) ;Integral absolute error (8.811); integral square error (14.5); integral time absolute error(280),;integral time square error (31.11) .The results allude to the superiority of the fuzzy-PID scheme over the PID scheme in tracking the optimal set point of riser temperature. More so, for tracking the regenerator set point temperature of 746oC, comparative study of step response under the two schemes gave the following results in six performance indicators: overshoot (PID (12.6%) / Fuzzy-PID (6%)); settling time (PID (80 seconds) / Fuzzy-PID (20seconds)); Integral absolute error (PID (14.29) / Fuzzy-PID (8.63)); integral square error (PID(6.713). Fuzzy-PID (4.506)); integral time absolute error(PID(2858)/Fuzzy-PID(305.9)), integral time square error (PID(77.55)/Fuzzy-PID(33.05)) . Moreover, the fuzzy-PID controller also showed superior performance over the conventional PID controller in terms disturbance rejection (regulatory response) of both riser and regenerator temperature. The results from this study suggest that the application of fuzzy-PID scheme to temperature control offers good promise of improved fluid catalytic cracking unit (FCCU) operations.

In this paper, a self-tuning hierarchical controller in which a Fuzzy logic controller supervises the control actions of a conventional PID has been proposed, implemented and presented. The controller has been applied to a control study of Fluid Catalytic Cracking (FCC) unit riser temperature, and regenerator temperature respectively. Performance comparison of the proposed Fuzzy-PID controller and the conventional PID was made in simulation studies of regulatory and servo performances of the two controller types. Six performance measures: Percent overshoot (OS), settling time (ST), integral absolute error (IAE), integral square error (ISE), integral time absolute error (ITAE) and integral time square error (ITSE) were employed as the tools for performance comparison between the conventional PID and the Fuzzy-PID controller. For the tracking of riser temperature with a set point at 524oC, the performance indicators under PID control gave the following results overshoot (14.5%); settling time (40 seconds) Integral absolute error (8.246), integral square error (3.3); integral time absolute error(1762);integral time square error (43.77) while for the same indicators under Fuzzy-PID control the following values: overshoot (3.3%); settling time (40 seconds) ;Integral absolute error (8.811); integral square error (14.5); integral time absolute error(280),;integral time square error (31.11) .The results allude to the superiority of the fuzzy-PID scheme over the PID scheme in tracking the optimal set point of riser temperature. More so, for tracking the regenerator set point temperature of 746oC, comparative study of step response under the two schemes gave the following results in six performance indicators: overshoot (PID(12.6%)/Fuzzy-PID(6%)); settling time (PID(80 seconds)/Fuzzy-PID(20seconds));Integral absolute error(PID(14.29)/Fuzzy-PID(8.63)); integral square error(PID(6.713).Fuzzy-PID(4.506)); integral time absolute error(PID(2858)/Fuzzy-PID(305.9)), integral time square error (PID(77.55)/Fuzzy-PID(33.05)).Moreover, the fuzzy-PID controller also showed superior performance over the conventional PID controller in terms disturbance rejection (regulatory response) of both riser and regenerator temperature. The results from this study suggest that the application of fuzzy-PID scheme to temperature control offers good promise of improved fluid catalytic cracking unit (FCCU) operations.

In contemporary hybrid power systems, persistent load fluctuations disrupt the delicate balance between electrical output and mechanical torque, thereby compromising frequency stability. Load frequency control (LFC) mechanisms are indispensable in maintaining this equilibrium, particularly in systems integrating renewable and thermal energy sources. This study introduces a three-degree-of-freedom proportional-integral-derivative (3DOF-PID) controller optimized via the novel chess optimization algorithm (COA) and evaluates its efficacy against the ant lion optimizer (ALO) and Harris Hawks optimization (HHO). Extensive MATLAB/Simulink simulations were conducted on a hydrothermal system, with performance assessed through objective functions—integral of absolute error (IAE) and integral of time-weighted absolute error (ITAE). The COA consistently yielded the lowest cumulative error values (IAE=0.1548 and ITAE=0.2965), demonstrating its superiority in steady-state performance. However, COA exhibited substantial dynamic deviations, including an overshoot of 387.79% and undershoot of 4513.8% in ∆ftie. Conversely, HHO offered a significantly enhanced transient response, achieving 0% undershoot in ∆ftie with minimal oscillatory behavior. ALO displayed moderate performance but struggled with higher undershoots and prolonged settling time. The findings underscore the criticality of algorithm selection in controller design. While COA excels in minimizing long-term errors, HHO is preferable for applications requiring heightened dynamic stability and responsiveness.

