Nonlinear Robust H-Infinity PID Controller for the Multivariable System Quadrotor

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 this paper design and real-time implementation of robust PID controller is performed for a Twin Rotor MIMO System (TRMS) which is a laboratory scale set-up of a helicopter. The robust PID controller is designed employing Kharitonov stability theorem. The controller design is based on the linearised model of highly nonlinear TRMS. The performance of the compensated system is investigated through experimental results with the laboratory prototype model. The time domain responses for the main and tail rotors are found to be satisfactory. The controller provides comparable performances as presented in the literature for similar system.

The design and implementation of a multi-stage PID (MS-PID) controller for non-inertial referenced UAVs are highly complex. Symmetrical multirotor UAVs are unstable systems, and it is thought that the kinematics of the symmetrical UAV rotor, such as the quadrotor and hexacopter resembles the kinematics of an inverted pendulum. Several researchers have investigated the structure and design of PID controllers for high-order systems during the last decade. The designs were always concerned with the enhanced response, robustness, model reduction and performance of PID controllers. An accurate tuning process of such a controller depends on the engineer’s experience level. This is due to the number of variables and hyperparameters tuned during the process. An adaptive genetic algorithm (AGA) is utilized to optimize the MS-PID controllers for controlling the quadrotor in this study. The proposed method optimizes the offline-planned approach, providing several possibilities for adapting the controllers with various paths and or varying weather conditions. The MS-PID parameters are optimized in parallel, as every PID controller affects the other controller’s behavior and performance. Furthermore, the proposed AGA generates new chromosomes for “new solutions” by randomly developing new solutions close to the previous best values, which will prevent any local minima solution. This study intends to investigate the design and development of a highly tuned robust multi-stage PID controller for a symmetrical multirotor UAV. The work presents a model for a non-referenced inertial frame multirotor UAV (quadcopter). Once the model is defined, a robust multi-stage PID controller for the non-inertial referenced frame symmetrical multirotor UAV is designed, tuned, and tested. A genetic algorithm (GA) will be used to tune the MS-PID controller. Finally, the performance comparison between the proposed and conventional methods is presented. The results show that the proposed method provides stability improvement, better transient response, and power consumption.

Design of intelligent nonlinear robust controller for hydro-turbine governing system based on state-dynamic-measurement hybrid feedback linearization method

The Dual Active Bridge converter (DABC), known for its bidirectional power transfer capability and high efficiency, plays a crucial role in various applications, particularly in electric vehicles (EVs), where it facilitates energy storage, battery charging, and grid integration. The Dual Active Bridge Converter (DABC), when paired with a high-performance CLLC filter, is well-regarded for its ability to transfer power bidirectionally with high efficiency, making it valuable across a range of energy applications. While these features make the DABC highly efficient, they also complicate controller design due to nonlinear behavior, fast switching, and sensitivity to component variations. We have used a Fractional-order PID (FOPID) controller to benefit from the simple structure of classical PID controllers with lower complexity and improved flexibility because of additional filtering gains adopted in this method. However, for a FOPID controller to operate effectively under real-time conditions, its parameters must adapt continuously to changes in the system. To achieve this adaptability, a Multi-Agent Reinforcement Learning (MARL) approach is adopted, where each gain of the controller is tuned individually using the Deep Deterministic Policy Gradient (DDPG) algorithm. This structure enhances the controller’s ability to respond to external disturbances with greater robustness and adaptability. Meanwhile, finding the best initial gains in the RL structure can decrease the overall efficiency and tracking performance of the controller. To overcome this issue, Grey Wolf Optimization (GWO) algorithm is proposed to identify the most suitable initial gains for each agent, providing faster adaptation and consistent performance during the training process. The complete approach is tested using a Hardware-in-the-Loop (HIL) platform, where results confirm accurate voltage control and resilient dynamic behavior under practical conditions. In addition, the controller’s performance was validated under a battery management scenario where the DAB converter interacts with a nonlinear lithium-ion battery. The controller successfully regulated the State of Charge (SOC) through automated charging and discharging transitions, demonstrating its real-time adaptability for BMS-integrated EV systems. Consequently, the proposed MARL-FOPID controller reported better disturbance-rejection performance in different working cases compared to other conventional methods.

