Interval Type-2 Fuzzy Controller Research Articles

Adaptive hierarchical interval type-2 fuzzy control for trajectory tracking of an underactuated AUV with uncertain dynamics

In this study, an adaptive hierarchical interval type-2 fuzzy control (AHIT2FC) scheme is presented for three-dimensional (3D) trajectory tracking control of an underactuated autonomous underwater vehicle (AUV), which has only three independent control inputs and is subject to partially parametric uncertainty and unknown external disturbances. To decrease reliance on hydrodynamic parameters, an interval type-2 fuzzy logic system (IT2FLS) is utilized, which exhibits superior capabilities in handling high levels of uncertainties prevalent in the underwater environment as compared to a type-1 fuzzy logic system. However, the traditional fuzzy system structure encounters the “curse of dimensionality” issue, which results in high computational complexity and imposes a significant burden on the limited computing resources underwater. The proposed AHIT2FC framework, based on a hierarchical structure, can substantially enhance computational speed while ensuring excellent control performance. Subsequently, Lyapunov’s theory is adopted to guarantee that all the tracking errors in the closed-loop system are semiglobally uniformly bounded (SGUB). Finally, comparative simulation results demonstrate the effectiveness and superiority of the proposed AHIT2FC scheme.

Advanced controller design based on interval type-2 fuzzy neural network for elementary super-lift Luo converter

The elementary super-lift Luo converter is a third-order DC/DC step-up converter developed using the super-lift method that increases input voltage with low current and voltage ripples and a high voltage gain. On account of the nonlinearity and uncertainty incorporated with voltage, load changes, and switching operation of elementary super-lift Luo (ESLL) converter, it is a challenging task to design an efficient controller. To overcome these problems, this study proposes a new control approach based on interval type-2 fuzzy neural network (IT2FNN) to regulate a DC output current and voltage of ESLL converter. The parameters of IT2FNN were trained offline using a gradient descent algorithm. Mean square error (MSE), one of the most used statistical performance indicators, was used to evaluate the convergence accuracy performance of gradient descent algorithm. The DC output voltage regulation performance of IT2FNN was evaluated via a comparative simulation with interval type-2 fuzzy controller (IT2FC) and proportional + integral (PI) controller in MATLAB/Simulink environment in terms of settling time, average computational time, and recovery time under three different operational conditions: various reference voltages, input voltage, and load. Moreover, the DC output current regulation performance of IT2FNN was evaluated via a comparative simulation with IT2FC and PI controller in MATLAB/Simulink environment in terms of settling time and steady-state error under various reference current changes. The detailed simulation results obtained from comparative simulation validated the effectiveness of IT2FNN.

Comparison of the Performance of Type-1 and Interval Type-2 Fuzzy PI Controllers for Liquid Level Control in a Coupled Tank System

In this study, liquid level control in a coupled tank system is realized with PI controllers whose parameters are adapted using fuzzy logic approximation methods. Type-1 fuzzy PI control, interval type-2 fuzzy PI control and classical PI+Feedforward control methods are applied to the tank system in real time for different reference liquid levels. The performances of the controllers are compared in terms of system response parameters such as rise time, settling time and overshoot percentage. In addition, the performance evaluation of the controllers over a certain period of time is also compared by calculating integral-based concepts that express error performance metrics such as integral square error (ISE), integral time square error (ITSE), integral absolute error (IAE) and integral time absolute error (ITAE). The obtained results show that the type-2 fuzzy PI controller shows the best performance, followed by type-1 fuzzy PI control and classical PI+FF controller, respectively.

