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The purpose of this paper is to stabilize the type-2 Takagi–Sugeno (T–S) fuzzy systems with the sufficient and guaranteed stability conditions. The given conditions efficaciously handle parameter uncertainties by the upper and lower membership functions of the type-2 fuzzy sets (FSs).

This paper reports on a relevant study of stable fuzzy controllers and type-2 T–S fuzzy systems and reported that the synthesis of controller for nonlinear systems described by the type-2 T–S fuzzy model is a key problem and it can be resolve to convex problems via linear matrix inequalities (LMIs).

The multigain fuzzy controllers are established to improve the solvability of the stability conditions, and the authors design multigain fuzzy controllers which have extensive information of upper and lower membership grades. Consequently, the authors derive the traditional stability condition in terms of LMIs. One simulation examples illustrate the effectiveness and robustness of the derived stabilization conditions.

The uncertain MIMO nonlinear system described by Type-2 Takagi-Sugeno (T-S) fuzzy model, and successively LMI approach used to determine the system stability conditions. The proposed control approach will give superior fault-tolerant control permanence under the actuator fault [partial loss of effectiveness (LOE)]. Also the controller robust against the unmeasurable process disturbances. Additionally, the statistical z-test are carried out to validate the proposed control approach against the control approach proposed by Himanshukumar and Vipul (2019a).

The two-tank level control system is one of the real-world's second-order system (SOS) widely used as the process control in industries. It is normally operated under the Proportional integral and derivative (PID) feedback control loop. The conventional PID controller performance degrades significantly in the existence of modeling uncertainty, faults and process disturbances. To overcome these limitations, the paper suggests an interval type-2 fuzzy logic based Tilt-Integral-Derivative Controller (IT2TID) which is modified structure of PID controller.

In this paper, an optimization IT2TID controller design for the conical, noninteracting level control system is presented. Regarding to modern optimization context, the flower pollination algorithm (FPA), among the most coherent population-based metaheuristic optimization techniques is applied to search for the appropriate IT2FTID's and IT2FPID's parameters. The proposed FPA-based IT2FTID/IT2FPID design framework is considered as the constrained optimization problem. System responses obtained by the IT2FTID controller designed by the FPA will be differentiated with those acquired by the IT2FPID controller also designed by the FPA.

As the results, it was found that the IT2FTID can provide the very satisfactory tracking and regulating responses of the conical two-tank noninteracting level control system superior as compared to IT2FPID significantly under the actuator and system component faults. Additionally, statistical Z-test carried out for both the controllers and an effectiveness of the proposed IT2FTID controller is proven as compared to IT2FPID and existing passive fault tolerant controller in recent literature.

Application of new metaheuristic algorithm to optimize interval type-2 fractional order TID controller for nonlinear level control system with two type of faults. Also, proposed method will compare with other method and statistical analysis will be presented.

In recent times, fuzzy logic is gaining more and more attention, and this is because of the capability of understanding the functioning of the system as per human knowledge-based system. The main contribution of the work is dynamically adapting the important parameters throughout the execution of the flower pollination algorithm (FPA) using concepts of fuzzy logic. By adapting the main parameters of the metaheuristics, the performance and accuracy of the metaheuristic have been improving in a varied range of applications.

The fuzzy logic-based parameter adaptation in the FPA is proposed. In addition, type-2 fuzzy logic is used to design fuzzy inference system for dynamic parameter adaptation in metaheuristics, which can help in eliminating uncertainty and hence offers an attractive improvement in dynamic parameter adaption in metaheuristic method, and, in reality, the effectiveness of the interval type-2 fuzzy inference system (IT2 FIS) has shown to provide improved results as matched to type-1 fuzzy inference system (T1 FIS) in some latest work.

One case study is considered for testing the proposed approach in a fault tolerant control problem without faults and with partial loss of effectiveness of main actuator fault with abrupt and incipient nature. For comparison between the type-1 fuzzy FPA and interval type-2 fuzzy FPA is presented using statistical analysis which validates the advantages of the interval type-2 fuzzy FPA. The statistical Z-test is presented for comparison of efficiency between two fuzzy variants of the FPA optimization method.

The main contribution of the work is a dynamical adaptation of the important parameters throughout the execution of the flower pollination optimization algorithm using concepts of type-2 fuzzy logic. By adapting the main parameters of the metaheuristics, the performance and accuracy of the metaheuristic have been improving in a varied range of applications.

The purpose of this article is about the design of controllers for conical two-tank noninteracting level (CTTNL) system in simulation. Local linearization around the equilibrium point has been done for the nonlinear CTTNL system to obtain a linearized model transfer function.

This article deals with the design of novel optimal fractional-order tilt-integral-derivative (TID) controller using type-1 fuzzy set for the CTTNL prototype system. In this study, type-1 fuzzy TID controller parameters have been optimized through genetic algorithm (GA) and those set of values have been employed for the design of proportional-integral-derivative (PID) controller.

A performance comparison between FTID and PID controller is then investigated. The analysis shows the superiority of FTID controller over PID controller in terms of integral absolute error (IAE), integral square error (ISE), integral of time multiplied absolute error (ITAE) and integral of time multiplied squared error (ITSE) integral errors. The transient and steady state performance of the FTID controller are superior as compared to conventional PID controller. In future, the FTID controller fault-tolerance capability tested on CTTNL system subject to actuator and system component (leak) faults. The detailed study of robustness in presence of model uncertainties will be incorporated as a scope of further research.

A performance comparison between FTID and PID controller is then investigated. The analysis shows the superiority of FTID controller over PID controller in terms of IAE, ISE, ITAE and ITSE integral errors. Additionally, fault-tolerant performance of the proposed controller evaluated with fault-recovery time (F_rt) parameter. The transient and steady state performance of the FTID controller are superior as compared to conventional PID controller.

Fuzzy-based metaheuristic algorithm is used to optimize the fuzzy controllers for the nonlinear level control system subject to uncertainty specially in the main actuator that has lost effectiveness (LOE). To optimize the fuzzy controller, type-1 harmonic search (HS) and interval type-2 (HS) will be used.

The type-1 and type-2 fuzzy-based HS algorithms are designed for optimization of fuzzy controllers for Fault-Tolerant Control (FTC) applications, and this research proposes a fuzzy-based HS metaheuristic method. The performance of a fuzzy logic-based HS algorithm applied to a nonlinear two-tank level control process with a main actuator that has lost effectiveness (LOE) and also the same controller will be tested on DC motor angular position control with and without noise.

The key contribution of this work is the discovery of the best approach for generating an optimal vector of values for the fuzzy controller's membership function optimization. This is done in order to improve the controller's performance, bringing the process value of the two-tank level control process closer to the target process value (set point). It is worth noting that the type-1 fuzzy controller that has been optimized is an interval type-2 fuzzy system, which can handle more uncertainty than a type-1 fuzzy system.

The type-1 and type-2 fuzzy-based HS algorithms are designed for optimization of fuzzy controllers for FTC applications, and this research proposes a fuzzy-based HS metaheuristic method. The performance of a fuzzy logic-based HS algorithm applied to a nonlinear two-tank level control process with a main actuator that has LOE will be tested on DC motor angular position control with noise. Two nonlinear uncertain processes are used to demonstrate the effectiveness of the proposed control scheme.