A two-degree-of-freedom (2-DOF) PID controller is designed for an AC servo ball screw driven XY table. XY table is widely used in manufacturing industry especially in CNC machineries. The most commonly used controller in industries is conventional PID controller. This controller has satisfactory performance, simple structure, and is one-degree-of-freedom (1DOF). Nonetheless, PID controller can only achieve either good set-point response or good disturbance response. This leads to introduction of 2-DOF PID controller which can achieve both good set-point response and disturbance response. In this project, 2-DOF PID is used for accurate tracking purpose. 2-DOF PID controller is designed using two-steps-tuning-method. Disturbance response is optimized by tuning parameters of KP, Ti, and TD using Ziegler-Nichols 2nd method, followed by optimization of set-point response by tuning of 2-DOF parameters, α and β. Tracking performance of 2-DOF PID controller is compared with conventional PI and 1-DOF PID. Maximum absolute error, sum of absolute error, and mean square error are analyzed for all tracking performance of compensated system. Result shows that tracking error compensation (set-point response) of 1-DOF PID controller is better than 2-DOF PID controller. However, this is due to tuning of α and β parameters in simulation in this project. α and β values should be tuned experimentally. Disturbance response of 1-DOF PID and 2-DOF PID are almost similar due to same KP, Ti, and TD values are used in both controllers.

Optimal fractional order PID controller design using Ant Lion Optimizer

This study investigates the optimization of a 2-Degree-of-Freedom Proportional-Integral-Derivative (2DOF-PID) controller for an air pressure monitoring sensor system using a Multi-Objective Genetic Algorithm (MOGA). The research addresses the common challenge of time delays in real-world control systems, which often stem from sensor latency, actuator dynamics, and signal transmission lags which are factors that compromise system stability and performance. To address this, the system was mathematically modeled using a transfer function to represent the dynamic behavior of the air pressure monitoring sensor, a key component in regulating pneumatic systems. The 2DOF-PID controller was implemented to independently manage reference tracking and disturbance rejection, providing greater control flexibility. The MOGA was employed to fine-tune the controller parameters based on three standard performance indices: Integral of Absolute Error (IAE), Integral of Squared Error (ISE), and Integral of Time-weighted Absolute Error (ITAE). For comparison, other optimization algorithms such as ChASO, GA, MOPSO, and ISCA were also applied. Simulation results demonstrated that the MOGA-optimized controller outperformed all other approaches, achieving superior performance metrics: -82.9% flow disturbance rejection, -76.8% temperature disturbance rejection, 1.24% overshoot, no undershoot, a fast-settling time of 44.25 seconds, and a rise time of 53.2 seconds. These results highlight the MOGA’s effectiveness in enhancing the robustness and responsiveness of pneumatic control systems.

Region of convergence by parameter sensitivity constrained genetic algorithm-based optimization for coordinated load frequency control in multi-source distributed hybrid power system

Each hydropower system incorporates with appropriate hydro turbine, and hydro governor unit. In the current work, an Automatic Generation Control (AGC) of two equal hydropower systems with Proportional-Integral-Derivative (PID) controller was investigated. The gain values of the PID controllers were tuned using Ant Colony Optimization (ACO) technique with one percent Step Load Perturbation (1% SLP) in area 1. The Integral Square Error (ISE), Integral Time Square Error (ITSE), Integral Absolute Error (IAE) and Integral Time Absolute Error (ITAE) were chosen as the objective function in order to optimize the controller's gain values. The experimental results reported that the IAE based PID controller improved the system performance compared to other objective functions during sudden load disturbance.

This paper addresses the problem of design of a two degree of freedom (2-DOF) PID controller for time delay systems. The proposed approach is to design 2-DOF PID controller using a novel method which combines model order reduction, approximate model matching (AMM) concepts as well as optimisation techniques. The conventional PID controllers are usually in 1-DOF structure. The problem of finding the parameters of the 2-DOF PID controller is formulated as that of obtaining the solution of a set of non-homogeneous linear equations. The proposed method not only ensures the stability of the closed loop system with a 2-DOF PID controller but also satisfies the required performance criteria. The developed method does not pose any restriction either on the order of the model or on the structure/order of the controller transfer function. Moreover, this method is computationally simple and easy to implement. Simulation results demonstrate the effectiveness of the proposed method.