Design of a novel intelligent adaptive fractional-order proportional-integral-derivative controller for mitigation of seismic vibrations of a building equipped with an active tuned mass damper

The primary objective of this study is to introduce a novel adaptive fractional order proportional–integral–derivative (FOPID) controller. The adaptive FOPID controller’s parameters are dynamically adjusted in real-time using five distinct multilayer perceptron neural networks. The extended Kalman filter (EKF) is employed to facilitate the parameter-tuning process. A multilayer perceptron neural network, trained using the error Backpropagation algorithm, is employed to identify the structural system and estimate the plant. The real-time estimated Jacobian is applied to the controller to control the model. The stability and robustness of the adaptive interval type-2 fuzzy neural networks controller are enhanced by utilizing the EKF and the feedback error learning strategy for compensator tuning. This improvement increases resilience against estimation errors, seismic disturbances, and unknown nonlinear functions. The primary objective is to address the challenges posed by maximum displacement, acceleration, and drift, as well as the uncertainties arising from variations in stiffness and mass. In order to validate the reliability of the proposed controller, the performance investigation is carried out on an 11-story building equipped with an active tuned mass damper under far and near-field earthquakes. Numerical findings show the remarkable effectiveness of the proposed controllers compared to their predecessors. In addition, it is revealed that the inclusion of the adaptive interval type-2 fuzzy neural networks compensator has increased the performance of the proposed controller and shows significant capabilities in reducing the seismic responses of structures during severe earthquake events.

Self-organizing interval type-2 function-link fuzzy neural network control for uncertain manipulators under saturation: A predefined-time sliding-mode approach

Robotic manipulators have extensive applications in academic and industrial fields such as grabbing, welding, and machining. Nowadays, better tracking performance and faster transient response have been the fundamental demands in the field of manipulator control. However, robotic manipulators suffer from uncertainties due to various factors in real-world environments. Therefore, achieving satisfactory tracking performance for the manipulator in the presence of uncertainties is a pressing problem. Moreover, most existing control schemes struggle to determine the convergence time of the whole system and rely on specifically designed parameters via experience and prior knowledge, which leads to poor transferability and generalization. To address the abovementioned issues, a predefined-time controller based on a self-organizing interval type-2 function-link fuzzy neural network (IT2FLFNN) is proposed in this paper. Different from most existing fuzzy neural network (FNN) based control schemes, the proposed network starts from an empty rule base and it is constructed by a self-organizing mechanism during the online control process, which provides greater flexibility in terms of network structure and input partition. Also, a function-link network (FLN) is integrated into IT2FLFNN to enhance its convergence speed and rejection of uncertainties. Furthermore, to ensure the predefined-time convergence, a predefined-time sliding-mode control part is merged into the control framework and online learning laws for IT2FLFNN are established via the Lyapunov stability analysis. Finally, a comparative simulation and an experiment demonstrate the superiority of the proposed IT2FLFNN control scheme.

Robust anti-disturbance interval type-2 fuzzy control for interconnected nonlinear PDE systems via conjunct observer

This paper investigates a robust anti-disturbance interval type-2 (IT2) fuzzy control for interconnected nonlinear partial differential equation (PDE) systems subject to parameter uncertainties by the conjunct observer. First, an IT2 fuzzy model is adopted to remodel the target system. Second, a state observer with mismatched premise variables is constructed to solve the problem that the original system and the observer do not share a uniform premise variable. Moreover, a disturbance observer is designed to estimate the unknown external disturbances, which can be modeled by exogenous PDE systems. Then, utilizing the conjunct observation information, an anti-disturbance IT2 fuzzy control strategy is proposed to attenuate the effect of disturbances on the system performance while ensuring that the closed-loop system is stable. Finally, simulation results verify the effectiveness of the proposed method.

Optimization of a fractional-order interval type-2 fuzzy PID controller based on BBO for real-time applications

This paper addresses the development of a robust controller for a nonlinear system to minimize the tracking errors and reduce the effects of external noise and disturbances. To achieve this, the biogeography-based optimization (BBO) algorithm is utilized for an optimally robust interval type 2 fractional-order fuzzy proportional integral derivative controller (BB0-IT2FO-FPID) is proposed. The proposed method offers several advantages. Firstly, the proposed controller is optimized to achieve robustness and minimize tracking errors. Secondly, it effectively handles external noise and disturbances, making it suitable for real-world applications. Thirdly, the use of the BBO algorithm enhances the controller's performance by dynamically adjusting its parameters based on system requirements. The performance of the proposed controller is validated by applying it to control a robotic manipulator, which presents challenges due to its nonlinear characteristics and interacting multi-input multi-output (MIMO) dynamics. Additionally, a real-time evaluation of the proposed controller is conducted by applying it to the speed control of a direct current (DC) machine. The effectiveness of the proposed controller is verified through simulation and practical experiments and comparisons with other optimized controllers, namely FO fuzzy type 1 PID (T1FO-FPID) and FOPID. The simulation and practical results demonstrate the superior performance of the BBO-IT2FO-FPID controller in the presence of system uncertainties and different types of disturbances.