The paper presents the novel online tool for robust PID controller design RobCont that enables to design robust PID controllers and to analyze the stability of the closed-loop control performance in an advanced way. This tool is an extension of modular system WebPIDDESIGN, a complex framework that provides features of system identification, PID controller design, and evaluation of control quality. RobCont extends the possibilities of framework by control design tasks focused on systems with interval uncertainties. The tool allows user to perform the step-by-step procedure from system definition, through open loop analysis, to selection of robust controller, closed loop simulation, and evaluation of control quality. The controller selection is based on Neimark's D-partition method and Kharitonov's 16 plant theorem. The RobCont extends also other features of the WebPIDDESIGN, i.e. enables to perform the polynomial approximation of the time-delay systems. The paper also contains a case study on a real laboratory process, where common RobCont usage procedure is illustrated. The presented tool is mainly intended for the education purposes in the field of automatic control.

Maintaining voltage level stability of islanded mode Micro Grids (MG) is a challenging objective due to the limited power flow between sources and loads. The objective of this work is to enhance the dynamic performance of islanded mode Micro grid in the presence of load disturbance using static VAR compensator (SVC). The contribution of this work is the implementation of PI fuzzy model reference learning controller (FMRLC) to SVC control loop. The control algorithm compensates for nonlinearity possessed by MG where fuzzy membership functions and implication imbedded in both controller and inverse model that achieve better presentation of both uncertainty and nonlinearity of the power system dynamics. Hence, MG keeps desired performance as required irrespective of the operating condition. In addition, learning capabilities of the proposed control algorithm compensates for grid parameter variation even with inadequate information about mathematical presentation of load dynamics. The reference model was designed to reject bus voltage disturbance, created by load and wind variation, with achievable desired performance. Accordingly, SVC with fuzzy controller was able to reject bus voltage disturbance by matching closely the reference model performance. Simulations were carried out to study the steady-state and transient performance of MG in islanded mode. The MG is composed of a PV bus supplied by wind turbine and induction generator, a PQ bus connected to nonlinear dynamic load and linear load, a single distribution line connecting the two buses, and SVC. The proposed control algorithm robustness was tested by providing load disturbance in different operating conditions and observing the system dynamic performance. The performance of the proposed controller is compared to a conventional PID controller using overshoot, transient oscillation, Integral-of-Time Multiplied Absolute Error (ITMAE), and integral square error (ISE) as performance parameters. Both ITMAE and ISE values for the proposed controller were much less than conventional PID controller. In addition, for the proposed controller, ITMAE values sustained stable increase while PID controller ITMAE values increased exponentially. These results indicates the progress achieved by proposed controller to enhance disturbance rejection with time due to learning process.

A robust adaptive PID controller design motivated from the sliding mode control is proposed for a class of uncertain chaotic systems in this paper. Three PID control gains, \(K_p, K_i\), and \(K_d\), are adjustable parameters and will be updated online with an adequate adaptation mechanism to minimize a previously designed sliding condition. By introducing a supervisory controller, the stability of the closed-loop PID control system under with the plant uncertainty and external disturbance can be guaranteed. Finally, a well-known Vanderpol oscillator is used as an illustrative to show the efectiveness of the proposed robust a PID controller.

Nonlinear PID (N-PID) Controller for SSSP Grid Connected Inverter Control of Photovoltaic Systems

Performance-guaranteed Robust PID Controller Design for Systems with Unstable Zero

This work presents an analysis, design, and comparison of the PI (Proportional and Integral) controller and control schemes PI linear and nonlinear controllers reset-based. The parameters of these control schemes have been set by trial and error to finally be tested in a nonlinear process with variable dead time. Controller performance is measured using integral square error (ISE), integral time square error (ITSE), total variations of control efforts (TVU), maximum overshoot (\(M_{p}\)) and settling time \(\left( {t_{s} } \right)\). The results show that reset control systems overcome fundamental limitations coming from linear control systems.

Improved Decentralized PID Controller design for MIMO Processes

Liquid level control in multiple connected tanks is a nonlinear control problem and is centre to various diverse industrial establishments, especially chemical process industries. The quality of products and process safety greatly relies upon the quality of control. In this paper, robust liquid level control for coupled tank systems has been proposed using optimal fractional order PID controllers. The controller tuning has been posed as multi-objective mixed sensitivity minimisation problem and is solved using multi-objective variant of particle swarm optimisation (MOPSO). At the end of the optimisation process, Pareto optimal set (POS) of solutions has been obtained. For choosing an optimal solution from the POS, there are several graphical methods like Pareto front, scatter matrices, parallel coordinate representations, etc. But these methods offer a very compact representation of the data and the problem arises for m-dimensional problems. So to ease the decision-making process, the paper also explores the use of level diagrams for aiding the decision maker in choosing the ideal solution from the Pareto optimal set. The designed fractional order PID controllers present robust behaviour to external disturbances and efficient tracking of the reference signal and the results obtained has been compared with different controller tuning algorithms.

Decision letter for "New design of robust PID controller based on meta‐heuristic algorithms for wind energy conversion system"

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