This paper addresses the problem of design of a two degree of freedom (2-DOF) PID controller for time delay systems. The proposed approach is to design 2-DOF PID controller using a novel method which combines model order reduction, approximate model matching (AMM) concepts as well as optimisation techniques. The conventional PID controllers are usually in 1-DOF structure. The problem of finding the parameters of the 2-DOF PID controller is formulated as that of obtaining the solution of a set of non-homogeneous linear equations. The proposed method not only ensures the stability of the closed loop system with a 2-DOF PID controller but also satisfies the required performance criteria. The developed method does not pose any restriction either on the order of the model or on the structure/order of the controller transfer function. Moreover, this method is computationally simple and easy to implement. Simulation results demonstrate the effectiveness of the proposed method.

Over the years, several forms of sliding mode control (SMC), such as conventional SMC, terminal SMC (TSMC) and fuzzy SMC (FSMC) have been developed to cater to the control needs of complex, non-linear and uncertain systems. However, the chattering phenomenon in conventional SMC and the singularity errors in TSMC make the application of these schemes relatively impractical. In this chapter, terminal full order SMC (TFOSMC), the recent development in this line, has been explored for efficient control of the uncertain chaotic systems. Two important chaotic systems, Genesio and Arneodo-Coullet have been considered in fractional order as well as integer order dynamics. The investigated fractional and integer order chaotic systems are controlled using fractional order TFOSMC and integer order TFOSMC, respectively and the control performance has been assessed for settling time, amount of chattering, integral absolute error (IAE) and integral time absolute error (ITAE). To gauge the relative performance of TFOSMC, a comparative study with FSMC, tuned by Cuckoo Search Algorithm for the minimum IAE and amount of chattering has also been performed using settling time, amount of chattering, IAE and ITAE performances. The intensive simulation studies presented in this chapter clearly demonstrate that the settling time, amount of chattering and steady-state tracking errors offered by TFOSMC are significantly lower than that of FSMC; therefore, making TFOSMC a superior scheme.

In this work Proportional-Integral (PI) controller was designed and proposed for Load Frequency Control (LFC) of a single area reheat thermal power system. The controller parameters, Proportional (Kp), Integral gain (Ki) values, were optimized and properly tuned using the Stochastic Particle Swarm Optimization (SPSO) technique. Investigate power system comprises suitable governor, reheater and generator units. Three different objective functions are considered for investigation, Integral Absolute Error (IAE), Integral Square Error (ISE) and Integral Time Absolute Error (ITAE) with one percent Step Load (1% SLP). Finally, simulation results show that IAE based PI controller response settled quickly with minimum over and undershoot compared to other objective function based controller performance.

This paper presents a novel control strategy for the drive loop of microgyroscope based on two degree-of -freedom (2-DOF) PID controller. Compared with the conventional AGC-1DOF PID controller, the proposed AGC-2DOF PID controller can realize self-oscillation of the microgyroscope with improved transient response by moving some portions of the proportional and the derivative components of the single PID controller to the feedback path. A tuning fork micromachined gyroscope is fabricated to verify the revised controller. The resonant frequency and the quality factor of the drive mode are measured to be 2.528 kHz and 84 at the atmosphere, respectively. The test results demonstrate that the percent overshoot is reduced from 36.2% (1DOF PID) to 4.35% with approximately 3.35% improved in setting time. The signal-to-noise ratio (SNR) of the excitation signal is larger than 88dB. The scale factor is measured to be about 33.5mv/deg/s with the non-linearity about 0.5% within the range of ±400deg/s.

Design and implementation of a 2-DOF PID compensation for magnetic levitation systems

In this paper, we demonstrate a novel control strategy for the drive mode of a microgyroscope using ascending frequency drive (AFD) with an AGC-2DOF PID controller, which drives a resonator with a modulation signal not at the resonant frequency and senses the vibration signal at the resonant frequency, thus realizing the isolation between the actual mechanical response and electrical coupling signal. This approach holds the following three advantages: (1) it employs the AFD signal instead of the resonant frequency drive signal to excite the gyroscope in the drive direction, suppressing the electrical coupling from the drive electrode to the sense electrode; (2) it can reduce the noise at low frequency and resonant frequency by shifting flicker noise to the high-frequency part; (3) it can effectively improve the performance of the transient response of the closed-loop control with a 2-DOF (degree of freedom) PID controller compared with the conventional 1-DOF PID. The stability condition of the whole loop is investigated by utilizing the averaging and linearization method. The control approach is applied to drive a lateral tuning fork microgyroscope. Test results show good agreement with the theoretical and simulation results. The non-ideal electrical antiresonance peak is removed and the resonant peak height increases by approximately 10 dB over a 400 Hz span with a flicker noise reduction of 30 dB within 100 Hz using AFD. The percent overshoot is reduced from 36.2% (1DOF PID) to 8.95% (2DOF PID, about 75.3% overshoot suppression) with 15.3% improvement in setting time.