Analysis of interval type-2 fuzzy controller based interleaved sepic PFC converter for PQ enhancement in power solutions

The Power solutions have become indispensable for all the devices in recent years with an appropriate power conversion circuitries and control methods to ensure good dynamic response, improved stability, reliability and efficiency. The main intent of this article is to impart the designing of interval type-2 fuzzy logic controller (IT2FLC) based interleaved Sepic power factor correction (PFC) converter. This work also involves the careful design of the robust controller with enhanced precision and good power quality (PQ) performance at the AC mains. In addition, the development of IT2FLC based power solution improves the overall power conversion with stabilized output in the perspective of its quick rise time, less overshoot and fast settling time in comparison to other traditional controllers. Further, the uncertainties and issues associated with the conventional proportional integral (PI) and fuzzy logic controllers (FLCs) are handled effectively by the proposed IT2FLC controller. Moreover, this preferred converter is modeled with an internal parasitics and its performances are evaluated and compared with other conventional Zeigler Nicholas (ZN) tuned PI controller and FLC by dint of MATLAB/Simulink platform. Finally, the experimental test bench set up of 250 W, 48 V power circuitry is devised and the test outcomes confirm the excellent transient behavior and PQ performances of the modeled power solution.

Transient response mitigation using type-2 fuzzy controller optimized by grey wolf optimizer in converter high voltage direct current

Long high voltage direct current (HVDC) transmission link is commonly used to transmit electrical energy via land or under-sea cable. The long HVDC avoids reactive power losses (RPL) and power stability problems (PSP). On the contrary, the RPL and PSP phenomena occur in long high voltage alternative current-link (HVAC) caused by the high reactive component in the HVAC-link. However, the HVDC produces a high and slow transient current response (TCR) on the high value of the up-ramp rate. Interval type-2 fuzzy (IT2F) control on converter-side HVDC is proposed to mitigate this TCR problem. The IT2F is optimized by grey wolf optimizer (GWO) to adjust input-output IT2F parameters optimally. The performance of IT2F-GWO is assessed by the minimum value of integral time squared error (ITSE), peak overshoot, and settling time of the TCR. The IT2FC-GWO performance is validated by the performance of IT2F control that is optimized by genetic algorithm (IT2F-GA) and proportional integral (PI) controller. Simulation results show that the IT2F-GWO performs better with small ITSE, low peak overshoot, and shorter settling times than competing controllers.

Event-triggered interval type-2 fuzzy control of networked systems with extended dissipative under Markovian switching

In this technical note, the problem of the extended dissipative control for interval type-2 fuzzy model with nonlinear network systems in the event-triggered framework is investigated. A novel dynamic event-triggered strategy is developed to ascertain the instants of activation. It has the advantage of reducing data transmission and optimising the utilisation of communication resources. On the basis of the proposed mechanism, the stochastic Lyapunov function including internal dynamic variables is constructed. Based on this function, coupled with the inequality scaling technique and the application of Dynkin's formula, we derive a sufficient condition for the system's stochastic asymptotic stability and extended dissipativity. The design of the dynamic event-triggered extended dissipative controller becomes challenging because the new sufficient condition is nonlinear for some matrix variables. However, utilising the Projection Lemma and the co-design approach, such a controller can be developed based on the obtained analysis result. The methodology is demonstrated through a rigorous numerical simulation case study.

Optimization of the energy management system in hybrid electric vehicles considering cabin temperature

The air conditioning (AC) system provides passengers with a comfortable temperature environment and is one of the main energy consumers in modern plug-in hybrid electric vehicles (PHEV). However, the AC system is often overlooked when designing the energy management system (EMS) for PHEVs. To improve the energy efficiency of PHEVs, this paper integrates the Genetic Simulated Annealing Algorithm (GASA) with fuzzy control to propose an energy management system for PHEVs that considers the internal temperature of the vehicle. First, considering the uncertainty of the vehicle's driving environment, an optimized Interval Type-2 Fuzzy Controller (IT2-FC) was designed for real-time torque distribution. Second, an iteratively modified genetic simulated annealing algorithm was used to optimize control parameters, correcting the defect of genetic algorithms tending to get trapped in local optima and lingering around optimal positions. Then, considering the energy consumption of the AC system, a vehicle-integrated thermal management model oriented towards control was established. Lastly, the performance of the proposed EMS was discussed. The results show that, compared to the rule-based methods, the proposed EMS reduces fuel consumption by 17.77% and 17.727% in cooling and heating modes, respectively, and compared to the A-ECMS methods, it reduces fuel consumption by 7.38% and 6.31% in cooling and heating modes, respectively. At the same time, the proposed EMS ensures thermal comfort in the cabin. In cooling mode, the traditional rule-based strategy failed to maintain the cabin temperature within the preset range, while the proposed EMS showed significant improvement. In heating mode, the EMS reaches and maintains the cabin's set temperature 35% faster than the rule-based strategy, and 8.75% faster than the A-ECMS strategy.

Derivation and characteristic investigation of a two-input, two-output interval type-2 fuzzy controller using product and operations

Interval type-2 (IT2) fuzzy logic, with the footprint of uncertainty (FOU) in membership functions, is very effective in dealing with disturbances and uncertainties of nonlinear systems. With this advantage, a two-input, two-output IT2 fuzzy controller with IT2 input and singleton type-1 fuzzy output sets is proposed for coupling systems. Firstly, the controller's input-output relationship is determined. Derivation results indicate that the controller is equivalent to the sum of a relay module and a local proportional-integral (PI) controller with variable gains. Next, analytical structure properties and gain variations are explored. It is demonstrated that the relay module is independent of the FOU, playing a dominant role in determining the control behavior of the IT2 controller. On the other hand, the control action of the PI controller diminishes when increasing the FOU and the number of fuzzy input sets. These properties contribute to the fast responsiveness of the controller and advantages in handling system uncertainty. Furthermore, the stability condition of this controller is established using the small gain theorem. Finally, both simulation and experiments are carried out to illustrate the applicability of the IT2 controller. The experimental results show that the controller's performance is embodied as the tracking errors of the two-linkage axes equal to ±4 μm, while the repeated positioning accuracy values are within ±3 μm.

An interval type-3 fuzzy PID control system design and its application in solid oxide fuel cells power plant

Compared with type-2 fuzzy sets, the secondary membership degree of interval type-3 fuzzy sets is an interval rather than crisp value, which makes interval type-3 fuzzy sets can obtain more degree of freedoms. This article studies an interval type-3 fuzzy PID controller based on interval type-3 fuzz sets. The framework of interval type-3 fuzzy PID controller is identical with type-2 fuzzy PID controller, but it contains more adjustment controller parameters and its type reduction procedure is more complex. In this paper, type reduction of interval type-3 fuzzy sets is derived from general type-2 fuzzy sets represented by α-plane and a direct NT type reduction algorithm is applied. The control effects of interval type-3 fuzzy PID controller are firstly tested by 2 nonlinear plants, the simulation results show that interval type-3 fuzzy PID controller has better control performance indexes than PID controller, type-1 fuzzy PID controller, interval type-2 fuzzy PID controller and general type-2 fuzzy PID controller. Furthermore, the interval type-3 fuzzy PID controller will be applied in rated voltage control of solid oxide fuel cells (SOFC) power plant. The output voltage control of SOFC is quite challenging because of the strong nonlinearity, limited fuel flow, and rapid variation of the load disturbance. The simulation results demonstrate the advantages and robustness of proposed interval type-3 fuzzy PID controller.

Tracking Control for Nonlinear Systems With Actuator Saturation via Interval Type-2 T-S Fuzzy Framework.

In this work, the problem of tracking control for discrete-time nonlinear actuator-saturated systems via interval type-2 (IT2) T-S fuzzy framework is investigated. Improved on the (type-1) T-S fuzzy system, the IT2 T-S fuzzy system has a better capability for the expression of system uncertainty, and correspondingly, it will increase the difficulty of analysis, especially for the membership-functions-dependent (MFD) method. In addition, in this case, the control input nonlinearity caused by actuator saturation will complicate the stability analysis of the systems. We make an attempt to address the challenges that the information of membership functions (MFs) is underutilized or not utilized, by developing an MFD analysis approach, which allows the enhancement of design flexibility of IT2 fuzzy controller and effectiveness of lessening the conservativeness of the analysis result. The piecewise MFs which are formed by connecting the sample point on or close to the original IT2 MFs are utilized to approximate the original IT2 MFs, and the error between the piecewise MFs and the original upper and lower MFs is taken into account in the stability analysis. To acquire the linear matrix inequality-based (LMI-based) constraint, the actuator saturation is converted to a sector nonlinear issue. performance is considered to limit the difference between the reference system and the control saturated system. Examples are presented to illustrate the validity of the results.

Robust Stabilization of an Autonomous Underwater Vehicle in Depth Channel by PID Interval Type-2 Fuzzy Controller

Robust Stabilization of an Autonomous Underwater Vehicle in Depth Channel by PID Interval Type-2 Fuzzy Controller

Effective Energy Management Strategy with Model-Free DC-Bus Voltage Control for Fuel Cell/Battery/Supercapacitor Hybrid Electric Vehicle System

This article presents a new design method of energy management strategy with model-free DC-Bus voltage control for the fuel-cell/battery/supercapacitor hybrid electric vehicle (FCHEV) system to enhance the power performance, fuel consumption, and fuel cell lifetime by considering regulation of DC-bus voltage. First, an efficient frequency-separating based-energy management strategy (EMS) is designed using Harr wavelet transform (HWT), adaptive low-pass filter, and interval type–2 fuzzy controller (IT2FC) to determine the appropriate power distribution for different power sources. Second, the ultra-local model (ULM) is introduced to re-formulate the FCHEV system by the knowledge of the input and output signals. Then, a novel adaptive model-free integral terminal sliding mode control (AMFITSMC) based on nonlinear disturbance observer (NDO) is proposed to force the actual values of the DC-link bus voltage and the power source’s currents track their obtained reference trajectories, wherein the NDO is used to approximate the unknown dynamics of the ULM. Moreover, the Lyapunov theorem is used to verify the stability of AMFITSMC via a closed-loop system. Finally, the FCHEV system with the presented method is modeled on a Matlab/Simulink environment, and different driving schedules like WLTP, UDDS, and HWFET driving cycles are utilized for investigation. The corresponding simulation results show that the proposed technique provides better results than the other methods, such as operational mode strategy and fuzzy logic control, in terms of the reduction of fuel consumption and fuel cell power fluctuations.

Optimization for Interval Type-2 Polynomial Fuzzy Systems: A Deep Reinforcement Learning Approach

It is known that the interval type-2 (IT2) fuzzy controllers are superior compared to their type-1 counterparts in terms of robustness, flexibility, etc. However, how to conduct the type reduction optimally with the consideration of system stability under the fuzzy-model-based (FMB) control framework is still an open problem. To address this issue, we present a new approach through the membership-function-dependent (MFD) and deep reinforcement learning (DRL) approaches. In the proposed approach, the reduction of IT2 membership functions of the fuzzy controller is completing during optimizing the control performance. Another fundamental issue is that the stability conditions must hold subject to different type-reduction methods. It is tedious and impractical to resolve the stability conditions according to different type-reduction methods, which could lead to infinite possibility. It is more practical to guarantee the holding of stability conditions during type-reduction rather than resolving the stability conditions, the MFD approach is proposed with the imperfect premise matching (IPM) concept. Thanks to the unique merit of the MFD approach, the stability conditions according to all the different embedded type-1 membership functions within the footprint of uncertainty (FOU) are guaranteed to be valid. During the control processes, the state transitions associated with properly engineered cost/reward function can be used to approximately calculate the deterministic policy gradient to optimize the acting policy and then to improve the control performance through determining the grade of IT2 membership functions of the fuzzy controller. The detailed simulation example is provided to verify the merits of the proposed approach.

Comparative Study of Takagi-Sugeno-Kang and Madani Algorithms in Type-1 and Interval Type-2 Fuzzy Control for Self-Balancing Wheelchairs

This study examines the effectiveness of four different fuzzy logic controllers in self-balancing wheelchairs. The controllers under consideration are Type-1 Takagi-Sugeno-Kang (TSK) FLC, Interval Type-2 TSK FLC, Type-1 Mamdani FLC, and Interval Type-2 Mamdani FLC. A MATLAB-based simulation environment serves for the evaluation, focusing on key performance indicators like percentage overshoot, rise time, settling time, and displacement. Two testing methodologies were designed to simulate both ideal conditions and real-world hardware limitations. The simulations reveal distinct advantages for each controller type. For example, Type-1 TSK excels in minimizing overshoot but requires higher force. Interval Type-2 TSK shows the quickest settling times but needs the most force. Type-1 Mamdani has the fastest rise time with the lowest force requirement but experiences a higher percentage of overshoot. Interval Type-2 Mamdani offers balanced performance across all metrics. When a 2.7 N control input cap is imposed, Type-2 controllers prove notably more efficient in minimizing overshoot. These results offer valuable insights for future design and real-world application of self-balancing wheelchairs. Further studies are recommended for the empirical testing and refinement of these controllers, especially since the initial findings were limited to four-wheeled self-balancing robotic wheelchairs.

Adaptive interval type-2 fuzzy fixed-time control for nonlinear MIMO fast-slow coupled systems with user-defined tracking performance

This paper focuses on the adaptive interval type-2 (IT2) fuzzy fixed-time self-triggered control issue for a class of multi-input and multi-output (MIMO) nonlinear fast-slow coupled systems (FSCSs) with preassigned tracking performance requirements. At first, the steady-state error and dynamic response of the investigated system are synthetically weighed by introducing an improved fixed-time prescribed performance function into coordinate transformation. Second, an IT2 fuzzy adaptive self-trigged controller is designed, where the unknown continuous functions are approximated by the interval type-2 fuzzy logic systems (IT2FLSs). In addition, the 1-bit encoding-decoding mechanism (EDM) is embedded in the signal transmission channel between the controller and the actuator, which also provides a feasible solution to further reduce network bandwidth consumption under the framework of the self-triggered protocol. Stability analysis indicates that the developed control method ensures that all states of the closed-loop system are practical fixed-time bounded, and the tracking error evolves to a pre-specified performance envelope within a predetermined time. Finally, a numerical example and an application example are provided to demonstrate the effectiveness and superiority of the proposed method.

Extended dissipative analysis of affine transformed IT2 fuzzy control systems with time delay and disturbances

This paper focuses on the problem of stability and stabilization for interval type-2 (IT2) fuzzy systems with time-varying delays and external disturbances using the extended dissipative theory. In particular, our approach is to develop a new type of IT2 fuzzy controller that uses affine parameter-based weighting variables. Based on appropriate augmented Lyapunov-Krasovskii functionals and recently developed integral inequalities, some less conservative sufficient conditions are derived in the existence of the zeros equations. Specifically, the required conditions for co-design of affine matched membership functions-based IT2 fuzzy control law are provided such that the generalized performance index, the L2−L∞, H∞, passivity and (Q,S,R)−γ-dissipative problems are investigated. Finally, four examples are represented to verify the advantages of the developed method by comparing it with some existing results.